Post on 09-Feb-2023
Structure and Depletion in Star Forming Clouds
Helen Christie
Thesis submitted for the Degree of Doctor of Philosophy
of the University of London
Department of Physics & Astronomy
UNIVERSITY COLLEGE LONDON
April 2012
I, Helen Christie, confirm that the work presented in this thesis is my own. Where information
has been derived from other sources, I confirm that this has been indicated in the thesis.
ABSTRACT
Observations of star forming molecular clouds reveal clumpiness on all scales, both in the spec-
tra of molecules and thermal continuum emission from the solid component of the interstellar
medium, the dust. Recent, high resolution maps have allowed us to probe down to extremely
small scales at which we see clumps of radii just several hundredths of a parsec. A good knowl-
edge of the structure of these regions, and of the chemical processes occurring within, is crucial
if we want to properly understand the early stages of star formation and the resulting stellar pop-
ulation. However, observations of cold, dense environments are challenging. Molecules emit at
long wavelengths which are notoriously difficult to observe. A comparison with models is also
complicated by the fact that in these conditions molecules will freeze-out onto dust grain surfaces
forming icy mantles. We know little about the rate at which this process occurs in interstellar con-
ditions, or the chemical reactions that happen on the grain surfaces. In this thesis we present two
alternative methods by which to investigate the underlying clumpy nature of a molecular cloud
and consider freeze-out in such an environment.
Small, quiescent regions of enhanced emission in several molecules (including ammonia and
HCO+) have been observed near to Herbig-Haro objects (HHOs) in star forming clouds. It was
suggested that these could be due to molecules in small dense clumps being liberated from the
dust grain surface by radiation from the shock front. Chemical modelling later proved this theory
to be viable, and it was further supported by observational surveys and more detailed modelling of
specific regions. In chapter 2 we simulate a dense clump near to an HHO, adapting the chemical
code used in the original models to allow the shock front to move past the clump, providing a
more realistic description of the effect of the radiation field. Chapter 3 describes how the outputs
from these models can be used to simulate observations of part of a molecular cloud made up of
small, transient density enhancements irradiated by a passing shock front. We briefly compare our
4
5
synthetic maps with HCO+ spectra in regions surrounding HHOs.
Commonly, researchers use decomposition algorithms on 2D and 3D maps to pick out clumps
of emission and evaluate their properties. The mass functions of these objects often appear to
emulate the stellar initial mass function, which has led researchers to conclude that the stellar mass
is set at a very early stage, prior to the switch on of the protostar. In Chapter 4 we introduce the
Gould Belt clouds for which we have HARP CO and SCUBA data (the HARP maps are presented
in Appendix B). It is these on which we perform the analysis described in the final 3 Chapters. In
Chapter 5 we investigate four popular clumpfinding algorithms, testing them on both synthetic and
real (HARP) data, and explore the impact of user defined input parameters on derived properties.
We choose one algorithm, with one set of input parameters, and use this to analyse the distribution
of CO clumps in five nearby molecular clouds. The results of this study are outlined in Chapter 6.
Chapter 7 focuses on the process by which CO freezes-out (depletes) onto the surfaces of
dust grains in dark clouds. A single value for the depletion of a particular molecule is difficult
to achieve because of its strong dependence on environmental factors and the past evolution of a
region. However, we have a consistent data set across a range of environments and so are able to
perform a statistical study in which we compare hydrogen densities derived from dust emission
with those calculated using the CO maps. We look for missing CO in the gas phase which we then
assume to be the result of depletion.
ACKNOWLEDGEMENTS
I tried to avoid too sentimental a paragraph here but, realising there are many people that I do
actually need to say a giant thank-you to, have decided that gushy is the only way; get ready or
stop reading. Firstly, to Serena: I am really not sure I would have stuck it out if I hadn’t had such a
supportive, sensitive and caring person as my supervisor. Thank you for the encouragement when
it was needed and for always being there. To Jeremy for being so kind and for spending all that
time with me sorting out small problems that felt huge! To mum and dad: Thank you for always
supporting John and I and for being proud of us, whatever we choose to do in our lives. To my
amazing grandparents Ruth and James for being the interesting, funny, loving people they are. To
John for a voice of sanity and good times. To Ben who has put up with a lot of angst and too many
tears over the last month. I love you to bits. Emily, Harps and Farah: what can I say!? You have
all given me so much and always been there to listen. You have made the last three years such
amazing fun and I am sure that we will still be laughing together in many years time when we
are all eccentric seventy year old women drinking wine and saying inappropriate things in posh
restaurants. Emily: I definitely owe you a drink or fifty for putting up with my moods at home,
you are an absolutely brilliant friend. To J, Rich and Freya who have always been on the end
of a phone and who I feel very lucky to have in my life. To Roger who probably doesn’t know
how much of a help and inspiration he has been to me over the years. Thank you and looking
forward to climbing Aconcagua! To all the lovely people in the astronomy department who give it
the atmosphere it has and have kept me company at the pub! Sylvia, Foteini, Ingo, Chris, Adam,
Hannah, Angela, Jaf, Steph, Luke, Patrick.
6
Contents
Abstract 4
Acknowledgements 6
Table of Contents 7
List of Figures 10
List of Tables 30
1 Introduction 32
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.2 Phases of the Interstellar Medium and Some Important Chemistry. . . . . . . . 33
1.2.1 Dust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.2.2 The clumpy ISM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.2.3 ISM Gas Phase Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . 38
1.2.4 Gas-Grain Interactions and Depletion. . . . . . . . . . . . . . . . . . . 39
1.3 Chemical modelling of star-forming regions. . . . . . . . . . . . . . . . . . . . 42
1.4 Column Densities from Molecular Line Emission and Dust. . . . . . . . . . . . 44
1.5 Low Mass Star Formation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2 Chemistry of dense clumps near moving Herbig-Haro objects 49
2.1 The Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3 The Effect of Herbig-Haro Radiation on a Clumpy Molecular Cloud 62
3.0.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1 Grid of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7
CONTENTS 8
3.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 The Gould Belt Clouds: An Overview 87
4.1 The JCMT Gould Belt Survey. . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 HARP CO Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3 SCUBA maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4 Properties of the Observed Regions. . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Testing Cupid Clumpfinding Algorithms 93
5.1 Description of the Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.1.1 CLUMPFIND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.2 FELLWALKER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.3 REINHOLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.1.4 GAUSSCLUMPS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3.1 CLUMPFIND Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.3.2 FELLWALKER Results . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.3 REINHOLD Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3.4 GAUSSCLUMPS Results. . . . . . . . . . . . . . . . . . . . . . . . . 157
5.4 Summary and Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6 Properties of CO Clumps in the Gould Belt Clouds 174
6.1 Results - The CO Clumps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.1.1 Clump Positions and Ellipticities. . . . . . . . . . . . . . . . . . . . . . 182
6.1.2 Clump Masses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.1.3 Clump virial masses - how bound are the clumps?. . . . . . . . . . . . . 189
6.1.4 Investigating the CO Clump Mass Functions. . . . . . . . . . . . . . . 190
6.2 Matches with SCUBA Cores. . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
6.2.1 Properties of the SCUBA Dust Cores. . . . . . . . . . . . . . . . . . . 203
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7 Depletion in the Gould Belt Clouds 208
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
CONTENTS 9
7.2 A depletion factor for the dust cores - LTE analysis. . . . . . . . . . . . . . . . 210
7.3 Results of the LTE analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.3.1 Serpens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.3.2 Orion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
7.3.3 Taurus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
7.3.4 Ophiuchus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
7.4 Analysis of depletion data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.4.1 Comparison of sources and previous results. . . . . . . . . . . . . . . . 219
7.4.2 Density versus depletion correlation. . . . . . . . . . . . . . . . . . . . 220
7.4.3 Protostellar versus starless core depletion. . . . . . . . . . . . . . . . . 222
7.5 Uncertainties in the LTE derived depletion factor. . . . . . . . . . . . . . . . . 223
7.6 Evaluating Depletion Factors usingRADEX . . . . . . . . . . . . . . . . . . . . . 225
7.6.1 LTE versusRADEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
8 Concluding Remarks and Proposals for Future Work 231
Bibliography 234
A Details of CO Column Density and Mass Calculations 245
A.1 Column Density Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A.2 Excitation Temperature from12CO . . . . . . . . . . . . . . . . . . . . . . . . . 249
A.3 LTE Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
A.4 Virial Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
B CO Maps from the JCMT Gould Belt Survey 251
B.1 NGC 2024 CO maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
B.2 NGC 2071 CO maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
B.3 Ophiuchus CO maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
B.4 Serpens CO maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
B.5 Taurus CO maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
C Chapter 3 Figures 282
List of Figures
1.1 The Dark Horse Nebula; the dark patch, like those observed by Herschel, is due
to the extinction of background starlight by interstellar dust (Osterbrock(1974)). 34
1.2 Interstellar dust grains (images from http://geosci.uchicago.edu/people/davis.shtml
and www.daviddarling.info/enyclopedia/C/cosmicdust.html).. . . . . . . . . . 36
1.3 SED fits for a pre-stellar core L1544 and a Class 0 protostar IRAS 16293 (Andre
et al. (2010)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1 Integrated emission of some molecular line transitions in the 6.2-7.2 kms−1 vLSR
range, where emission (especially in HCO+) follows the HH 38-43-64 outflow.
The molecular line transition is shown on the top of each panel. For the C18O and
H13CO+ panels, the contour levels are from 25% to 95% of the peak intensity
in steps of 20%. For the other panels the contour levels are from 25% to 95%
of the peak intensity in steps of 10%. The triangles show, from left to right, the
Herbig-Haro objects HH 38, HH 43 and HH 64. The cross shows the position of
HH 43 MMS 1, where the powering source of the HH system is located (Stanke
et al. (2000)). Note that the two well defined clumps in HCO+ ahead and south
of HH 43 and HH38 have very narrow spectral lines associated (line widths of
around∆v ' 0.7 kms−1), which suggests that they are dynamically quiescent
relative to the cloud.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2 Column density (cm−2) versus time (years). The solid black line represents the
inter-clump medium, Av ∼2 mags, irradiated by a moving field of 30 G0 (model
i3), dashes - a clump at 105 cm−3, Av ∼5 mags, irradiated by a moving field of
30 G0 (model 6), dots - the inter-clump medium, Av ∼2 mags, irradiated by a
static field of 30 G0 (model i3 with a static field) and dots and dashes - a clump
at 105 cm−3, Av ∼5 mags, irradiated by a static field of 30 G0 (model 6 with a
static field). In the moving case the radiation field source is at its closest point at
around 1000 years.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10
LIST OF FIGURES 11
2.3 HCO+ column density vs. time. Top left plot - varying Av: solid line repre-
sents a clump at 105 cm−3 with a moving source of 20 G0 (model 5) at 1 mag,
dashes - 3 mags, dots - 4 mags, dots and dashes - 6 mags. Top right hand plot
- varying clump density: solid line represents model 2 (104 cm−3 with a mov-
ing source of 20 G0), dashed line - model 5 (105 cm−3), dotted line - model 11
(106 cm−3). Lower left hand plot - varying radiation field strength: solid line
represents model 4 (5 G0), dashed line - model 5(20 G0) , dotted line - model
6 (30 G0)and single dots and dashes - model 14 (50 G0) . Bottom right hand
plot - varying shock velocity: solid line represents model 4 (5 G0 at 300 kms−1),
dashed line - model 16 (5 G0 at 1000 kms−1), the dotted line - model 6 (20 G0
at 1000 kms−1) and dots and dashes - model 18 (30 G0 at 1000 kms−1). Apart
from the top left hand plot Av ∼ 6 . . . . . . . . . . . . . . . . . . . . . . . . 60
3.1 Flow chart of phases in the chemical model. The light grey circles are at 103
cm−3 in the centre and the dark grey at 105 cm−3 illustrating a clump at the
peak of collapse. The yellow arrows denote the presence of a radiation field.. . 65
3.2 Radiation field strengths over the pc2 map area for a 1000 G0 field. . . . . . . . 65
3.3 HCO+ column density maps at 10 years without HH field (top left), with 1000
G0 field at 10 years (top right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 3.93×1013 cm−2. . . . 69
3.4 H2CO column density maps at 10 years without HH field (top left), with 1000
G0 field at 10 years (middle right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 6.15×1015 cm−2. . . . 70
3.5 SO column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (middle right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 2.45×1015 cm−2. . . . 71
LIST OF FIGURES 12
3.6 CH3OH column density maps at 10 years without HH field (top left), with 1000
G0 field at 10 years (middle right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 6.28×1016 cm−2. . . . 72
3.7 CO column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (top right) without HH field at 1000 years (middle left) and with
1000 G0 field at 1000 years (middle right). Without radiation field at 5000 years
(bottom left) and with 1000 G0 field at 5000 years (bottom right). Minimum
contour level of 1×1011 cm−2, maximum of 3.17×1018 cm−2. . . . . . . . . . 73
3.8 N2H+ column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (top right) without HH field at 1000 years (middle left) and with
1000 G0 field at 1000 years (middle right). Without radiation field at 5000 years
(bottom left) and with 1000 G0 field at 5000 years (bottom right). Minimum
contour level of 1×1011 cm−2, maximum of 1.08×1012 cm−2. . . . . . . . . . 74
3.9 HCO+ column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 3.93×1013 cm−2. . . . . . . . . . . . . . . . . . . 75
3.10 CH3OH column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 6.28×1016 cm−2. . . . . . . . . . . . . . . . . . . 76
3.11 CS column density maps at 10 years with 100 G0 field (top left), with 1000 G0
field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0
field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 3.22×1015 cm−2. . . . . . . . . . . . . . . . . . . 77
LIST OF FIGURES 13
3.12 N2H+ column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 1.05×1012 cm−2. . . . . . . . . . . . . . . . . . . 78
3.13 N2H+ column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.07×1012 cm−2. 79
3.14 CH3OH column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.28×1016 cm−2. 80
3.15 N2H+ column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right). Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.08×1012 cm−2. 81
3.16 CH3OH column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right). Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 5.60×1016 cm−2. 82
3.17 HCO+ column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.13×1013 cm−2. 83
5.1 Peak values for synthetic uniform clump catalogue andCLUMPFIND output . . . 108
LIST OF FIGURES 14
5.2 Sums for synthetic uniform clump catalogue andCLUMPFIND output . . . . . . . 108
5.3 CLUMPFIND, clump positions - sparse cube, changing Tlow. . . . . . . . . . . . 109
5.4 CLUMPFIND, clump positions - crowded cube, changing Tlow. . . . . . . . . . . 109
5.5 CLUMPFIND, clump positions - uniform sparse cube, changing Tlow. . . . . . . 110
5.6 CLUMPFIND, clump positions - uniform crowded cube, changing Tlow. . . . . . 110
5.7 CLUMPFIND, clump positions - sparse cube, changing DeltaT. . . . . . . . . . . 110
5.8 CLUMPFIND, clump positions - crowded cube, changing DeltaT. . . . . . . . . . 110
5.9 CLUMPFIND, clump positions - uniform sparse cube, changing DeltaT. . . . . . 110
5.10 CLUMPFIND, clump positions - uniform crowded cube, changing DeltaT. . . . . 110
5.11 CLUMPFIND, clump positions - Taurus, changing Tlow. . . . . . . . . . . . . . 111
5.12 CLUMPFIND, clump positions - Taurus, changing DeltaT. . . . . . . . . . . . . 111
5.13 CLUMPFIND, clump positions - NGC 2024, changing Tlow. . . . . . . . . . . . 111
5.14 CLUMPFIND, clump positions - NGC 2024, changing DeltaT. . . . . . . . . . . 111
5.15 CLUMPFIND, data sums - sparse cube, changing Tlow. . . . . . . . . . . . . . . 112
5.16 CLUMPFIND, data sums - crowded cube, changing Tlow. . . . . . . . . . . . . . 112
5.17 CLUMPFIND, data sums - uniform sparse cube, changing Tlow. . . . . . . . . . 113
5.18 CLUMPFIND, data sums - uniform crowded cube, changing Tlow. . . . . . . . . 113
5.19 CLUMPFIND, data sums - sparse cube, changing DeltaT. . . . . . . . . . . . . . 113
5.20 CLUMPFIND, data sums - crowded cube, changing DeltaT. . . . . . . . . . . . . 113
5.21 CLUMPFIND, data sums - uniform sparse cube, changing DeltaT. . . . . . . . . 113
5.22 CLUMPFIND, data sums - uniform crowded cube, changing DeltaT. . . . . . . . 113
5.23 CLUMPFIND, data sums - Taurus, changing Tlow. . . . . . . . . . . . . . . . . . 114
5.24 CLUMPFIND, data sums - Taurus, changing DeltaT. . . . . . . . . . . . . . . . . 114
5.25 CLUMPFIND, data sums - NGC 2024, changing DeltaT. . . . . . . . . . . . . . 114
5.26 CLUMPFIND, data sums - NGC 2024, changing DeltaT. . . . . . . . . . . . . . 114
5.27 CLUMPFIND, clump mass function - sparse cube, changing Tlow. . . . . . . . . 116
5.28 CLUMPFIND, clump mass function - sparse uniform cube, changing Tlow. . . . . 116
5.29 CLUMPFIND, clump mass function - crowded cube, changing Tlow. . . . . . . . 117
5.30 CLUMPFIND, clump mass function - crowded uniform cube, changing Tlow. . . 117
5.31 CLUMPFIND, clump mass function - sparse cube, changing DeltaT. . . . . . . . 118
5.32 CLUMPFIND, clump mass function - sparse uniform cube, changing DeltaT. . . . 118
5.33 CLUMPFIND, clump mass function - crowded cube, changing DeltaT. . . . . . . 119
5.34 CLUMPFIND, clump mass function - crowded uniform cube, changing DeltaT. . 119
LIST OF FIGURES 15
5.35 Clump mass function - synthetic cubes, changing mean clump peak (fwhm of
distribution 5K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.36 CLUMPFIND, clump mass function -CLUMPFIND output (Tlow=3×rms, DeltaT=2×rms,
changing mean clump peak of input cube. . . . . . . . . . . . . . . . . . . . . 121
5.37 Peak values for synthetic uniform clump catalogue andFELLWALKER output . . . 123
5.38 Sums for synthetic uniform clump catalogue andFELLWALKER output . . . . . . 123
5.39 FELLWALKER, clump positions - sparse cube, changing Noise. . . . . . . . . . . 124
5.40 FELLWALKER, clump positions - crowded cube, changing Noise. . . . . . . . . . 124
5.41 FELLWALKER, clump positions - uniform sparse cube, changing Noise. . . . . . 125
5.42 FELLWALKER, clump positions - uniform crowded cube, changing Noise. . . . . 125
5.43 FELLWALKER, clump positions - sparse cube, changing MinDip. . . . . . . . . . 125
5.44 FELLWALKER, clump positions - crowded cube, changing MinDip. . . . . . . . 125
5.45 FELLWALKER, clump positions - uniform sparse cube, changing MinDip. . . . . 125
5.46 FELLWALKER, clump positions - uniform crowded cube, changing MinDip. . . . 125
5.47 FELLWALKER, clump positions - sparse cube, changing FlatSlope. . . . . . . . . 126
5.48 FELLWALKER, clump positions - crowded cube, changing FlatSlope. . . . . . . . 126
5.49 FELLWALKER, clump positions - uniform sparse cube, changing FlatSlope. . . . 126
5.50 FELLWALKER, clump positions - uniform crowded cube, changing FlatSlope. . . 126
5.51 FELLWALKER, clump positions - Taurus, changing Noise. . . . . . . . . . . . . 126
5.52 FELLWALKER, clump positions - NGC 2024, changing Noise. . . . . . . . . . . 126
5.53 FELLWALKER, clump positions - Taurus, changing MinDip. . . . . . . . . . . . 127
5.54 FELLWALKER, clump positions - NGC 2024, changing MinDip. . . . . . . . . . 127
5.55 FELLWALKER, clump positions - Taurus, changing FlatSlope. . . . . . . . . . . 127
5.56 FELLWALKER, data sums - sparse cube, changing Noise. . . . . . . . . . . . . . 128
5.57 FELLWALKER, data sums - crowded cube, changing Noise. . . . . . . . . . . . . 128
5.58 FELLWALKER, data sums - uniform sparse cube, changing Noise. . . . . . . . . 129
5.59 FELLWALKER, data sums - uniform crowded cube, changing Noise. . . . . . . . 129
5.60 FELLWALKER, data sums - sparse cube, changing MinDip. . . . . . . . . . . . . 129
5.61 FELLWALKER, data sums - crowded cube, changing MinDip. . . . . . . . . . . . 129
5.62 FELLWALKER, data sums - uniform sparse cube, changing MinDip. . . . . . . . 129
5.63 FELLWALKER, data sums - uniform crowded cube, changing MinDip. . . . . . . 129
5.64 FELLWALKER, data sums - sparse cube, changing FlatSlope. . . . . . . . . . . . 130
5.65 FELLWALKER, data sums - crowded cube, changing FlatSlope. . . . . . . . . . . 130
LIST OF FIGURES 16
5.66 FELLWALKER, data sums - uniform sparse cube, changing FlatSlope. . . . . . . 130
5.67 FELLWALKER, data sums - uniform crowded cube, changing FlatSlope. . . . . . 130
5.68 FELLWALKER, data sums - Taurus, changing Noise. . . . . . . . . . . . . . . . . 130
5.69 FELLWALKER, data sums - Taurus, changing FlatSlope. . . . . . . . . . . . . . . 130
5.70 FELLWALKER, data sums - NGC 2024, changing Noise. . . . . . . . . . . . . . 131
5.71 FELLWALKER, data sums - NGC 2024, changing MinDip. . . . . . . . . . . . . 131
5.72 FELLWALKER, data sums - NGC 2024, changing FlatSlope. . . . . . . . . . . . 131
5.73 FELLWALKER, clump mass function - sparse cube, changing Noise. . . . . . . . 133
5.74 FELLWALKER, clump mass function - uniform sparse cube, changing Noise. . . 133
5.75 FELLWALKER, clump mass function - crowded cube, changing Noise. . . . . . . 134
5.76 FELLWALKER, clump mass function - uniform crowded cube, changing Noise. . 134
5.77 FELLWALKER, clump mass function - sparse cube, changing MinDip. . . . . . . 135
5.78 FELLWALKER, clump mass function - uniform sparse cube, changing MinDip. . 135
5.79 FELLWALKER, clump mass function - crowded cube, changing MinDip. . . . . . 136
5.80 FELLWALKER, clump mass function - uniform crowded cube, changing MinDip. 136
5.81 FELLWALKER, clump mass function - sparse cube, changing FlatSlope. . . . . . 137
5.82 FELLWALKER, clump mass function - uniform sparse cube, changing FlatSlope. 137
5.83 FELLWALKER, clump mass function - crowded cube, changing FlatSlope. . . . . 138
5.84 FELLWALKER, clump mass function - uniform crowded cube, changing FlatSlope138
5.85 Clump mass function - synthetic cubes, changing mean clump peak (fwhm of
distribution 5K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.86 FELLWALKER, clump mass function -FELLWALKER output changing mean clump
peak of input cube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.87 Peak values for synthetic uniform clump catalogue andREINHOLD output . . . . 140
5.88 Sums for synthetic uniform clump catalogue andREINHOLD output . . . . . . . 140
5.89 REINHOLD, clump positions - sparse cube, changing Noise. . . . . . . . . . . . 142
5.90 REINHOLD, clump positions - crowded cube, changing Noise. . . . . . . . . . . 142
5.91 REINHOLD, clump positions - uniform cube, changing Noise. . . . . . . . . . . 143
5.92 REINHOLD, clump positions - uniform crowded cube, changing Noise. . . . . . 143
5.93 REINHOLD, clump positions - sparse cube, changing MinLen. . . . . . . . . . . 143
5.94 REINHOLD, clump positions - crowded cube, changing MinLen. . . . . . . . . . 143
5.95 REINHOLD, clump positions - uniform sparse cube, changing MinLen. . . . . . 143
5.96 REINHOLD, clump positions - uniform crowded cube, changing MinLen. . . . . 143
LIST OF FIGURES 17
5.97 REINHOLD, clump positions - sparse cube, changing FlatSlope. . . . . . . . . . 144
5.98 REINHOLD, clump positions - crowded cube, changing FlatSlope. . . . . . . . . 144
5.99 REINHOLD, clump positions - uniform sparse cube, changing FlatSlope. . . . . 144
5.100 REINHOLD, clump positions - uniform crowded cube, changing FlatSlope. . . . 144
5.101 REINHOLD, clump positions - sparse cube, changing CaIterations. . . . . . . . . 144
5.102 REINHOLD, clump positions - crowded cube, changing CaIterations. . . . . . . 144
5.103 REINHOLD, clump positions - uniform sparse cube, changing CaIterations. . . . 145
5.104 REINHOLD, clump positions - uniform crowded cube, changing CaIterations. . . 145
5.105 REINHOLD, data sums - sparse cube, changing Noise. . . . . . . . . . . . . . . 146
5.106 REINHOLD, data sums - crowded cube, changing Noise. . . . . . . . . . . . . . 146
5.107 REINHOLD, data sums - uniform sparse cube, changing Noise. . . . . . . . . . . 147
5.108 REINHOLD, data sums - uniform crowded cube, changing Noise. . . . . . . . . 147
5.109 REINHOLD, data sums - sparse cube, changing MinLen. . . . . . . . . . . . . . 147
5.110 REINHOLD, data sums - crowded cube, changing MinLen. . . . . . . . . . . . . 147
5.111 REINHOLD, data sums - uniform sparse cube, changing MinLen. . . . . . . . . 147
5.112 REINHOLD, data sums - uniform crowded cube, changing MinLen. . . . . . . . 147
5.113 REINHOLD, data sums - sparse cube, changing FlatSlope. . . . . . . . . . . . . 148
5.114 REINHOLD, data sums - crowded cube, changing FlatSlope. . . . . . . . . . . . 148
5.115 REINHOLD, data sums - uniform sparse cube, changing FlatSlope. . . . . . . . . 148
5.116 REINHOLD, data sums - uniform crowded cube, changing FlatSlope. . . . . . . 148
5.117 REINHOLD, data sums - sparse cube, changing CaIterations. . . . . . . . . . . . 148
5.118 REINHOLD, data sums - crowded cube, changing CaIterations. . . . . . . . . . . 148
5.119 REINHOLD, data sums - uniform sparse cube, changing CaIterations. . . . . . . 149
5.120 REINHOLD, data sums - uniform crowded cube, changing CaIterations. . . . . . 149
5.121 REINHOLD, clump mass function - sparse cube, changing Noise. . . . . . . . . 151
5.122 REINHOLD, clump mass function - uniform sparse cube, changing Noise. . . . . 151
5.123 REINHOLD, clump mass function - crowded cube, changing Noise. . . . . . . . 152
5.124 REINHOLD, clump mass function - uniform crowded cube, changing Noise. . . . 152
5.125 REINHOLD, clump mass function - sparse cube, changing MinLen. . . . . . . . 153
5.126 REINHOLD, clump mass function - uniform sparse cube, changing MinLen. . . . 153
5.127 REINHOLD, clump mass function - crowded cube, changing MinLen. . . . . . . 154
5.128 REINHOLD, clump mass function - uniform crowded cube, changing MinLen. . 154
5.129 REINHOLD, clump mass function - sparse cube, changing FlatSlope. . . . . . . 155
LIST OF FIGURES 18
5.130 REINHOLD, clump mass function - uniform sparse cube, changing FlatSlope. . . 155
5.131 REINHOLD, clump mass function - crowded cube, changing FlatSlope. . . . . . 156
5.132 REINHOLD, clump mass function - uniform crowded cube, changing FlatSlope. . 156
5.133 Peak values for synthetic uniform clump catalogue andGAUSSCLUMPSoutput . . 157
5.134 Sums for synthetic uniform clump catalogue andGAUSSCLUMPSoutput . . . . . 157
5.135 GAUSSCLUMPS, clump positions - sparse cube, changing Thresh. . . . . . . . . 158
5.136 GAUSSCLUMPS, clump positions - crowded cube, changing Thresh. . . . . . . . 158
5.137 GAUSSCLUMPS, clump positions - sparse uniform cube, changing Thresh. . . . . 159
5.138 GAUSSCLUMPS, clump positions - crowded uniform cube, changing Thresh. . . . 159
5.139 GAUSSCLUMPS, clump positions - sparse cube, changing MaxNF. . . . . . . . . 159
5.140 GAUSSCLUMPS, clump positions - crowded cube, changing MaxNF. . . . . . . . 159
5.141 GAUSSCLUMPS, clump positions - sparse uniform cube, changing MaxNF. . . . 159
5.142 GAUSSCLUMPS, clump positions - crowded uniform cube, changing MaxNF. . . 159
5.143 GAUSSCLUMPS, clump data sums - sparse cube, changing Thresh. . . . . . . . . 160
5.144 GAUSSCLUMPS, clump data sums - crowded cube, changing Thresh. . . . . . . . 160
5.145 GAUSSCLUMPS, clump data sums - sparse uniform cube, changing Thresh. . . . 161
5.146 GAUSSCLUMPS, clump data sums - crowded uniform cube, changing Thresh. . . 161
5.147 GAUSSCLUMPS, clump data sums - sparse cube, changing MaxNF. . . . . . . . . 161
5.148 GAUSSCLUMPS, clump data sums - crowded cube, changing MaxNF. . . . . . . 161
5.149 GAUSSCLUMPS, clump data sums - sparse uniform cube, changing MaxNF. . . . 161
5.150 GAUSSCLUMPS, clump data sums - crowded uniform cube, changing MaxNF. . . 161
5.151 GAUSSCLUMPS, clump mass function - sparse cube, changing Thresh. . . . . . . 163
5.152 GAUSSCLUMPS, clump mass function - sparse uniform cube, changing Thresh. . 163
5.153 GAUSSCLUMPS, clump mass function - crowded cube, changing Thresh. . . . . . 164
5.154 GAUSSCLUMPS, clump mass function - uniform crowded cube, changing Thresh. 164
5.155 GAUSSCLUMPS, clump mass function - sparse cube, changing MaxNF. . . . . . 165
5.156 GAUSSCLUMPS, clump mass function - uniform sparse cube, changing MaxNF. . 165
5.157 GAUSSCLUMPS, clump mass function - crowded cube, changing MaxNF. . . . . 166
5.158 GAUSSCLUMPS, clump mass function - uniform crowded cube, changing MaxNF. 166
6.1 Positions of clumps identified in the original C18O maps and C18O maps with
large-scale emission removed.. . . . . . . . . . . . . . . . . . . . . . . . . . 179
LIST OF FIGURES 19
6.2 Radius vs. LTE mass for clumps identified in the original C18O maps and C18O
maps with large-scale emission removed.. . . . . . . . . . . . . . . . . . . . . 179
6.3 LTE mass vs. Virial mass for clumps identified in the original C18O maps and
C18O maps with large-scale emission removed.. . . . . . . . . . . . . . . . . 179
6.4 Positions of clumps identified in the original12CO maps and12CO maps with
large-scale emission removed.. . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.5 Radius vs. LTE mass for clumps identified in the original12CO maps and12CO
maps with large-scale emission removed.. . . . . . . . . . . . . . . . . . . . . 180
6.6 LTE mass vs. Virial mass for clumps identified in the original12CO maps and
12CO maps with large-scale emission removed.. . . . . . . . . . . . . . . . . 180
6.7 LTE mass vs. Virial mass of CO clumps in Serpens assuming an excitation
temperature of 15 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.8 LTE mass vs. Virial mass of CO clumps in Serpens assuming an excitation
temperature of 10 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.9 CO clump positions for NGC 2024. . . . . . . . . . . . . . . . . . . . . . . . 183
6.10 CO clump positions for NGC 2071. . . . . . . . . . . . . . . . . . . . . . . . 183
6.11 CO clump positions for Ophiuchus. . . . . . . . . . . . . . . . . . . . . . . . 183
6.12 CO clump positions for Serpens. . . . . . . . . . . . . . . . . . . . . . . . . 183
6.13 CO clump positions for Taurus. . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.14 Ellipticity of the CO clumps in NGC 2024. . . . . . . . . . . . . . . . . . . . 184
6.15 Ellipticity of the CO clumps in NGC 2071. . . . . . . . . . . . . . . . . . . . 184
6.16 Ellipticity of the CO clumps in Ophiuchus. . . . . . . . . . . . . . . . . . . . 185
6.17 Ellipticity of the CO clumps in Serpens. . . . . . . . . . . . . . . . . . . . . 185
6.18 Ellipticity of the CO clumps in Taurus. . . . . . . . . . . . . . . . . . . . . . 185
6.19 Radius vs LTE mass for CO clumps in NGC 2024. . . . . . . . . . . . . . . . 187
6.20 Radius vs LTE mass for CO clumps in NGC 2071. . . . . . . . . . . . . . . . 187
6.21 Radius vs LTE mass for CO clumps in Ophiuchus. . . . . . . . . . . . . . . . 187
6.22 Radius vs LTE mass for CO clumps in Serpens. . . . . . . . . . . . . . . . . 187
6.23 Radius vs LTE mass for CO clumps in Taurus. . . . . . . . . . . . . . . . . . 187
6.24 LTE mass vs. virial mass for CO clumps in NGC 2024. . . . . . . . . . . . . 189
6.25 LTE mass vs virial mass for CO clumps in NGC 2071. . . . . . . . . . . . . . 189
6.26 LTE mass vs. virial mass for CO clumps in Ophiuchus. . . . . . . . . . . . . 189
6.27 LTE mass vs virial mass for CO clumps in Serpens. . . . . . . . . . . . . . . 189
LIST OF FIGURES 20
6.28 LTE mass vs. virial mass for CO clumps in Taurus. . . . . . . . . . . . . . . . 190
6.29 Clump mass functions for CO clumps in NGC 2024. . . . . . . . . . . . . . . 193
6.30 Clump mass functions for CO clumps in NGC 2071. . . . . . . . . . . . . . . 193
6.31 Clump mass functions for CO clumps in Ophiuchus. . . . . . . . . . . . . . . 194
6.32 Clump mass functions for CO clumps in Serpens. . . . . . . . . . . . . . . . 194
6.33 Clump mass functions for CO clumps in Taurus. . . . . . . . . . . . . . . . . 195
6.34 12CO matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 198
6.35 12CO matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 198
6.36 12CO matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 198
6.37 12CO matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 198
6.38 12CO matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 198
6.39 12CO matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 198
6.40 12CO matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 199
6.41 12CO matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 199
6.42 13CO matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 199
6.43 13CO matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 199
6.44 13CO matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 199
6.45 13CO matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 199
6.46 13CO matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 200
6.47 13CO matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 200
6.48 13CO matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 200
6.49 13CO matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 200
6.50 13CO matches with SCUBA cores in Taurus.. . . . . . . . . . . . . . . . . . . 200
6.51 13CO matches with SCUBA cores in Taurus.. . . . . . . . . . . . . . . . . . . 200
6.52 C18O matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 201
6.53 C18O matches with SCUBA cores in NGC 2024.. . . . . . . . . . . . . . . . 201
6.54 C18O matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 201
6.55 C18O matches with SCUBA cores in NGC 2071.. . . . . . . . . . . . . . . . 201
6.56 C18O matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 201
6.57 C18O matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 201
6.58 C18O matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 202
6.59 C18O matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 202
6.60 SCUBA cores in NGC 2024, coloured to illustrate a match with a CO clump.. 203
LIST OF FIGURES 21
6.61 SCUBA cores in NGC 2024, coloured to illustrate a match with a CO clump.. 203
6.62 SCUBA cores in NGC 2071, coloured to illustrate a match with a CO clump.. 204
6.63 SCUBA cores in NGC 2071, coloured to illustrate a match with a CO clump.. 204
6.64 SCUBA cores in Ophiuchus, coloured to illustrate a match with a CO clump.. 204
6.65 SCUBA cores in Ophiuchus, coloured to illustrate a match with a CO clump.. 204
6.66 SCUBA cores in Serpens, coloured to illustrate a match with a CO clump.. . . 204
6.67 SCUBA cores in Serpens, coloured to illustrate a match with a CO clump.. . . 204
6.68 SCUBA cores in Taurus, coloured to illustrate a match with a CO clump.. . . . 205
6.69 SCUBA cores in Taurus, coloured to illustrate a match with a CO clump.. . . . 205
6.70 SCUBA cores in Ophiuchus, coloured to illustrate a match with a CO clump.
Here we set the noise parameter to 10*rms when running the FELLWALKER
algorithm to locate CO clumps.. . . . . . . . . . . . . . . . . . . . . . . . . . 205
6.71 SCUBA cores in Ophiuchus, coloured to illustrate a match with a CO clump.
Here we set the noise parameter to 15*rms when running the FELLWALKER
algorithm to locate CO clumps.. . . . . . . . . . . . . . . . . . . . . . . . . . 205
7.1 H2 Column density in Serpens vs. Fdep (left, with H2 column densities cal-
culated using visual extinction measurements and right, using the dust thermal
emission at 850 microns). Crosses represent the protostars and diamonds the
starless cores.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.2 H2 Column density derived from dust emission vs. Fdep for Orion NGC 2024
(left) and NGC 2071 (right). Squares represent starless cores and crosses proto-
stellar cores.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.3 H2 Column density derived from dust emission vs. Fdep for Serpens (left -
dashed line shows the line of best fit of a linear regression on protostellar cores)
and Taurus (right - solid line shows the line of best fit of a linear regression on
starless cores).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.4 H2 Column density derived from dust emission vs. Fdep for Ophiuchus. . . . . 215
7.5 Depletion factor vs. position in cloud for Orion NGC 2024 (left) and NGC 2071
(right). Squares represent starless cores and crosses protostellar cores.. . . . . 215
7.6 Ophiuchus (left) and Serpens (right).. . . . . . . . . . . . . . . . . . . . . . . 215
7.7 Taurus (left) and Taurus with south east region (right).. . . . . . . . . . . . . . 216
LIST OF FIGURES 22
7.8 Fdep vs. dust column density for all clouds. Trends are plotted for Serpens
(dotted line) and Taurus (solid line).. . . . . . . . . . . . . . . . . . . . . . . 221
7.9 Orion NGC 2024 using CO derived temperatures to estimate Fdep (left) and us-
ing dust temperatures (right). Squares represent starless cores and crosses pro-
tostellar cores.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7.10 Serpens using CO derived temperatures to estimate Fdep (left) and using dust
temperatures (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7.11 RADEX versus LTE depletion factors. Left - all cores fitted withRADEX (starless
cores are squares, protostellar cores are crosses). Right - only cores with a good
(χ2 less than 2), uniqueRADEX fit. . . . . . . . . . . . . . . . . . . . . . . . . 227
B.1 NGC 202412CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1
(top left) and 16 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 252
B.2 NGC 202412CO integrated intensity map from HARP (in units of Kkms−1). . . 253
B.3 NGC 202413CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1
(top left) and 16 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 254
B.4 NGC 202413CO integrated intensity map from HARP (units of Kkms−1). . . . 255
B.5 NGC 2024 C18O channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1
(top left) and 16 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 256
B.6 NGC 2024 C18O integrated intensity map from HARP (units of Kkms−1). . . . 257
B.7 NGC 207112CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5
kms−1 (top left) and 15 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . 258
B.8 NGC 207112CO integrated intensity map from HARP (units of Kkms−1). . . . 259
B.9 NGC 207113CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5
kms−1 (top left) and 15 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . 260
B.10 NGC 207113CO integrated intensity map from HARP (units of Kkms−1). . . . 261
LIST OF FIGURES 23
B.11 NGC 2071 C18O channel map from HARP showing mean intensity (in Kelvin)
in channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5
kms−1 (top left) and 15 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . 262
B.12 NGC 2071 C18O integrated intensity map from HARP (units of Kkms−1). . . . 263
B.13 Ophiuchus12CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 2 kms−1, 4 kms−1, 6 kms−1 and 8 kms−1. . . . . . . . . 264
B.14 Ophiuchus12CO integrated intensity map from HARP (units of Kkms−1). . . . 265
B.15 Ophiuchus13CO channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 2 kms−1 (bottom left), 4 kms−1 (bottom right), 6 kms−1
(top left) and 8 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 266
B.16 Ophiuchus13CO integrated intensity map from HARP (units of Kkms−1). . . . 267
B.17 Ophiuchus C18O channel map from HARP showing mean intensity (in Kelvin)
in channels centred at 2 kms−1 (bottom left), 4 kms−1 (bottom right), 6 kms−1
(top left) and 8 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 268
B.18 Ophiuchus C18O integrated intensity map from HARP (units of Kkms−1). . . . 269
B.19 Serpens12CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1
(top left) and 14 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 270
B.20 Serpens12CO integrated intensity map from HARP (units of Kkms−1). . . . . 271
B.21 Serpens13CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1
(top left) and 14 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 272
B.22 Serpens13CO integrated intensity map from HARP (units of Kkms−1). . . . . 273
B.23 Serpens C18O channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1
(top left) and 14 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 274
B.24 Serpens C18O integrated intensity map from HARP (units of Kkms−1). . . . . 275
B.25 Taurus12CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1
(top left) and 8 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 276
B.26 Taurus12CO integrated intensity map from HARP (units of Kkms−1). . . . . . 277
LIST OF FIGURES 24
B.27 Taurus13CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1
(top left) and 8 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 278
B.28 Taurus13CO integrated intensity map from HARP (units of Kkms−1). . . . . . 279
B.29 Taurus C18O channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1
(top left) and 8 kms−1 (top right). . . . . . . . . . . . . . . . . . . . . . . . . 280
B.30 Taurus C18O integrated intensity map from HARP (units of Kkms−1). . . . . . 281
C.1 CS column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (top right) without HH field at 1000 years (middle left) and with
1000 G0 field at 1000 years (middle right). Without radiation field at 5000 years
(bottom left) and with 1000 G0 field at 5000 years (bottom right). Minimum
contour level of 1×1011 cm−2, maximum of 3.22×1015 cm−2. . . . . . . . . . 283
C.2 NH3 column density maps at 10 years without HH field (top left), with 1000
G0 field at 10 years (middle right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 2.73×1017 cm−2. . . . 284
C.3 HCN column density maps at 10 years without HH field (top left), with 1000
G0 field at 10 years (middle right) without HH field at 1000 years (middle left)
and with 1000 G0 field at 1000 years (middle right). Without radiation field at
5000 years (bottom left) and with 1000 G0 field at 5000 years (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 1.05×1016 cm−2. . . . 285
C.4 CO column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 3.17×1018 cm−2. . . . . . . . . . . . . . . . . . . 286
LIST OF FIGURES 25
C.5 NH3 column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 2.73×1017 cm−2. . . . . . . . . . . . . . . . . . . 287
C.6 H2CO column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 6.15×1015 cm−2. . . . . . . . . . . . . . . . . . . 288
C.7 SO column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 2.45×1015 cm−2. . . . . . . . . . . . . . . . . . . 289
C.8 HCN column density maps at 10 years with 100 G0 field (top left), with 1000
G0 field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100
G0 field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field
(bottom left) and a 1000 G0 field (bottom right). Minimum contour level of
1×1011 cm−2, maximum of 1.05×1016 cm−2. . . . . . . . . . . . . . . . . . . 290
C.9 HCO+ column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.93×1013 cm−2. 291
C.10 CO column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.17×1018 cm−2. 292
LIST OF FIGURES 26
C.11 CS maps at 10 years with 1000 G0 static field (top left), with 1000 G0 moving
field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with
1000 G0 moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0
static field (bottom left) and a 1000 G0 moving field (bottom right). Minimum
contour level of 1×1011 cm−2, maximum of 4.27×1015 cm−2. . . . . . . . . . 293
C.12 NH3 column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.73×1017 cm−2. 294
C.13 H2CO column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.15×1015 cm−2. 295
C.14 SO column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.45×1015 cm−2. 296
C.15 HCN column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years
(3rd) and with 1000 G0 moving field at 1000 years (top right). Maps at 5000
years for a 1000 G0 static field (bottom left) and a 1000 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.09×1016 cm−2. 297
C.16 HCO+ column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right). Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.76×1013 cm−2. 298
LIST OF FIGURES 27
C.17 CO column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd)
and with 100 G0 moving field at 1000 years (top right) . Maps at 5000 years
for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 2.96×1018 cm−2. . . . 299
C.18 CS column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd)
and with 100 G0 moving field at 1000 years (top right) . Maps at 5000 years
for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 3.41×1015 cm−2. . . . 300
C.19 NH3 column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right) . Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.42×1017 cm−2. 301
C.20 H2CO column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right) . Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.30×1015 cm−2. 302
C.21 SO column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd)
and with 100 G0 moving field at 1000 years (top right) . Maps at 5000 years
for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom right).
Minimum contour level of 1×1011 cm−2, maximum of 2.30×1015 cm−2. . . . 303
C.22 HCN column density maps at 10 years with 100 G0 static field (top left), with
100 G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years
(3rd) and with 100 G0 moving field at 1000 years (top right) . Maps at 5000
years for a 100 G0 static field (bottom left) and a 100 G0 moving field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 7.72×1015 cm−2. 304
LIST OF FIGURES 28
C.23 CO column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000
G0 static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 4.20×1018 cm−2. 305
C.24 CS column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.74×1015 cm−2. 306
C.25 N2H+ column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.08×1011 cm−2. 307
C.26 CH3OH column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.00×1017 cm−2. 308
C.27 NH3 column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.93×1017 cm−2. 309
LIST OF FIGURES 29
C.28 H2CO column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.15×1015 cm−2. 310
C.29 SO column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.81×1015 cm−2. 311
C.30 HCN column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0
static field and 200 cores at 1000 years (3rd) and with 1000 G0 static field and
400 cores at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
with 200 cores (bottom left) and a 1000 G0 static field with 400 cores (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.36×1016 cm−2. 312
List of Tables
1.1 Phases of the Interstellar Medium - Adapted fromWoodenet al. (2004). . . . . . 35
1.2 Important reaction types in dark cloud conditions. . . . . . . . . . . . . . . . . 39
2.1 Model Input Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2 Initial elemental abundances as a function of total hydrogen column density (from
Sofia & Meyer 2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.3 Comparing the effects of moving and static sources for model 5 with the clump
at an Av of 5 magnitudes. E denotes early times, L late times (after around 300
years). Up arrows indicate molecules that increase in abundance with a moving
source rather than static, right arrows those that do not change and down arrows
those that decrease in abundance.. . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4 Timescales of abundance enhancements - Model 5. Timescale defined as the time
taken for column density to drop below 1012 cm−2 or to stop falling. . . . . . . . 59
3.1 Map parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2 HCO+ (left) and CO (right) maximum column densities. . . . . . . . . . . . . 67
3.3 CS (left) and N2H+ (right) maximum column densities (cm−2). . . . . . . . . . 67
3.4 CH3OH (left) and NH3 (right) maximum column densities (cm−2). . . . . . . . . 68
3.5 H2CO (left) and SO (right) maximum column densities (cm−2). . . . . . . . . . 68
3.6 HCN maximum column densities (cm−2). . . . . . . . . . . . . . . . . . . . . . 68
4.1 Details of the observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2 GBS Cloud Propertiesa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.1 Parameters Investigated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Clump numbers -CLUMPFIND . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Clump numbers -FELLWALKER . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4 Clump numbers -REINHOLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
30
LIST OF TABLES 31
5.5 Clump numbers -GAUSSCLUMPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.6 CLUMPFIND performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.7 FELLWALKER performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.8 REINHOLD performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.9 GAUSSCLUMPSperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.1 Number of Clumps Identified withFELLWALKER . . . . . . . . . . . . . . . . . . 182
6.2 LTE masses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.3 Values of alpha from clump mass distributions. . . . . . . . . . . . . . . . . . . 192
6.4 Number of matches with SCUBA cores. . . . . . . . . . . . . . . . . . . . . . 197
7.1 Depletion factor (Fdep) - mean, standard deviation and range. Brackets indicate
the number of cores in each sample.. . . . . . . . . . . . . . . . . . . . . . . . 220
7.2 A comparison with previous studies.. . . . . . . . . . . . . . . . . . . . . . . . 221
7.3 Intercept, gradient and coefficient of determination (R2) values for the fits to den-
sity vs. depletion plots for starless and protostellar cores in all clouds.. . . . . . 222
7.4 LTE andRADEX results - Taurse refers to the south-eastern region of L1495 (the
ridge). Brackets indicate powers of 10.. . . . . . . . . . . . . . . . . . . . . . . 230
CHAPTER 1
I NTRODUCTION
1.1 Overview
In the late 18th century, William Herschel puzzled over his observations of mysterious dark
patches on the night sky. These were later shown to be star-forming clouds, their high dust con-
tent acting to obscure background stars and causing them appear as voids. Now the eponymous
Herschel Space Telescope is able to deliver detailed images of the same regions, and the field will
continue to advance as data from the likes of ALMA becomes available over the next few years.
Powerful radio and IR telescopes, which enable us to study emission from these heavily ex-
tincted clouds at high resolution (see Figure 1.1), have provided evidence for their clumpy nature.
Via a combination of turbulence, magnetic fields and gravitational coalescence material is ma-
neuvered into filaments, clumps and cores, allowing the densities required for stellar birth to be
reached. Probing the chemical make-up of these clouds is of paramount importance to under-
standing their physical evolution. Line emission from molecules is the most important cooling
mechanism in the dense interiors and as such directly affects the structure of the cloud and the
development of pre-stellar cores. While chemical models historically account for reactions in the
gas phase, it has become evident that the surfaces of solid dust grains in the interstellar medium
also play a crucial role in the chemistry (Williams & Taylor (1996)). Species can stick to the
surface of these grains forming icy mantles (a process sometimes referred to as depletion), thus
providing excellent catalysts for important chemical reactions (Hollenbach & Salpeter(1970)). A
good understanding of the rate at which this process occurs for different species is crucial if we
want to continue using gas phase abundances as probes of the evolution of stellar cores or the
overall masses of star-forming clouds.
32
1.2. Phases of the Interstellar Medium and Some Important Chemistry 33
This thesis investigates the structure and chemistry of clumpy molecular clouds, approaching
the issue from two completely different angles. The first (Chapters 2 and 3) is more theoretical,
utilising complex chemical models to reproduce emission from clouds surrounding Herbig-Haro
objects, this way probing the chemistry and filling factor of the constituent dense clumps. The
second half of the thesis deals with the treatment of observational data. Decomposition algorithms
are investigated and then used to study the clumpy nature of the CO emission from five nearby
star-forming clouds. CO and dust emission are compared both in terms of their distribution and
by looking specifically at the centres of dust cores for signs of CO freeze-out.
I begin by introducing a general picture of the interstellar medium (ISM) and its phases, before
focusing on chemical processes that occur in the dense molecular clouds that form the topic of this
thesis. I present evidence for the clumpy nature of these clouds and address gas-grain molecular
processes, first outlining some basic properties of the solid phase of the ISM known as dust, and
then summarising what we currently know about processes on the grain surfaces and interstellar
ices. I describe how chemical models can be used to make predictions about and interpret obser-
vations of star-forming regions, explain how column densities can be derived from molecular line
data in the gas phase and from dust emission, and finally give an overview of the formation of an
isolated, low-mass star (as the simplest case) including both the starless and the protostellar phases
which form the sample for the depletion study in Chapter 7.
1.2 Phases of the Interstellar Medium and Some Important Chem-
istry
The material lying between the stars, the ISM, is invisible to the naked eye, and yet there is a
wealth of observational data that supports its existence and allows us to study its properties. Al-
though we can infer mean quantities, the interstellar material is very inhomogeneous and different
regions have diverse temperatures, densities and, as a result, also chemical make-up. Aside from
gravitational effects, we can directly observe emission from atoms and molecules in the ISM that
have been excited into higher energy states by the light from nearby stars. Excited species radiate
as they de-excite and we see the resulting glow as a nebula. Radio telescopes allow us to target the
lower energy rotational transitions from molecules such as CO, which are abundant in the ISM.
We see these both in absorption and in emission.
Early models describe a two phase ISM made up of warm and cold neutral media (Field
et al. (1969)). The theory relies on thermal balance (heating rate equal to cooling rate) and a
1.2. Phases of the Interstellar Medium and Some Important Chemistry 34
Figure 1.1: The Dark Horse Nebula; the dark patch, like those observed by Herschel, is due to the
extinction of background starlight by interstellar dust (Osterbrock(1974)).
pressure balance between the two phases.McKee & Ostriker (1977) expanded this model to
include a third, hot phase for regions near to supernova explosions. Modern ideas of the ISM
range from a many phase model to a continuum of phases; here we describe the basic properties
of stereotypical regions as distinct and divide the ISM into five main components which we briefly
describe (referring toWoodenet al.(2004)). The hot ionised medium, or coronal gas, is equivalent
to the hot phase of McKee& Ostriker and is heated by supernova shocks. It is characterised
by fairly low densities (around 0.003 cm−3) and high temperatures (a million Kelvin or so). In
the warm ionised medium hydrogen is still in its ionised state but densities are slightly higher
than in the hot ionised medium and, as the name suggests, temperatures are lower. The warm
neutral medium has densities of 0.1 cm−3-300 cm−3 and temperatures in the range 8×103-104 K.
Here hydrogen is no longer completely ionised but is still in its atomic form. In the atomic cold
neutral medium some of the hydrogen atoms have now combined to form molecular hydrogen. The
diffuse (and translucent) clouds fall into this category which covers temperatures around 100 K
and densities 10-100 cm−3. The final phase is the molecular cold neutral medium which comprises
the well known dense molecular clouds, sites of star formation and the main focus of this thesis.
1.2. Phases of the Interstellar Medium and Some Important Chemistry 35
Table 1.1: Phases of the Interstellar Medium - Adapted fromWoodenet al. (2004).
Name Temperature (K) Density (cm−3)
Hot ionised medium 106 0.003
Warm ionised medium 104 >10
Warm neutral medium 8×103-104 0.1
Atomic cold neutral medium 100 10-100
Molecular cold neutral medium 5-50 103-105
The temperatures there range from 5-50 K and densities from around 103-105 cm−3. Hydrogen is
mostly in its molecular form and many other molecules are present including CO, CS, NH3 and
others, whose rotational spectra provide a useful probe of the physical conditions in these regions
(e.g.Morataet al. (1997); Tafalla(2011)). The 5 phases are summarised in Table 1.1.
1.2.1 Dust
In addition to the gas phase ISM, in dense regions a fraction of material is locked up in small, solid
particles (dust grains, see figure 1.2). Dust plays an important role in regulating the temperature of
pre-stellar cores which are observed to have fairly constant temperatures throughout of around 10-
20K previous to the switch-on of the central source (Tafalla(2005)). This is due to the combined
effect of two processes. At lower densities cooling occurs mainly through molecular line emission
whereas at higher densities above around 104.5cm−3 (Goldsmith(2001)) gas and dust temper-
atures become coupled so that the temperature is regulated by thermal emission from the dust.
The gas to dust ratio (by mass) in the Milky-way ISM is thought to be fairly constant at around
100:1 (e.g.Savage & Mathis(1979)). We observe these grains via their interaction with starlight,
either absorbing or scattering photons, and thermal emission in the infrared due to warm dust.
Achieving an accurate description of the composition, sizes and abundances of dust grains is very
difficult. The only way we can really derive these properties is through absorption features in the
spectrum of a background radiation source, or general features of the extinction curve combined
with a knowledge of the optical properties of different types of grain or different grain mixtures.
The extinction curve describes how dust along a particular line of sight will remove energy from
a background source as a function of wavelength. This curve has a particular form, and scientists
strive to reproduce the observed wavelength dependence with grain distribution models (e.gWein-
gartner & Draine(2001)). This has proved very tricky and results are often degenerate. Absorption
1.2. Phases of the Interstellar Medium and Some Important Chemistry 36
Figure 1.2: Interstellar dust grains (images from http://geosci.uchicago.edu/people/davis.shtml
and www.daviddarling.info/enyclopedia/C/cosmicdust.html).
features seen at 9.7 and 18 microns are attributed to bonds between Si and O and a bump in the
extinction curve at 2175 Angstrom to carbon rich materials such as graphite (Draine(1989)). We
also see absorption features in the infrared from ices on the surfaces of the grains (e.g. at 3.1 mi-
crons due to the O-H bond in water ice). The current picture is of a mixture of around 5 nanometer
to 1 micron sized silicate and carbonaceous grains. Silicate grains are thought to be preferentially
formed in the dense winds of oxygen rich stars during their Asymptotic Giant Branch or Red Giant
phases. Carbon in these winds will already be locked up in CO leaving the oxygen free to form
silicates such as SiO, Pyroxenes (MgxFe1−xSiO3) or Olivines (Mg2xFe2−2xSiO4). In carbon rich
winds carbonaceous grains are formed. These may be crystalline (regular in structure e.g graphite
or diamond) or amorphous (aliphatic molecules or PAHs). It is thought that around 95% of the
grain material is amorphous and the rest crystalline, likely made up mainly of silicates containing
impurities (see review byDraine(2003)).
Light passing through dusty regions is partially linearly polarised, which points to non-spherical
dust grains that are aligned to some degree, probably by the magnetic field lines that thread through
the ISM and can induce fields in the paramagnetic grains. The grains, which rotate, will tend to
align their spin axis with the field lines and light whose electric vector is parallel to the longer
axis of the grain will be preferentially absorbed. Grains are heated by the absorption of starlight,
by collisions with cosmic rays, electrons and other grains and by chemical reactions (such as the
exothermic reaction forming H2 on the grain surfaces). Large grains in regions exposed to stellar
1.2. Phases of the Interstellar Medium and Some Important Chemistry 37
radiation will generally have temperatures of around 20-40 K, radiating in the infrared after hav-
ing absorbed light at shorter wavelengths. In contrast to the larger grains, small grains are heated
stochastically, meaning that because their heat capacities are lower, their temperature will increase
a lot on absorption of a single photon but they will cool rapidly (Draine & Anderson(1985)). The
temperature of a single grain will therefore tend to spike, and the temperature spectrum of many
grains combined will be broader than for the larger grains. Although neither dust grains nor in-
terstellar conditions can presently be reproduced in the laboratory, it is likely that grains grow by
coagulation and hence are fractal in nature, made up of several smaller sub-units. They are prob-
ably destroyed in supernova shocks, via photo-evaporation of molecules or sputtering (collisions
with fast moving particles knocking atoms and molecules off the grain surfaces).
1.2.2 The clumpy ISM
Although describing the ISM in terms of phases is useful for clarifying the basic physical proper-
ties of important regions, the real picture is more likely to represent a continuum of phases and a
constant cycling of material between them. In all regions, material cannot really be described by
global properties, although these may represent averages, since it tends to be distributed in clumps
rather than an homogeneous gas. Stars must necessarily form from the gravitational collapse of
small, dense regions in a larger cloud, and this in itself confirms the existence of these conden-
sations. The clumpy nature of the interstellar medium is also evident in the data from telescopes
that are now able to image at higher resolution, and it is of the utmost importance to studies of
star formation that we have an idea of the properties and filling factors of these clumps. In all
cases, properties are averaged over the beam and smaller beams reveal more and more structure.
Peaks of emission in tracers of dense gas are often displaced (Morataet al.(2003)) which suggests
the evolution of dense clumps and a time dependent chemistry (Garrodet al. (2006)). 3D radia-
tive transfer models produce much better agreement with observation if the material considered
is distributed in clumps which, in most cases, acts to reduce the overall optical depth of a region,
and fragmentation is a universal outcome of hydrodynamical models that include the effects of
turbulence (Klessen(2001)). It is common to study the nature of clumpy emission in a particular
molecule using clump decomposition algorithms such asGAUSSCLUMPSandCLUMPFIND (Stutzki &
Guesten(1990) andWilliams et al. (1994)) to divide emission into distinct regions and then to
study the properties of these‘clumps’ which are generally of sub-parsec scales and may be either
gravitationally bound or unbound. Lacking the required high resolution data we are led towards al-
ternative means of studying the chemistry of the clumps. Compact regions of emission have been
1.2. Phases of the Interstellar Medium and Some Important Chemistry 38
observed near to or ahead of Herbig-Haro (HH) objects in nearby star-forming regions (Girart
et al. (1994)). It was postulated that these could be denser condensations in a clumpy surrounding
medium, illuminated by UV radiation from the HH shock which would act to release molecules
from icy mantles on the grain surfaces. Their narrow line widths excluded the possibility of them
being swept up material from the shock.Viti & Williams (1999) used chemical models to test this
hypothesis and found that the observed abundances of several models could be well reproduced by
UV desorption of species in dense clumps and a subsequent gas phase photochemistry producing
emission which allows us to study their chemistry and physical structure.
1.2.3 ISM Gas Phase Chemistry
The ISM is so rarefied that only 2 body reactions are important in the gas phase, it being extremely
unlikely that a third particle will be present during a reaction. Low temperatures usually preclude
endothermic reactions with high activation barriers from proceeding in the denser, cooler regions.
In areas where UV radiation fields are high, known as Photo-dissociation regions (PDRs), species
mainly exist in their atomic form due to rapid photo-dissociation of molecules. The formation and
destruction of molecular hydrogen plays an important role in the chemistry and the ionisation bal-
ance is maintained by electron recombination forming neutrals from positive ions, charge transfer
and photoionisation. Where the optical depth is higher, H2 survives and CO forms which cools
the gas via its rotational transitions (Goldsmith & Langer(1978)).
In the dark clouds, where temperatures are lower and radiation can barely penetrate, ion-
neutral reactions are arguably the most important mechanism (Herbst & Klemperer(1973)). A
charged ion can interact with a neutral species to induce a small gradient in electric charge (or
dipole) and the resulting attractive forces between the two increase the reaction cross-section. In
dark clouds, where temperatures are lowest, positive ions are formed via cosmic ray bombardment
of neutrals rather than photoionisation. Perhaps the most important ionisation reaction is that of
H2 which forms protonated molecular hydrogen (H3+). H3
+ is extremely reactive and will readily
donate its proton to other species, forming complex ions. These ions can undergo dissociative re-
combination reactions leading to the formation of neutrals. H3+ reacts in this manner with atomic
oxygen to form OH+, with further reactions leading to the formation of other simple molecules
that are crucial to the chemistry, such as HCO+ and CO, which cannot be formed via neutral ex-
change reactions in very cool regions due to high energy barriers for the transitions. In addition
to ion-neutral and dissociative recombination, radiative association and neutral-neutral reactions
play an important role. Examples of these four main reaction mechanisms are given in Table 1.2.
1.2. Phases of the Interstellar Medium and Some Important Chemistry 39
Table 1.2: Important reaction types in dark cloud conditions
Reaction type Example Rate Coefficient (cm3s−1)
Ion-molecule H2+ + H2 → H3
+ + H 2.08(-9)
Dissociative recombination H3+ + e−→ H2 + H 4.36(-8)
Radiative association C+ + H2 → CH2+ + hν 4.00(-16)
Neutral-neutral C + C2H2 → C3H + H 1.45(-10)
With reference toHerbst & Klemperer(1973), Watson(1978) andWakelamet al. (2010), rate
coefficients from the UMIST database (Woodallet al. (2007)).
1.2.4 Gas-Grain Interactions and Depletion
The study of grain surface chemistry has developed quickly over the past decade or so since it
became evident how large a role it may play in ISM chemistry; many processes with a barrier in
the gas phase have none on the grain surface. Reactions on grains are necessary to produce the
abundances of molecular hydrogen observed in dark clouds and complex organic molecules in hot
cores (Charnleyet al. (1992); Bernsteinet al. (1995); Oberget al. (2009a)). Water and methanol
also lack an effective gas phase formation route at low temperatures, but are formed efficiently on
the grains. Coatings, or mantles, are created on the dust grain surfaces as species deplete. This
process locks up material, removing it from the gas phase and forming ices.
Molecules depleting onto dust grains can form a covalent bond with species already on the
grains (chemisorption) or become more weakly bound to the surface by Van der Waals forces
(physisorption). Once attached, most molecules are likely to stay bound to a particular site, with
the exception of hydrogen which scans the grain surfaces, to come into contact with other species
and then to react. Hydrogenation (which can occur at 10 K) and oxygenation (which requires
temperatures closer to 30 K,Cazauxet al. (2010)) are the most important processes and produce
molecules such and CH4, CO2, H2O and NH3 as well as methanol and formaldehyde. Reaction
can occur via the Eley-Ridael mechanism, where only one molecule is adsorbed and reacts with
another, nearby, gas-phase molecule, or via the Langmuir-Hinshelwood mechanism involving two
adsorbed particles. H2 usually leaves the grain surface as it forms (due to the energy released
in the exothermic reaction) but other molecules can remain attached and participate in further
reactions. Strong UV radiation, cosmic rays, secondary photons from cosmic ray hits and the
exothermicity of certain grain surface reactions can all cause desorption of mantle species back
1.2. Phases of the Interstellar Medium and Some Important Chemistry 40
into the gas phase.Robertset al. (2007) studied the efficiency of the latter three mechanisms and
concluded that all three were probably significant in dark cloud conditions, with the release of
energy during H2 formation on the grains likely being dominant over the other two mechanisms.
The term thermal desorption is often used and refers to the removal of molecules from the mantle
due to an increase in the temperature of the dust grain.
1.2.4.1 Direct Observations of Ices
It is possible to directly observe ices via their mid-infrared absorption against a background source.
The first ices to be detected (around 40 years ago byGillett & Forrest(1973)) were H2O and CO,
the two most abundant ice species. With the advent of space telescopes such as ISO (the Infrared
Space Observatory) and Spitzer, CO2 ice, which could not previously be observed due to strong
atmospheric absorption, was also discovered (Whittetet al.(1998)) and now we detect many solid
phase species. Projects such as WISH (water in star forming regions with Herschel,van Dishoeck
et al. (2011)) have been set up to study the relationship between ice formation and environment.
It is thought that abundances of water and CO ices can, in some regions, rival the most common
species in the gas phase (Oberget al. (2011)). Typically, ice observations are analysed using
laboratory spectra of various pure and mixed ices by decomposing the spectra into its various
components. This is a complicated process and often several species are quoted as possible carriers
of a particular band. Protostellar envelopes have been widely studied thanks to the utility of the
protostar in providing a useful mid-IR emitter just behind the icy region. The Spitzer c2d project
(Evans & c2d Team(2005)) observed 50 such sources with IRS andOberg and co-authors collate
this, along with data from ISO, Keck and the VLT, to statistically study the ice formation process.
Since H2O ice is the most common, abundances of other ices are usually given as fractions of
the water ice abundance. A small spread in relative abundances thus indicates co-formation with
water ice and a large spread the contrary. Identified ice species include (aside from CO, CO2 and
water) CH4, NH3, CH3OH, OCN− and some complex organic molecules.
To summariseOberget al. (2011), the formation of ices in the dark cloud environment can
be divided into three main phases. The first, during which atomic carbon is prevalent in the gas
phase, is dominated by the hydrogenation of atoms on the grain surface. Water ice is dominant
and forms alongside CH4 and NH3 as well as forming CO2:H2O ice, a mixture of CO2 and H2O.
As the ratio of gas phase CO to atomic oxygen rises, the second phase of ice formation begins
in which CO freeze-out results in the formation of CO:H2O mixture ice, OCN−, CO2:CO ice
and CH3OH ice from the hydrogenation of frozen-out CO. The third phase takes place near to a
1.2. Phases of the Interstellar Medium and Some Important Chemistry 41
protostar as the grains are heated. Thermal processing leads to the segregation of existing ices and
pure CO and CO2 ices are observed. There appears to be little difference in the abundances of ices
(other than those requiring thermal processing) between low and high mass protostellar sources.
Ice formation in dark clouds also appears to proceed similarly.
1.2.4.2 Laboratory Studies of Grain Surface Processes
An important contributor to the study of grain surface processes has been the laboratory stud-
ies, which attempt to reproduce ISM conditions in order to simulate and study the desorption of
molecules, surface reactions and energetic processing of ices (e.g.Bisschopet al. (2006); Fuchs
et al. (2009); Oberget al. (2009b)). Experiments generally comprise a substrate (usually gold,
silicate or graphite) representing the dust grain surface and contained in an ultra high vacuum
chamber. Pressures as low as 10−10 mbar and temperatures down to 15 K can be achieved. Ices
are then grown layer by layer and monitored using RAIRS (reflection absorption IR spectroscopy).
The surface is irradiated with infrared light and absorbed, on the ice surface, at certain frequencies
depending on the vibrational modes of the molecules present. Absorption spectra can therefore
help to determine which molecules, and in which quantities make up the mantles at any one time.
To study desorption (the return of the molecule to the gas phase), either the temperature can be
slowly increased (temperature programmed desorption) or light of a particular frequency or range
of frequencies used to irradiate the ice (in which case photo-desorption ensues). As molecules
leave the mantles they can be detected in the gas phase using mass spectrometry and molecules
remaining on the surface continue to be monitored. In this way accurate rates of freeze-out and
desorption can be determined for particular conditions (e.g.Prasad & Tarafdar(1983); Charnley
et al.(1995); Burke & Brown(2010)). Although these methods do provide accurate rates, it is im-
possible to properly reproduce the exact conditions in the interstellar medium. The temperatures
there are too low and the gas phase contains many more species than are considered in this type
of experiment. No-one is really sure what the surface of a dust grain will look like and it is likely
that it will be far from smooth so that some binding sites will hold molecules better than others. It
does seem, however, that the type of substrate used, the thickness of the ice and the isotope of the
particular molecule under study do not make a great deal of difference to the resulting freeze-out
rates (Oberget al.(2009b)). Rates from experiments such as these can be introduced into chemical
codes including grain surface reactions and freeze-out, however an accurate picture is still a long
way off.
1.3. Chemical modelling of star-forming regions 42
1.3 Chemical modelling of star-forming regions
In the latter part of the last century, the advent of telescopes observing at sub-mm and IR wave-
lengths led to the detection of many molecules in a wide variety of astrophysical sources. The
need for models to describe the formation and destruction of these molecules in particular condi-
tions led to the arrival of the first chemical models. The codes included chemical networks (at first
simple and containing only a few species) for which the change in abundance of a species over
time were defined by rate coefficients and the abundances of reactants.
To illustrate how these equations are formulated, consider the simple example of speciesA
which is formed and destroyed in the following reactions:
A+B→ C+D, reaction ratek1 m3s−1molecule−1
E+F→ A+G, reaction ratek2 m3s−1molecule−1
The change in number density of species A is then given by:
dn(A)dt
= k2n(E)n(F )− k1n(A)n(B) (1.1)
The earliest models were either steady-state (or time independent so that the left hand term in
equation 1 is set to zero), or time-dependent and depth independent (considering just one depth
point or one set of physical conditions). Early on,Herbst & Klemperer(1973) used a simple
steady-state model to show that in dense cores the chemistry is dominated by cosmic ray ionisation
facilitating a network of ion-molecule reactions. For all these models various input parameters
were required, each with associated uncertainties such as the initial elemental abundances, the
cosmic ray ionisation rate and of course the reaction rates themselves.
Nowadays, chemical modellers make use of large databases (the result of extensive laboratory
work measuring reaction rates in as close as possible to interstellar conditions) containing known
reactions and rates at astrophysically relevant temperatures. These are constantly updated as ex-
periments become more accurate and new reactions are found to be significant, however, even now
many rates are extrapolated from experiments at higher temperatures or from similar reactions.
When it became evident that grain surface processes played an important part in ISM chem-
istry, models were expanded to account for the solid phase of the ISM.Pickles & Williams(1977)
extended the gas phase chemical network of existing models to include reactions on grain surfaces,
diffusion, adsorption and desorption with rates estimated in laboratory studies. These processes
1.3. Chemical modelling of star-forming regions 43
have associated barrier energies for each type of molecule and rough or porous grain surfaces can
be simulated by adjusting these energies at different sites to make it easier or harder for a molecule
to bind, or to diffuse, into and out of the site. Early on, the rate equations had the same form as
the gas phase reactions, however these are not accurate in situations (as is fairly common in the
ISM) where the average number of reactants on a grain is very low (Tielens & Hagen(1982)).
To counteract this, stochastic models are now becoming popular, using either Monte-Carlo meth-
ods (e.g.Charnley(1998), Vasyuninet al. (2009), Cuppen & Garrod(2011)) or the master-rate
approach (Stantchevaet al.(2002)). Another, maybe simpler, technique is to modify the rate equa-
tions to reproduce the results of more complicated methods (e.gCaselliet al. (1998)). Although
studies of surface processes have taken off recently, there is still a lack of accurate rates for both
reactions on the grains and desorption processes as well as great difficulty in reproducing realistic
ISM conditions in the lab.
The chemical code used in Chapters 2 and 3 of this thesis is both time and depth dependent in
that it tracks changes in chemical abundances over time at several depth points from edge to centre
of a dense clump of material. These points have increasing visual extinction or Av which acts
to dilute the radiation field as one moves into the clump reducing the effects of photo-reactions.
Freeze-out is accounted for in the model via the following equation (Rawlingset al.(1992)) which
describes the rate of depletion of a gas-phase species in terms of the local conditions and grain
properties;
dn(i)dt
= 4.57× 104dga2T 1/2CnSim
−1/2i n(i)cm−3s−1 (1.2)
wheredg is the ratio of the number density of grains to that of hydrogen nuclei,a is the grain
radius in cm,Si the sticking probability (ranging from 0 to 1),mi is the molecular mass of species
i in amu andC is a factor included to account for electrostatic effects and has slightly higher
values for positive ions since grains carry a small negative charge. The equation is adapted from
that for the rate of change in mass of a single dust grain due to collisions with gas phase particles
quoted inSpitzer(1978). The factor accounting for collisions of negative grains with positive
and neutral species is calculated inUmebayashi & Nakano(1980). The constant (4.57×104) thus
encompasses several further constants from the conversion to a rate of change of number density
equation and the rate of collision of positively charged particles with a negatively charged grain.
Due to the prevalence of hydrogen, atoms sticking to the surface are considered to be rapidly
hydrogenated after sticking. Hydrogen forms H2 and immediately desorbs while other molecules
1.4. Column Densities from Molecular Line Emission and Dust 44
remain on grain surfaces affecting abundances in the gas phase (where chemical reactions are
monitored via the usual rate equations). The selection of a value for the sticking probability,Si is
usually fairly arbitrary which is not ideal. It is imperative for the use of these models that more
accurate rates of freeze-out for individual species are measured.
1.4 Column Densities from Molecular Line Emission and Dust
The extent of depletion onto dust grains for a particular molecule is also sometimes inferred from
gas-phase observations (e.gBacmannet al. (2002), Redmanet al. (2002)). The established pro-
cedure is to compare either thermal emission from dust or extinction measurements against back-
ground sources with direct observations of a molecule in the gas phase. If a standard ratio between
a molecule and the total hydrogen density is assumed, one can determine how far short of the
expected gas phase abundance is that molecule. Starless and protostellar cores are enshrouded in
a thick envelope of material, still in-falling onto the central star and forming disk-like structures
which are the sites of planet formation. This material is optically thick, so that to study a star in
the very early evolutionary stages requires the imaging of radiation that has been absorbed and
re-emitted at long (sub-mm and IR) wavelengths. Likewise for the cold material in dense starless
cores and regions of the molecular clouds in which they are housed. Lines of carbon monoxide
(CO) are extremely well suited to the study of these regions. It is the most common molecule (after
H2) in the ISM and low-J transitions have critical densities similar to those of molecular clouds.
The critical density of a transition is the density at which the rate of collisional de-excitation out
of the upper level is equal to the rate of spontaneous, radiative transitions out of the same level. At
densities much higher than this, the level populations are said to be thermalised and are character-
ized by the Boltzmann distribution. The more common isotopologues (and even the less common
ones to some extent) may be optically thick at pre-stellar core densities so rarer ones, such as
13CO, C18O and C17O are used to probe the densest regions. Radiation at the frequency of a par-
ticular transition will less readily be absorbed by these less common isotopologues simply due to
the fact that they are fewer in number. Since CO has been so widely used for many applications,
including the determination of core and cloud masses and the study of cloud kinematics, it is of
the utmost importance to account for processes that may remove or destroy gas phase CO.
CO has only one axis of rotation so that its rotational spectrum is fairly simple, transition en-
ergies being described by E=BJ(J+1) with J the total angular momentum quantum number (the
selection rule∆J=±1 applies) and B the rotational constant. B is inversely proportional to the mo-
1.5. Low Mass Star Formation 45
ment of inertia of a molecule, thus larger molecules have smaller level spacings in their rotational
spectra. The spectra become more complex for molecules with more than one axis of rotation and
an extra term is required to describe the projection of the total angular momentum on the symme-
try axis. CO is linear and has a permanent dipole moment due to the distribution of charge across
the molecule, which results in the allowed transitions between rotational levels.
In order to derive a column density from gas phase observations of CO (or another molecule),
the simplest method (in the correct conditions) is to assume local thermodynamic equilibrium
(LTE) and one requires an optically thin isotope to probe the entire column, which can sometimes
be problematic. One can then use the equation of radiative transfer (describing the emission and
absorption of radiation by a medium) to directly relate the observed radiation to the amount of
material present (see Appendix A for a full description). In doing this we assume that the emission
at long wavelengths follows the Rayleigh-Jeans law, so that the temperature of the source measured
by the telescope can be directly related to a brightness temperature (the temperature of a black body
emitting the same intensity of radiation at the frequency of interest). If, as is likely the case, some
radiation is being absorbed and the source is not emitting as a perfect black-body this brightness
temperature will be underestimated, as will the column density of the emitting material.
The hydrogen density can be directly related to the optically thin thermal emission from dust
by again considering radiative transfer. A knowledge of the dust emissivity per unit mass allows
the derivation of dust mass directly from the emission at a particular wavelength and this can then
be converted to a total gas mass using the canonical gas:dust ratio for our galaxy (100:1). Alterna-
tively, extinction can be used to estimate total mass using a direct relation between extinction and
hydrogen density derived from measurements of reddening on background sources whose spectra
are known. In order to get an idea of how depletion may vary within the galaxy we require consis-
tent data in both molecular emission and dust continuum covering many regions. This is provided,
for example, by the Gould Belt Survey on the James Clark Maxwell Telescope (JCMT) in Hawaii,
which we introduce in Chapter 4.
1.5 Low Mass Star Formation
Small (∼0.1 pc sized), dense (up to 106 cm−3) cores, some of which will eventually collapse to
form stars, are at the bottom of a hierarchy of structure. Within the galaxy, some of the largest
known structures are the HI super-clouds. These house smaller regions with higher than average
densities on 100 pc scales known as giant molecular clouds (or GMCs). Again, these clouds are
1.5. Low Mass Star Formation 46
highly inhomogeneous. Denser than average regions within GMCs are often referred to as cloud
cores which in turn house smaller cores which may be star-forming. The self-similar, fractal nature
of star-forming regions has fueled the belief that structure may be heavily related to turbulent
motions on scales down to the Jeans length, above which perturbations are expected to grow
exponentially (Boldyrevet al.(2002)). Recent surveys with Herschel (Andreet al.(2010)) support
the view that star-forming cores fragment, due to gravity, out of long, filamentary, turbulence-
driven structures in GMCs.
The standard model of pre-stellar core collapse was introduced byShu(1977), who studied
the collapse of an isothermal sphere in hydrostatic equilibrium (a Bonnor-Ebert sphere). This
model was later expanded upon to include magnetic effects, such as the movement of material
towards the center of a core via ambipolar diffusion (Shuet al. (1987), Nakano(1979). Charged
particles are tied to magnetic field lines but neutrals are not. There is some weak coupling of
the ions and neutrals due to collisions but the overall mass slips relative to the field lines. This
reduces the ratio of mass to magnetic flux and the core is less well supported against collapse,
resulting in a more centrally condensed structure. The collapse that follows is coined an ‘inside-
out’ collapse since the free fall time, dependent on the mean density within a shell, is smaller in
the centre of the core causing it to collapse more rapidly than the outer parts. The radius of the
collapsing region travels outwards at the sound speed. As the centre becomes more opaque, the
material is no longer isothermal and an adiabatic‘first core’ is formed. As the temperature at the
centre continues to increase, hydrogen begins to dissociate which consumes energy and reduces
the outward pressure in the core centre. The central region collapses again forming a‘second core’
which will eventually become a protostar. The model has been very successful and is still widely
used despite many modifications by later authors to include different geometries and the effects of
rotation and magnetic fields during the collapse (Fryer & Heger(2000); Price & Bate(2009)). The
idea of stars forming via the gravitational collapse of a dense region in a molecular cloud is fairly
old, however the details of this process are still not clear. It appears that turbulence and magnetic
fields may play a much more dominant role than was previously thought.
This early collapse phase is associated with rapid accretion of material onto the central core.
Conservation of angular momentum sets the core rotating and the enveloping material tends to
form a disk, the site of planet formation, around the central condensation. Cores which exhibit
neither emission from a central source nor infall are known as starless cores. These may or may
not be gravitationally bound and so will later either disperse or collapse, in which case a protostar
will form in the center. These protostars can be roughly divided into 4 classes (0-III) based on
1.5. Low Mass Star Formation 47
Figure 1.3: SED fits for a pre-stellar core L1544 and a Class 0 protostar IRAS 16293 (Andreet al.
(2010)).
their observed spectral energy distributions (SEDs), some examples are shown in Figure 1.3 (from
Andreet al.(2010)). These are thought to represent consecutive evolutionary phases. Class 0 emit
mostly at sub-mm wavelengths, the protostar is still extremely embedded in a thick envelope and
accretion is occurring rapidly and conservation of angular momentum leads to the production of
strong, bipolar jets of material, outflows, that flow from the poles. These energetic flows travel at
speeds of several hundred kms−1 and their impact with the surrounding interstellar material leads
to the production of intense bow shocks known as Herbig-Haro objects (Falle & Raga(1993))
which emit strongly in the UV and at other wavelengths. Class I objects appear to have a reduced
accretion rate compared to the Class 0s. A disk has now formed, the objects are visible at infrared
(IR) wavelengths and outflows are more powerful. Classical T-Tauri stars make up the Class II
protostars. These are highly variable and still embedded in a thick surrounding disk. By the class
III stage protostars are surrounded by an optically thin disk and are visible in the near infrared and
optical wavelengths.
We analyse molecular emission from the envelopes of such young stellar objects in Chapter 7
of this thesis with the aim of quantifying depletion of CO onto dust grains in the centers of starless
and protostellar cores. Chapters 2 and 3 investigate the chemistry of the dense clumps observed
near to Herbig-Haro objects discussed in section 1.2.2, and their use as a probe of clumpy molec-
ular cloud structure, and in Chapters 5 and 6 we outline a CO clumpfinding study on data from
1.5. Low Mass Star Formation 48
nearby molecular clouds (we give some details of particular regions in Chapter 4). In summary,
we investigate several unique means to explore structure and molecular freeze-out in dark clouds,
housing objects in the very earliest stages of star formation.
CHAPTER 2
CHEMISTRY OF DENSE CLUMPS NEAR
MOVING HERBIG -HARO OBJECTS
The work in this chapter is based on the paper by Christie et al. 2011 in collaboration with S.Viti,
D.Williams, J-M.Girart and O.Morata
Herbig-Haro objects (HHOs) are knots of optical emission, produced when the jet from a
young star collides with the ambient interstellar material to produce a shock front (Falle & Raga
(1993)). These HHOs are strong line emitters at optical and other wavelengths and are often seen
along a protostellar outflow as a series of bow shocks moving away from the star. A number of
observational surveys have detected localised regions of enhanced emission in several molecules,
among them NH3 and HCO+, just ahead of Herbig-Haro objects (Girartet al.(1994); Girartet al.
(1998); Torrelleset al. (1992)). The regions appear chemically similar to each other and are
quiescent and cool. Therefore they are probably dynamically unaffected by the jet. Girart and co-
authors suggested that emission may be from molecules in icy mantles on dust being released by
UV radiation from the Herbig-Haro object.Taylor & Williams (1996) supported this theory with
a simple chemical model which reproduced the abundances inferred from observations of these
quiescent regions. A more complex chemical model was then investigated byViti & Williams
(1999) and used to predict other molecular species expected to show enhanced emission under the
same conditions. Many of these, including CH3OH, H2CO and SO2, were later observed both in
clumps ahead of HH2 (Girart et al. (2002)) and near to five other Herbig-Haro objects (Viti et al.
(2006)).
49
50
The model used byViti & Williams (1999), Girartet al.(2002) andWilliams & Viti (2003) de-
scribed the particular photochemistry that is produced when radiation from these HHOs impinges
on clumps of gas, located ahead of the bow shock, in which ices have returned to the gas phase. In
particular, the HHO (and hence the source of UV radiation) was assumed to be static. However,
recent observations of the object HH43 (Morataet al. in preparation) reveal the presence of several
molecular speciesalongthe jet, where at least three HH objects are present (see Figure 2.1). From
the H13CO+ emission it is clear that the emission is in clumps or small filaments along the outflow
and that they are quiescent (as they show narrow line widths). HCO+ and CS emission also show
such distinct clumps, and, consistent with previous observations of clumps ahead of HH objects,
there seems to be a stronger contrast in intensity between clumps and elsewhere nearby in HCO+
than in CS (consistent also with the fact that CS should trace larger scale gas). These observations
seem to indicate that quiescent clumps, chemically (but not dynamically) affected by the HH ob-
ject, are presentalong the jet and not only ahead as previous surveys indicated. While previous
modelling was successful at providing an explanation for the chemical enhancement ahead of the
HHO, what is now required is a model that can explain different degrees of chemical quiescent en-
hancements along the jet. The model needs therefore to be dynamical in order to take into account
the movement of the shock front, typically travelling at a few hundred kms−1 through a molecular
cloud. Raga & Williams(2000) investigated, using a simple chemistry, the effect of a moving
field on the expected morphology of the emission but the full consequences on the chemistry of
allowing the radiation source to move was not explored. In this scenario, the HHO (the source
of the radiation driving the photochemistry) approaches a clump and then passes it, so that the
radiation intensity rises to a peak value and then decays.
In this chapter we explore how the chemistry induced in the clump differs from that in the static
case previously discussed, and consider the sensitivity of the chemistry to assumed geometry and
physical conditions. Figure 2.1 suggests that in HH43 a clump may be affected by the passage of
more than one HHO. However, in this work we examine the photochemistry induced by a single
HHO passage.
Figure 2.1 shows the HH 38-43-64 system in emission lines of several molecular species. This
system of HHOs is initiated by a source, HH 43 MMS1, indicated by a cross in the figure. The
source appears to have initiated several HHO events, but in our treatment we consider only a single
event. The figure shows clearly that emitting molecules are distributed along the line of the jet,
and are not confined to discrete objects in front of the jet head.
2.1. The Model 51
Figure 2.1: Integrated emission of some molecular line transitions in the 6.2-7.2 kms−1 vLSR
range, where emission (especially in HCO+) follows the HH 38-43-64 outflow. The molecular
line transition is shown on the top of each panel. For the C18O and H13CO+ panels, the contour
levels are from 25% to 95% of the peak intensity in steps of 20%. For the other panels the contour
levels are from 25% to 95% of the peak intensity in steps of 10%. The triangles show, from left
to right, the Herbig-Haro objects HH 38, HH 43 and HH 64. The cross shows the position of HH
43 MMS 1, where the powering source of the HH system is located (Stankeet al. (2000)). Note
that the two well defined clumps in HCO+ ahead and south of HH 43 and HH38 have very narrow
spectral lines associated (line widths of around∆v ' 0.7 kms−1), which suggests that they are
dynamically quiescent relative to the cloud.
2.1 The Model
The basic model used is UCLCHEM (Viti & Williams (1999)) which runs in two phases, the first
simulating the collapse of molecular cloud gas from a fairly diffuse state to a clump of uniform
high density, and the second the illumination of the clump by a static radiation source.
In the model, the clump is treated as a one-dimensional slab of fixed temperature, increasing in
visual extinction throughout up to a maximum value representing the clump centre. Abundances
are calculated for 10 depth points through the slab. We assume the clump to be spherically sym-
metric and the radiation field to be isotropic at the clump surface so that the 1D slab is able to
represent the whole clump. Using classic rate equations and the abundances in the previous time
step, abundances of species are calculated at each depth point and for each time step (the gap
between time steps is varied according to how quickly abundances are likely to be changing so
that where abundances are rapidly varying, they are evaluated more often, which is not necessary
when abundances remain steady). This way the chemistry of the whole clump is tracked for the
duration of the model run. Self-shielding of molecular hydrogen and CO is taken into account so
that photo-dissociation of these species depends on the abundances in outer depth points.
The model follows the chemical evolution of 170 species including 1858 separate reactions for
the 10 depth points of increasing visual extinction (Av). Reaction rates are taken from the UMIST
2.1. The Model 52
database (Woodallet al. (2007)).
During phase I the clump undergoes a free-fall collapse during which molecules are allowed
to freeze-out or deplete onto dust grains. Once on the surface, species hydrogenate as far as chem-
ically possible until the most stable hydrogenated molecule is reached (some molecules could
theoretically hydrogenate further but an unstable product would result). So, for example, C, CH,
and CH3 will all immediately hydrogenate to CH4 which remains on the grain surface. CO does
not completely hydrogenate because observations preclude the possibility of all CO being con-
verted into methanol on the dust grain surfaces and because, being a heavier molecule than many
others, it could be harder to hydrogenate. Ions are neutralized on hitting the grain surface and re-
action rates on the surfaces take into account the small negative charge on the dust grains resulting
in their having a slightly higher rate in the case of the positive ions. The radiation field in phase I
is fixed at 1 Habing (G0) to represent the ambient interstellar field.
Depletion of species from the gas phase as they are frozen out onto grains is controlled within
the model by effectively altering the grain surface area available for gas species to freeze-out.
The freeze-out fraction of CO at the end of phase I was set to around 20% for models with a
final clump density of 104 cm−3 (regardless of the initial clump density), around 50% for final
densities of 105 cm−3 and 70% for final densities of 106 cm−3. These values are consistent with
observational depletion studies of isolated dark clouds, where denser objects show a higher degree
of freeze-out of CO (e.g.Redmanet al. (2002)). All models assumed that 5% of the CO freezing
out onto the grains was converted into methanol. The fraction of CO converted to methanol on
the grain surface is still very uncertain. In order too match observations of gas phase methanol,
models suggest that around 5-10% of CO on the grains must be converted (Hatchellet al.(1998)).
Viti & Williams (1999) experimented with altering the fraction of CO converted to methanol in
their chemical code and found it to make little difference within a sensible range. We therefore
choose our value of 5% fairly arbitrarily to roughly agree with observations of methanol in the gas
phase and note that changes to the output abundances should not be too great.
The initial number density of hydrogen nuclei in the clump (before collapse) is assumed to be
103 cm−3. It is also assumed that, initially, only carbon is ionised and half of the hydrogen is in
its molecular form. Nitrogen, oxygen, magnesium, sulphur and helium are all neutral and atomic.
As assumed by Viti & Williams (1999), the first phase continues until a specified number density
is reached. This number density is observationally determined to be in the range 104 to 105 cm−3
(e.g. Girart et al. (2005); Whyatt et al. (2010)). We have also explored the effect of allowing
somewhat higher densities in several models (see Table 2.1). For simplicity, the clump is assumed
2.1. The Model 53
to be of uniform density at all times.
The second phase commences immediately after the specified density is attained, when it is
assumed that the radiation from the HHO is switched on. There is no collapse in this phase, the
clump remains at a constant density (equal to that at the end of phase I) and a constant temperature
throughout. In reality, the clump would continue to collapse throughout phase II while under
the influence of the radiation field from the HHO. However, because of the short timescale of
phase II compared to that of phase I, the density of the clump would not be expected to change
dramatically from the start to the end of phase II, and keeping the clump at a constant density
throughout should not affect the results. The HH radiation field is again isotropic but stronger
than the ambient field irradiating the clump in phase I. The chemistry in the second phase is then
computed for a model time of about a million years which is long enough for the effect of the
radiation field from the HHO to be negligible (the object having moved some distance away from
the clump) and, according to previous modelling, is much longer than the predicted period of
enhancement of most molecules (104 years,Viti & Williams (1999)).
The radiation field of the HHO is represented in the model in terms of multiples, G0, of the
mean interstellar radiation field intensity. This is clearly an approximation, since the spectra of
the two fields are not the same. Unfortunately, most astrochemical codes use the interstellar field
as the basis of their treatments of photo-processes, and to do otherwise would be a major project
beyond the scope of this work. While the approximation we have used could give misleading
results, the prediction of a rich characteristic photochemistry in HHO-illuminated clumps (Viti
& Williams (1999); Williams & Viti (2003)) has been confirmed by observations of a number of
sources (Girart et al. (2002); Viti et al. (2006)) and by a very detailed study of HH2 (Girart et al.
(2005)). A more realistic representation of the radiation field would involve wavelength specific
intensities. This could in theory be included in the chemical code and would be an interesting
extension of this work which, due to time constraints, we chose not to undertake. With either the
approximation used here or a more realistic field, molecules would be expected to evaporate from
grain surfaces on illumination by the HHO, so the effect in terms of abundances of molecules
formed on the grains and their secondary products in the gas phase should be similar.
In the model used here, which was adapted for this work, the moving source of this radiation
field (representing the HHO) passes the clump on a straight path with a minimum distance to the
edge of the clump, here chosen to be 0.05 pc. This distance is similar to values found byWhyatt
et al. (2010) in an observational study of regions around 22 HHOs. For a source moving at 300
kms−1, there will be enough time for it to reach closest approach (at around 1000 years) and
2.2. Results 54
move some distance away before phase II is terminated. There is a range of values observed for
HHO velocities from∼100 to∼1000 kms−1. Faster HHOs have a shorter interaction time. We
have used 300 kms−1 for most of the models considered, but have also explored the effects of a
higher velocity in models 16-18 (see Table 2.1). The flux reaching the edge of the clump is time-
dependent, changing with the distance from source to clump and reaching a specified peak value.
Absorbing material along the line of sight to the clump is represented by an Av of 1 magnitude
at the clump edge. This low extinction material will, in any case, have little effect on the model
outputs. Models with a static radiation source (kept at 0.05pc from the clump throughout phase II)
were run for comparison.
The main parameters affecting the model chemistry are the density of the molecular cloud
from which the clump forms in phase I and the density of the clump at the end of phase I; the final
clump radius which, along with the density, will determine the visual extinction, Av, of the clump;
the radiation peak strength of the field from the Herbig-Haro object at the clump boundary; and
the source velocity. The values of these parameters adopted for each model are shown in Table 2.1.
We also ran a few models to represent the inter-clump medium, i1, i2 and i3, with an initial density
in phase I of 102 cm−3 and a final density of 103 cm−3. No freeze-out occurs in either phase for
the inter-clump models and phase I is extended for a time after the final density is reached. The
relative radiation strengths, G0, listed in Table 2.1 are up to a few tens; these are the strengths
found in previous modelling work (Viti & Williams (1999)) to be necessary to create the rich
variety of photochemistry subsequently observed byGirart et al. (2002) andViti et al. (2006).
Elemental abundances, adapted fromSofia & Meyer(2001), are listed in Table 2.2.
Column densities are calculated by summing fractional abundances at all 10 depth points for
each species, taking into account the value of Av at each point.
2.2 Results
Our results are summarized in Figures 2.2 and 2.3. While we find that the fractional abundances
of a given species in the gas surrounding an Herbig-Haro object are clearly different between the
‘moving’ and‘static’ cases, it is clear that the theory proposed by Viti & Williams is still valid,
even if the radiation source is moving with respect to the clumps. In fact, some species seem to
survive longer if a moving source is included. Figure 2.2 plots column densities of four selected
species throughout phase II. Both the moving and static source models are shown as well as column
densities for the inter-clump medium, also under the influence of moving and static fields. The four
2.2. Results 55
Table 2.1: Model Input Parameters
Model Number Initial Cloud
Density
(cm−3)
Final Clump
Density
(cm−3)
Clump Radius
(pc)
Radiation
Field Strength
(G0)
Source velocity
(kms−1)
i1 102 103 3 5 300
i2 102 103 3 20 300
i3 102 103 3 30 300
1 103 104 0.3 5 300
2 103 104 0.3 20 300
3 103 104 0.3 30 300
4 103 105 0.03 5 300
5 103 105 0.03 20 300
6 103 105 0.03 30 300
7 104 105 0.03 5 300
8 104 105 0.03 20 300
9 104 105 0.03 30 300
10 104 106 0.003 5 300
11 104 106 0.003 20 300
12 104 106 0.003 30 300
13 103 104 0.3 50 300
14 103 105 0.03 50 300
15 104 106 0.03 50 300
16 103 105 0.03 5 1000
17 103 105 0.03 20 1000
18 103 105 0.03 30 1000
2.2. Results 56
Table 2.2: Initial elemental abundances as a function of total hydrogen column density (from Sofia
& Meyer 2001)
Element Initial
abundance
(X(N)/X(H))
Helium 0.075
Carbon 1.79×10−4
Oxygen 4.45×10−4
Nitrogen 8.52×10−5
Sulphur 1.43×10−6
Magnesium 5.12×10−6
species included in Figure 2.2 were selected because their abundances were particularly altered by
a moving source or because they are particularly important observationally. Discrepancies were
largest for lower Av (smaller or more diffuse clumps) but similar for radiation field strengths in
the range 5-50 G0, so the fact that the radiation source is moving is important, regardless of field
strength. Table 2.3 compares the effects of moving and static sources for several observationally
important species. Species whose abundances differ at least three orders of magnitude at any
point in phase II between the moving and static cases are considered very strongly affected by
the presence of the moving field. Where abundances differ at least two orders of magnitude but
less than three, species are considered strongly affected. If abundances differ at least one order of
magnitude and less than two, species are considered weakly affected and where abundances differ
less than one order of magnitude between the two cases species are considered unaffected. Table
2.3 refers to model 5 with Av of 5 magnitudes. Arrows indicate the way in which the moving
source affects the abundance of each species both at early times and later, during the passage of
the HHO.
In general, including a moving source implies that the radiation field decays quickly enough
that the chemistry is being driven more slowly. This way the specially created species arising in
the photochemistry survive for longer. For most of the strongly affected species, with a moving
radiation source, column densities may remain high at least up to 30,000 years (and possibly much
longer) after the passage of the source. Table 2.4 illustrates this point: here we list the length of
2.2. Results 57
log(column density, cm-2)
time, years / 10**3
ch3oh
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6 7 8 9 10
log(column density, cm-2)
log(time, years) / 10**3
cs
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
0 1 2 3 4 5 6 7 8 9 10
log(column density, cm-2)
log(time, years) / 10**3
hco+
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
0 1 2 3 4 5 6 7 8 9 10
log(column density, cm-2)
log(time, years) / 10**3
so
456789
1011121314151617
0 1 2 3 4 5 6 7 8 9 10
Figure 2.2: Column density (cm−2) versus time (years). The solid black line represents the inter-
clump medium, Av ∼2 mags, irradiated by a moving field of 30 G0 (model i3), dashes - a clump
at 105 cm−3, Av ∼5 mags, irradiated by a moving field of 30 G0 (model 6), dots - the inter-clump
medium, Av ∼2 mags, irradiated by a static field of 30 G0 (model i3 with a static field) and dots
and dashes - a clump at 105 cm−3, Av ∼5 mags, irradiated by a static field of 30 G0 (model 6 with
a static field). In the moving case the radiation field source is at its closest point at around 1000
years.
2.2. Results 58
Table 2.3: Comparing the effects of moving and static sources for model 5 with the clump at an Av
of 5 magnitudes. E denotes early times, L late times (after around 300 years). Up arrows indicate
molecules that increase in abundance with a moving source rather than static, right arrows those
that do not change and down arrows those that decrease in abundance.
Very Strongly Affected Strongly Affected Weakly Affected Not Affected
Mol E L Mol E L Mol E L Mol E L
CH3OH → ↑ OCS → ↑ CN → ↓ H2CO ↓ ↓
NH3 → ↑ HC3N ↑ ↑ HCN ↑ → HCO ↓ ↑
SO2 ↓ ↑ C+ ↓ ↓ C3H5+ ↑ → CS → ↓
SO ↓ ↑ OCN → ↑ H2CN → ↓ HCO+ ↑ ↓
H2S → ↑ NS → ↑ HNC → ↓
CH3CN → ↑ HCS+ ↑ ↓
C3H4 ↑ → H2CS ↓ ↑
CO ↓ → NO+ → ↑
C2H ↑ ↑ C ↓ ↓
time selected species survive for both the static and moving source cases.
Most species chosen for the study are first enhanced and later destroyed by the radiation field
and hence show similar behaviour under the influence of a moving source. Their abundances are
marginally lower than for the static field for up to a few hundred years (in which time the HHO
moves only a very small distance) but later, as species begin to be destroyed by the radiation, the
abundances in the moving case remain higher for longer. In some cases the chemistry appears to
be such that abundances may not return to their initial values for long periods. CH3OH, H2S and
NH3 have higher abundances in the moving case than in the static case for the evolutionary time
shown in Figure 2.2. C and C+ are enhanced by the radiation field and abundances are lower at all
times in the moving case. HCO+ and HCS+ have higher abundances in the moving case at very
early times but drop more later and are lower than for the static field at later times.
Models 13-15 were run with a 50 G0 field. The changes in abundances are similar to models
with a weaker field although more extreme, with species such as CH3OH and NH3 decreasing in
abundance at late times. This is illustrated in Figure 2.3 which shows the effect (on HCO+) of
altering Av, field strength, shock velocity and final clump density on the model output in phase II.
It appears counter intuitive that the density affects the abundance of HCO+ in the opposite
sense to the Av. However, because the Av for the different density models is fixed (at around
6 magnitudes for the innermost depth point) the radiation field penetrates to the same extent in
all models. The difference in abundance thus arises from differences in reaction rates due to the
density of material for the main reactions forming and destroying HCO+. These are, respectively,
the association of CH and O and the recombination of HCO+ with electrons.
2.3. Conclusions 59
Table 2.4: Timescales of abundance enhancements - Model 5. Timescale defined as the time taken
for column density to drop below 1012 cm−2 or to stop falling.
Molecule Timescale (Moving) Timescale (Non-moving)
CH3OH 105 yrs 103 yrs
NH3 105 yrs 104 yrs
SO 106 yrs 5×105 yrs
HCO+ 5×103 yrs 5×103 yrs
CN 105 yrs 105 yrs
HCN 106 yrs 5×105 yrs
CS 5×106 yrs 5×105 yrs
OCS 5×106 yrs 103 yrs
CO 106 yrs 105 yrs
NS 106 yrs 106 yrs
H2CO 106 yrs 5×105 yrs
H2S 5×104 yrs 5×103 yrs
H2CS 5×106 yrs 5×105 yrs
The influence of the radiation source speed on the model output was investigated in models
16-18 (again see Figure 2.3). It appears that a faster moving source allows several important
molecular species to sustain, up to 30,000 years at least, higher column densities than in the case
of a 300 kms−1 shock. Generally, the effects are seen later than about 300 years.
2.3 Conclusions
Clumps containing enhanced molecular abundances are routinely observed near Herbig-Haro ob-
jects (HHOs) in low-mass star-forming regions. The characteristic chemistry displayed by these
clumps is consistent with a model in which the gas of evaporated ices is subjected to a photochem-
istry driven by the nearby HHO. Previous models have been successful in reproducing the variety
in the observed chemical species; however, it was not obvious that they could explain the observed
clumps along a jet which would be subject to a varying radiation field during the passage of the
2.3. Conclusions 60
log(hco+ column density, cm-2)
time(years) / 10**3
Changing Av
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
0 1 2 3 4 5 6 7 8 9 10 log(hco+ column density, cm-2)
time(years) / 10**3
Changing clump density in phase II
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.0
0 1 2 3 4 5 6 7 8 9 10
log(hco+ column density, cm-2)
time(years) / 10**3
Changing radiation field strength
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
0 1 2 3 4 5 6 7 8 9 10 log(hco+ column density, cm-2)
time(years) / 10**3
Changing shock velocity
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
0 1 2 3 4 5 6 7 8 9 10
Figure 2.3: HCO+ column density vs. time. Top left plot - varying Av: solid line represents a
clump at 105 cm−3 with a moving source of 20 G0 (model 5) at 1 mag, dashes - 3 mags, dots - 4
mags, dots and dashes - 6 mags. Top right hand plot - varying clump density: solid line represents
model 2 (104 cm−3 with a moving source of 20 G0), dashed line - model 5 (105 cm−3), dotted
line - model 11 (106 cm−3). Lower left hand plot - varying radiation field strength: solid line
represents model 4 (5 G0), dashed line - model 5(20 G0) , dotted line - model 6 (30 G0)and single
dots and dashes - model 14 (50 G0) . Bottom right hand plot - varying shock velocity: solid line
represents model 4 (5 G0 at 300 kms−1), dashed line - model 16 (5 G0 at 1000 kms−1), the dotted
line - model 6 (20 G0 at 1000 kms−1) and dots and dashes - model 18 (30 G0 at 1000 kms−1).
Apart from the top left hand plot Av ∼ 6
2.3. Conclusions 61
HHO. Moreover, the chemical effects in previous models were transient on a short timescale so
that clumps were required to be extremely young and short-lived, causing some concern. In this
work, we investigate the effect of adapting the earlier models to include a moving, rather than
static, radiation source. The main conclusions of the work are as follows:
• Results from the moving source model confirm that it is still possible to reproduce the
particular chemistry observed in clumps near to HHOs while allowing the radiation source to
move rather than remain static relative to the clump. This supports the idea that emission is
due to the evaporation of species frozen out onto dust grains in dense regions of a molecular
cloud.
• The new model enables several important molecules to maintain detectable abundances for
longer periods.
• Species can be grouped into roughly three categories displaying similar behaviour under
the influence of the moving source. Some (such as CH3OH, NH3 and H2S) have much
higher abundances at all times with a moving source than with a static source. Most species
investigated (including SO2, SO, NO+, HCO+, HCN, CN, CS and OCS) are first formed
and then destroyed by reactions initiated by the radiation field and hence are less abundant
with the moving field up to about 1000 years (for a source moving at 300 kms−1) and then
more abundant (this is most apparent for lower Av clumps, hence is not obvious in figure
2.2 which plots those of higher Av). C+ and C abundances are enhanced by the field and
are lower with the moving field at all times.
• Species with most noticeably increased abundances in the‘moving’ case (as opposed to the
‘static’ case) are CH3OH, NH3, SO2, SO and H2S.
• The discrepancy between the moving and static cases is greater for a faster moving, stronger
source and clumps of smaller size or lower density.
The results of this investigation support the idea that the observed chemistry ahead of Herbig-
Haro objects is a result of species on the grains returning to the gas phase. The moving source
allows the chemistry to persist for longer, helping to explain the large number of these clumps
observed.
CHAPTER 3
THE EFFECT OF HERBIG -HARO RADIATION
ON A CLUMPY M OLECULAR CLOUD
There is plenty of evidence to suggest that molecular clouds are clumpy on small scales. The ad-
vent of telescopes such as SCUBA-2 and Herschel have made high resolution images of dark star-
forming clouds a possibility and condensations at sub-parsec scales are evident (e.g.di Francesco
et al. (2010)). Taylor & Williams (1996) first suggested that this might be a necessary picture
in order to understand the different spatial distributions of CS and NH3 observed in molecular
clouds. Garrodet al. (2006) used chemical models to represent dark clouds as a collection of
randomly distributed dense clumps. They modelled each clump as a small density enhancement
growing out of the ambient cloud material up to a maximum density and then re-expanding over
a period of 2 Myrs. Taking the clumps at a random time during their evolution and distributing
them over a map, the authors could then use the chemical abundances of molecules, convolved
with a Gaussian beam, to simulate the emission from each small region in a particular molecule.
The authors were successful in reproducing observations of dark clouds in lines of CS, N2H+ and
NH3 (Morataet al. (2003)).
The work presented here follows on from the modelling detailed in Chapter 2. We use outputs
from the UCLCHEM chemical code and adapt the approach used byGarrodet al. (2006) in
which cores of random age are distributed over a map and the output abundances from chemical
codes simulating a single core used to create a grid of column density values over a map for each
species. We produce synthetic maps of 0.9 pc× 0.9 pc regions containing dense clumps that are
undergoing a process of collapse and re-expansion over a period of 2 Myr (the codes to do this
were provided by R.Garrod). We remove the outer 0.05 pc of our 1 pc2 maps because these are
62
63
affected by the fact that we do not consider emission from clumps outside of this range. At some
point in their evolution these clumps are irradiated by a strong UV field from a nearby HHO.
On irradiation, materials locked-up in ices can immediately leave the grains and a rich gas-phase
chemistry ensues. We investigate both static radiation sources and moving sources for which the
radiation strength increases to a maximum point, representing a shock front passing the clump, and
then falls off again. We randomly distribute the cores, which are either collapsing, at a maximum
density or re-expanding, also at random, across the map. We can then calculate the contribution
from every core to the column density of each molecule of interest at all points on a grid covering
the map. After convolving these column densities with a Gaussian of a certain width (for the
maps shown here, a 20 arcsecond beam at the frequency of the HCO+ (3→2) line and at 150 pc
distance) we have a map of the expected emission for each molecule.
3.0.1 Method
As for the work outlined in Chapter 2, we use UCLCHEM to simulate the time-dependent chem-
istry in the dense clumps ahead of an HHO. We run the code in three phases (represented in Figure
3.1). There are some notable adaptations to the code used the previous chapter. In phase II the
density of the clump now evolves in both space and time following a Gaussian relation so that
the cores collapse to a maximum density and then re-expand, representing the transient clumps of
Garrodet al.(2006) (this modification to UCLCHEM was made by R.Garrod and adapted for this
work to include both‘moving’ and‘static’ radiation sources representing the HHO). We use the
fractional abundances of molecules at the end of each phase as input for the next. During the first
phase the density of the clump is constant with a maximum value in the centre of 103 cm−3. This
stage represents the molecular cloud material prior to the collapse of the core, and the chemistry
is allowed to run to equilibrium. The second phase represents the collapse and re-expansion of the
clump. The Gaussian profile evolves over a period of 1 Myr, becoming more peaked. The central
density increases up to this point and then decreases, the Gaussian again becomes shallower. The
central density falls again up to 2 Myr at which point the original density profile is recovered. In
all three phases, where the radiation field is below 3 Habing (G0), species freeze-out onto dust
grains above a visual extinction (Av) of 2 magnitudes with a sticking probability of 0.1. Where
the field is between 3 and 5 G0, the critical Av rises to 3 magnitudes. Above 5 G0 all molecules
in the mantle are returned to the gas phase. Once in the mantle, species hydrogenate as far as
possible and remain attached to the grain until the visual extinction of the depth point in question
again falls below 2 or 3 magnitudes (depending on the radiation field strength at that point in time.
64
In phase III the UV field from the HHO is switched on and thus this phase represents the illumina-
tion of the clump by the radiation field and the movement of the field source past the clump. We
run this phase 3 times, once with the clump still collapsing, once at maximum density and a third
time during the re-expansion phase. We effectively pause the evolution of the density profile and
irradiate the clump with a strong UV field for several thousand years.
Figure 3.2 illustrates the radiation field strength used at all points in the map for a static source
at 1000 G0. For simplicity, we split the map into 9 squares and all cores within a square are
irradiated with the same strength of field. A more realistic map could be achieved by calculating
the radiation field strength more accurately for a particular region by dividing the map into smaller
regions rather than the sparse 3×3 grid used), but to get a rough idea of what the molecular
emission should look like this is not necessary. The radiation source, or HHO, is located 0.05 pc
above the central square in the Figure. Since the field strength is fixed, this makes a difference
only in the geometry used to calculate the dilution of the field from central to outer regions of the
map. It is the outputs from this third phase that we use to make the maps. We simulate a moving
HHO in phase three, as in Chapter 2, by gradually increasing the field strength up to a maximum
value (in this case 1000 G0 or 100 G0, and then decreasing it again. We choose these particular
values of the radiation field strength because, despite this property being relatively unconstrained
by observation, these values are similar to the radiation field strengths found byViti et al. (2003)
to be necessary to excite the observed chemistry near to HH2. The maximum represents closest
approach for an HHO travelling at 300 kms−1 past a particular clump. Here the HHO moves from
the bottom of the region illustrated in Figure 3.2, over the central square, and off the top of the
map, located 0.05 pc above the map at all times and moving parallel to it. The same geometry
applies in Figures 3.3 to 3.17 so that in the moving case, the HHO again passes over the centre of
the map from bottom to top.
65
Figure 3.1: Flow chart of phases in the chemical model. The light grey circles are at 103 cm−3 in
the centre and the dark grey at 105 cm−3 illustrating a clump at the peak of collapse. The yellow
arrows denote the presence of a radiation field.
Figure 3.2: Radiation field strengths over the pc2 map area for a 1000 G0 field.
3.1. Grid of Models 66
Table 3.1: Map parameters
Model number Radiation field
strength in cen-
tre of map (G0)
Number of
cores within 1
pc2
Core max cen-
tral density
(cm−3)
Moving source?
1 1 (no HHO) 200 105 no
2 1000 200 105 no
3 100 200 105 no
4 1000 200 105 yes
5 100 200 105 yes
6 1000 400 105 no
3.1 Grid of Models
We run phase three, during which collapse is halted and the clump is irradiated, several times in
order to produce maps with varying characteristics. This involves running the code with varying
field strengths, and with moving or static fields, for each of the collapsing core, the core at max-
imum density and the re-expanding core in order to combine outputs and create the maps. We
experiment with changing the number of cores per pc2 and the strength of the radiation field from
the HHO, as well as investigating both moving and static sources. Table 3.1 lists parameters for
the sets of maps produced.
Table 3.1 lists parameters for the sets of maps produced.
3.2 Results
Tables 3.2-3.6 list maximum column densities of important molecules at three different times dur-
ing the irradiation (phase three) to give an idea of the quantitative difference between the models.
The nine selected molecules either stood out as being particularly affected by the inclusion of a
moving rather than static field during the work described in Chapter 2 or have previously been
mapped ahead of HHOs (Viti et al. (2006); Whyatt et al. (2010)) and so facilitate a comparison
with observation. In Figures 3.3-3.17 we plot 0.9 pc×0.9 pc regions for each molecule, again at
10 years, 1000 years and 5000 years after the start of phase three. Symbols mark the positions of
the cores with plus signs representing cores undergoing collapse, small crosses cores at maximum
density and large crosses the re-expanding cores. There are 200 cores in all maps other than those
3.2. Results 67
with 400 cores. The highest contour level is at 95% of the maximum column density in the map,
the next at 90% and then down in 10% decrements until 1×1011 cm−2 which is set as the lowest
contour to represent a minimum observable level. We display a selection of our synthetic maps
to illustrate the main results and show the rest in Appendix A. We compare maps for which cores
have been irradiated with 1000 G0 static radiation field with an ambient radiation field in Figures
3.3-3.8. In Figures 3.9-3.12 we compare the effects of a weaker 100 G0 field with the original
1000 G0 field (both static). Figures 3.13 and 3.14 allow a comparison of the original 1000 G0
static field with an HHO that moves over the map, the strength of the radiation field thus increas-
ing and then decreasing over time with the passage of the object. Figures 3.15 and 3.16 are the
same but for a 100 G0 field. The strength of the field represents a maximum in the case of the
moving HHO. Lastly, illustrated by Figure 3.17, we investigate the effect of increasing the number
of cores within a given area. We summarize our results below.
Table 3.2: HCO+ (left) and CO (right) maximum column densities
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 9.80(12) 9.77(12) 9.70(12)
2 4.14(13) 1.56(12) 3.67(11)
3 2.90(13) 8.91(12) 8.49(12)
4 3.12(13) 1.12(13) 3.68(11)
5 1.17(13) 9.70(12) 8.46(12)
6 6.45(13) 2.08(12) 5.03(11)
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 2.08(18) 2.08(18) 2.07(18)
2 3.34(18) 3.27(18) 2.86(18)
3 3.04(18) 2.40(18) 1.99(18)
4 3.06(18) 3.27(18) 3.34(18)
5 2.08(18) 3.12(18) 2.73(18)
6 4.42(18) 4.15(18) 3.51(18)
Table 3.3: CS (left) and N2H+ (right) maximum column densities (cm−2).
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 1.33(15) 1.33(15) 1.32(14)
2 1.34(15) 3.39(15) 2.45(15)
3 1.32(15) 2.34(15) 1.43(15)
4 1.38(15) 3.79(15) 4.49(18)
5 1.33(15) 3.12(15) 3.59(15)
6 1.52(15) 3.94(15) 2.76(15)
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 1.14(12) 1.13(12) 1.12(12)
2 7.49(10) 3.69(10) 2.15(10)
3 1.10(12) 1.03(12) 9.29(11)
4 1,13(12) 9.75(11) 4.27(10)
5 1.14(12) 1.12(12) 9.45(11)
6 1,14(11) 5.13(10) 2.69(10)
3.2. Results 68
Table 3.4: CH3OH (left) and NH3 (right) maximum column densities (cm−2).
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 1.90(11) 1.90(11) 1.89(11)
2 6.61(16) 3.69(16) 2.02(16)
3 5.89(16) 2.00(16) 5.67(15)
4 6.18(16) 3.71(16) 3.28(16)
5 2.47(16) 5.29(16) 2.53(16)
6 1.05(17) 5.00(16) 2.54(16)
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 3.23(14) 3.23(14) 3.27(14)
2 2.87(17) 1.54(17) 8.62(16)
3 2.55(17) 8.48(16) 2.21(16)
4 2.70(17) 1.54(17) 1.37(17)
5 1.11(17) 2.23(17) 1.08(17)
6 4.14(17) 1.99(17) 1.09(17)
Table 3.5: H2CO (left) and SO (right) maximum column densities (cm−2).
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 2.78(12) 2.78(12) 2.80(12)
2 6.47(15) 7.94(14) 1.74(14)
3 2.51(15) 8.23(14) 1.34(14)
4 1.14(15) 1.98(15) 6.41(13)
5 1.72(14) 1.80(15) 7.88(13)
6 2.82(15) 1.09(15) 2.27(14)
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 7.00(13) 7.05(13) 7.21(13)
2 3.46(14) 2.58(15) 2.40(15)
3 1.14(14) 2.51(15) 1.71(15)
4 8.15(13) 2.54(15) 2.50(15)
5 7.00(13) 1.22(15) 2.40(15)
6 2.84(14) 4.01(15) 3.28(15)
Table 3.6: HCN maximum column densities (cm−2).
Model
number
Max 10
yrs
Max
1000 yrs
Max
5000 yrs
1 2.26(15) 2.27(15) 2.29(15)
2 5.00(15) 1.10(16) 5.81(15)
3 4.18(15) 4.12(15) 2.74(15)
4 3.99(15) 1.11(16) 1.15(16)
5 2.26(15) 8.13(15) 4.93(15)
6 5.77(15) 1.43(16) 6.83(15)
3.2. Results 69
Figure 3.3: HCO+ column density maps at 10 years without HH field (top left), with 1000 G0 field
at 10 years (top right) without HH field at 1000 years (middle left) and with 1000 G0 field at 1000
years (middle right). Without radiation field at 5000 years (bottom left) and with 1000 G0 field
at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.93×1013
cm−2.
3.2. Results 70
Figure 3.4: H2CO column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (middle right) without HH field at 1000 years (middle left) and with 1000 G0
field at 1000 years (middle right). Without radiation field at 5000 years (bottom left) and with
1000 G0 field at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 6.15×1015 cm−2.
3.2. Results 71
Figure 3.5: SO column density maps at 10 years without HH field (top left), with 1000 G0 field at
10 years (middle right) without HH field at 1000 years (middle left) and with 1000 G0 field at 1000
years (middle right). Without radiation field at 5000 years (bottom left) and with 1000 G0 field
at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 2.45×1015
cm−2.
3.2. Results 72
Figure 3.6: CH3OH column density maps at 10 years without HH field (top left), with 1000 G0
field at 10 years (middle right) without HH field at 1000 years (middle left) and with 1000 G0
field at 1000 years (middle right). Without radiation field at 5000 years (bottom left) and with
1000 G0 field at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 6.28×1016 cm−2.
3.2. Results 73
Figure 3.7: CO column density maps at 10 years without HH field (top left), with 1000 G0 field at
10 years (top right) without HH field at 1000 years (middle left) and with 1000 G0 field at 1000
years (middle right). Without radiation field at 5000 years (bottom left) and with 1000 G0 field
at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.17×1018
cm−2.
3.2. Results 74
Figure 3.8: N2H+ column density maps at 10 years without HH field (top left), with 1000 G0 field
at 10 years (top right) without HH field at 1000 years (middle left) and with 1000 G0 field at 1000
years (middle right). Without radiation field at 5000 years (bottom left) and with 1000 G0 field
at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 1.08×1012
cm−2.
3.2. Results 75
Figure 3.9: HCO+ column density maps at 10 years with 100 G0 field (top left), with 1000 G0field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years
(top right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.93×1013 cm−2.
3.2. Results 76
Figure 3.10: CH3OH column density maps at 10 years with 100 G0 field (top left), with 1000 G0field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years
(top right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.28×1016 cm−2.
3.2. Results 77
Figure 3.11: CS column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field
at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years (top
right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.22×1015 cm−2.
3.2. Results 78
Figure 3.12: N2H+ column density maps at 10 years with 100 G0 field (top left), with 1000 G0field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years
(top right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.05×1012 cm−2.
3.2. Results 79
Figure 3.13: N2H+ column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 1.07×1012 cm−2.
3.2. Results 80
Figure 3.14: CH3OH column density maps at 10 years with 1000 G0 static field (top left), with
1000 G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with
1000 G0 moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field
(bottom left) and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011
cm−2, maximum of 6.28×1016 cm−2.
3.2. Results 81
Figure 3.15: N2H+ column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
1.08×1012 cm−2.
3.2. Results 82
Figure 3.16: CH3OH column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
5.60×1016 cm−2.
3.2. Results 83
Figure 3.17: HCO+ column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 6.13×1013
cm−2.
3.2. Results 84
• Comparing models with and without contribution from the HHO radiation field we find
that HCO+ abundances are high enough to be detectable at early times with the radiation
field and emission appears fairly compact nearest to the HHO in the centre of the map
(Figure 3.3). Later the HCO+ is destroyed by liberated electrons and abundances drop
to below those of the radiation-less model (becoming nearly undetectable). Emission is
strongest around the edges of the map at 1000 years and in very small clumps of weak
emission at 5000 years. H2CO behaves similarly to HCO+ and displays even more compact
structure just after irradiation (Figure 3.4). This, along with HCO+, may be one of the
better indicators that this kind of photo-chemistry is occurring. SO column densities are
highest under the influence of a radiation field at around 1000 years. Emission is strongest
towards the edges of the map at this point and towards the centre earlier on. Emission is
stronger than for the radiation-less model at all times (Figure 3.5). CH3OH and NH3 are
both highly enhanced by the HHO field (Figure 3.6). The emission is widespread in the
case of the stronger field (due mainly to the direct evaporation of the molecule from grain
mantles which can occur over the whole region). CO and CS maps look very similar with
and without the radiation field (Figure 3.7). Emission always covers the whole map. There
is some evidence for destruction of these molecules near the centre of the map at later times.
Overall, CO is slightly enhanced by the field at all times and CS (again only slightly) after
about 1000 years. N2H+ is completely destroyed by the 1000 G0 field (to the level where
it is undetectable, Figure 3.8). Again this is due to dissociation by electrons, freed by the
ionizing radiation.
• When a weaker radiation field is included in the models (we choose 100 G0) molecular
abundances are both enhanced and then destroyed to a lesser extent by the field. In the
case of HCO+, for example, this leads to weaker emission at early times but stronger at
around 1000 years (just after the passage of the HHO; Figure 3.9). Several molecules dis-
play much more localized emission in the 100 G0 model as opposed to the 1000 G0 model
due to molecules remaining frozen-out towards the edges of the maps (evident in the plots
of CH3OH, NH3, H2CO, SO and to some extent HCN; see Figure 3.10 for CH3OH and
Appendix A for other maps). Most molecules show weaker emission at all times than for a
stronger field. CS reaches similar abundances at 10 years with 100 G0 and 1000 G0 fields
but weaker with the 100 G0 field at 1000 years and later (Figure 3.11). In the case of N2H+,
however, abundances reach detectable levels only with the weaker 100 G0 field (Figure
3.2. Results 85
3.12).
• Comparing a moving with a static field for both 1000 G0 and 100 G0 fields; emission in
enhanced species is strongest at later times in the moving case due to the slow increase in
field strength early on. N2H+ is only visible at early times with the moving field or weaker
static field (Figures 3.12, 3.13 and 3.15). The distribution of emission for several species
is different under the influence of a moving field. Several molecules, including NH3 and
CH3OH (Figures 3.14 and 3.16), display a much more compact emission than in the static
case. At much later times (around 5000 years) emission of molecules under the influence
of a moving field remains stronger than for a static field, where most of the molecules have
been destroyed by the continuing photo-chemistry. This effect is more obvious at 100 G0
field than at 1000 G0.
• Positions of the cores on the map make little difference to the outcome if randomly dis-
tributed.
• Increasing the number of cores results in a higher column density of all species over the
entire map (Figure 3.17). This effect is fairly small, at most a factor of two increase in
the column densities (see Tables 3.2-3.6, model number 6). Relationships between column
densities at different times remain unchanged.
• Convolving with a larger beam (in this case, three times the size of the original 20 arcsecond
beam used) results in a dilution of the emission (because column densities are averaged over
the beam) as well as apparently larger emitting regions.
• We briefly compare maps produced using models with an ambient radiation field to those
of Morataet al. (1997), who observed N2H+ and CS in a dark cloud core. We observe the
same discrepancy between emission peaks for these two molecules asGarrodet al. (2006)
who used the same method (although we simplify by irradiating cores at one of three times
in their evolution rather than at completely random times, a necessary simplification to allow
for the inclusion of a radiation field and desorption from dust grains, which complicate the
model). NH3 emission peaks, however, observationally appeared to coincide with the N2H+
whereas in the synthetic maps they peak along with the CS.
3.3. Summary 86
3.3 Summary
Chemical modelling of molecular clouds as a collection of transient dense cores appears to repro-
duce well the observed structure of emission both in dark clouds and in regions near to HHOs emit-
ting radiation. When the field from a nearby HHO is simulated, several species (H2CO, CH3OH,
NH3, HCO+ early on) are strongly enhanced. How compact or widespread the detectable emission
is depends both on the strength of radiation field used and whether the field is allowed to move
over the map or remains static. Observations of regions ahead of HHOs are available (e.g.Whyatt
et al.(2010) for HCO+) and after some work on the models, a comparison with these should yield
some interesting results.
CHAPTER 4
THE GOULD BELT CLOUDS: A N OVERVIEW
4.1 The JCMT Gould Belt Survey
The GBS images a large sample of nearby star-forming regions, all within 500 pc, in the J=(3→2)
lines of three isotopologues of CO and the sub-millimeter dust continuum at 450 and 850 microns.
The imaged regions lie within the Gould Belt, a ring of O stars with a radius of around 350 pc
centred 200 pc from the Sun, inclined slightly to the plane of the galaxy and housing some of
the most well studied nearby star-forming clouds. The survey was initially awarded 500 hours
of observing time on the JCMT between 2007 and 2009 and the original survey paper (Ward-
Thompsonet al. (2007)) stated that it aimed to achieve a large, unbiased sample of data at high
resolution focusing on the very earliest stages of star formation. CO (3→2) lines are excited in
cold, dense prestellar core conditions making the chosen CO observations, along with the 850
micron continuum, near the peak of the emission spectrum for cold dust, well suited to meeting
this goal.
The survey utilises two instruments, HARP (Heterodyne Array Receiver Programme, see
Buckle et al. (2009) for more details) and the newly implemented SCUBA-2 (Sub-millimeter
Common User Bolometer Array 2). A Heterodyne receiver mixes an incoming signal non-linearly
with a reference frequency (local oscillator) bringing the frequency of the signal into a range eas-
ier for processing and equal to the difference between the local oscillator and signal frequencies.
Two signal frequencies can thus produce the same intermediate frequency allowing simultaneous
imaging at two wavelengths (double sideband mode). Often the second (or‘image’) sideband
does not contain information of interest in which case it can be removed to reduce noise in the first
87
4.2. HARP CO Maps 88
band. HARP works with the back-end Auto-Correlation Spectrometer Imaging System (ACSIS)
producing 3 dimensional images in the atmospheric window at 325 to 375 GHz.
Bolometer arrays (such as SCUBA-2 and its predecessor SCUBA) comprise material that al-
ters its electrical resistance when heated, making it sensitive to photon hits. SCUBA-2, uses a
beam splitter to allow two frequencies to be observed simultaneously. For the GBS, continuum
emission is imaged at 450 and 850 microns. The instrument can be used in various observing
modes, photometry for point sources, jiggle mapping for more extended sources, achieved by
moving the secondary mirror slightly in order to fill in gaps between pixels, and scanning, for
mapping large areas, where the telescope field of view moves continually across the sky. Chops
or nods, where the telescope switches at intervals to a blank region of sky, allow for background
removal. The JCMT itself is a 15 meter, single-dish telescope on Mauna Kea, a dry site at over
4000 ft, which helps to minimise absorption by atmospheric water vapour.
4.2 HARP CO Maps
HARP was used to map regions in Orion, Taurus, Serpens and Ophiuchus as part of the JCMT
GBS. Table 4.1 lists the sizes of and distance to each cloud as well as the centre, area and noise
of each respective map. In conjunction with ACSIS (Auto-Correlation Spectral Imaging System),
spectra were obtained for the12CO J=(3→2) line at 345.796 GHz at high and low resolution.
HARP used wide-band imaging (up to 1.9 GHz bandwidth) in single sideband mode to cover
both the J=(3→2) transitions of13CO and C18O at 330.588 GHz and 329.331 GHz respectively.
Narrow band imaging results in higher resolution spectra with channels of up to 31 kHz.12CO
maps generally cover physically larger areas. The data had a spectral resolution of 0.05 kms−1 or
0.85 kms−1 for the high and low resolution setups respectively. We use only the smaller sections of
maps for which spectra from all 3 isotopologues are available and use the high resolution images
of 12CO. We have trimmed the images to remove noisy edges and have binned the data to 0.15
kms−1 (0.42 kms−1 in the case of Serpens, for which data with a higher velocity resolution was
not available).
HARP has 16 receivers, separated by 30 arcseconds in the focal plane, resulting in a footprint
of around 2 arcminutes projected on the sky. The beam width of the JCMT is∼14 arcseconds
FWHM at the frequencies of the CO lines. For a fully sampled map, telescope scans were made
in the raster position-switched observing mode where the telescope scans along the direction par-
allel to the edges of the map, taking spectra separated by 7.3 arcseconds. This is done first in
4.2. HARP CO Maps 89
Table 4.1: Details of the observations
Region Distance
(pc)
Isotopologue Map centre (J2000) Map area
(arcsec2)
rms noise
(K)a
Serpens 260 12CO 18h30m 260 0.12
114’
13CO 18h30m 77 0.24
113’
C18O 18h30m 77 0.25
113’
Taurus 140 12CO 4h18m 264/120(se)b 0.10/0.13(se)
4h20m(se)
2822’
2711’(se)
13CO as12CO 450/378(se) 0.15/0.24(se)
C18O as12CO 450/378(se) 0.18/0.29(se)
Ophiuchus 125 12CO 16h28m 900 0.49
-2433’
13CO as12CO 256 0.18
C18O as12CO 256 0.16
NGC 2024 415 12CO 05h42m 243 0.11
-0154’
13CO as12CO as12CO 0.18
C18O as12CO as12CO 0.14
NGC 2071 415 12CO 05h47m 292 0.21
0020’
13CO as12CO as12CO 0.10
C18O as12CO as12CO 0.13
a - rms noise values in 0.1 kms−1 channels
b - The letters se refer to the south-eastern region of Taurus L1495
4.3. SCUBA maps 90
Table 4.2: GBS Cloud Propertiesa
Region Distance
(pc)
Mass (M) area (deg2) Dust core
temperature
(K)
Serpens 260 1.9×104 12.3 17
Orion 450 2.6×105 147 20
Taurus 140 3.9×104 250 13
Ophiuchus 125 1.0×104 67 15
a - Adapted from Tables 1 and 2 ofSadavoyet al. (2010)
one direction and then again in the perpendicular direction for better coverage (the basket weave
technique). Pixels thus represent regions on the sky that are around 7 arcseconds apart (seeBuckle
et al. (2010) for more detail). Noise levels vary from map to map depending on weather condi-
tions at the time of data acquisition and total hours dedicated to each observation. We used the
current best reductions for each cloud. The resulting maps were not reduced entirely similarly but
the differences in reduction techniques for the separate regions (type of binning used etc) have a
minor effect on the results. Integrated intensity and channel maps are shown for all the regions in
Figures 4.1-4.30.
4.3 SCUBA maps
We also use results from dust emission data produced using SCUBA and forming part of the SLC
(SCUBA Legacy Catalogue,Di Francescoet al. (2008)). SCUBA is comprised of two hexagonal
arrays of detectors, a long-wave array with 37 pixels and a short wave array with 91 pixels. The
relevant data are maps of 850 micron emission taken using the long-wave array and smoothed with
a 1 sigma Gaussian (see Di Francesco et al. 2008 for details), resulting in a spatial resolution for
each SLC map of 22.9 arcseconds at 850 microns.
4.4 Properties of the Observed Regions
The Serpens main cluster, a region of the Serpens molecular cloud particularly rich in star for-
mation, has been extensively studied and shown to contain a population of Class 0/I sources (e.g.,
4.4. Properties of the Observed Regions 91
Daviset al.(1999)) as well as an apparently older one containing more evolved Class II/III sources
Harveyet al.(2007). Kaaset al.(2004) suggested that the region underwent a burst of star forma-
tion roughly 2 Myr ago followed by a later one around 105 yr ago. The main cluster is complex,
made up of two distinct sub-clusters, the NW and SE. These two regions are joined by dusty,
finger-like structures or filaments. The NW is more quiescent and cooler, whereas the SE is more
filamentary, more turbulent, and hotter (Duarte-Cabralet al. (2010)). The Serpens main cluster
contains several known HH objects and outflows (Graveset al. (2010)).
NGC 2024 and NGC 2071, in contrast to the other clouds discussed here, are both high-mass
star-forming regions. As a result, they contain many more O/B-type stars, producing high velocity
outflows and stellar winds that interact with the surrounding cloud material to form complex, fila-
mentary structures. Star formation in Orion B occurs in clusters (predominantly in three massive
cores and within the dense gas only,Lada(1992)). From 12CO and13CO maps of NGC 2071,
White & Phillips (1981) suggested that the region may resemble a rotating disc (at a temperature
of around 20 K) with an opaque cloud lying between it and the observer. More recently,Buckle
et al. (2010) found NGC 2024 to be the more massive of the two regions and to have a higher
average gas temperature (31.8 K as opposed to 19.6 K for NGC 2071). NGC 2071, on the other
hand, is dominated by kinetic energy from high velocity outflows that are at high temperatures
compared to the rest of the cloud. Both regions contain optically bright cavities in CO emission
surrounded by dust and CO lanes. Buckle et al. also commented that the C18O emission in NGC
2071 does not follow the dust emission as closely as it does in NGC 2024, the first possible sign
that some CO freeze-out is occurring.
The GBS data for Taurus cover a region of the molecular cloud known as L1495. This region
contains a compact‘ridge’ of CO and dust emission and a ‘bowl’ of more diffuse emission in
the north. The12CO observations cover the entire ridge and bowl, but13CO and C18O maps are
only available for a small section of each, allowing a comparison of conditions in the two regions.
The bowl is more evolved than the ridge, containing a larger number of T-Tauri stars but fewer
molecular outflowsDaviset al. (2010). The ridge is more compact and fragmented.
Ophiuchus is the closest of the four clouds in this study, located just 125 pc from the solar
system (Lombardiet al.(2008)). The GBS images cover the Ophiuchus main cloud core (L1688),
a dense region in the centre of the molecular cloud housing many YSOs at varying stages of evo-
lution, including a large population of T-Tauri stars. Within the main cloud core, several smaller
condensations have been identified in dust continuum maps. These clumps, referred to as Oph
A-F, are dense, high extinction regions, probably made up themselves of several sub-clumps that
4.4. Properties of the Observed Regions 92
may be star-forming (Marutaet al. (2010), Friesenet al. (2009)).
CHAPTER 5
TESTING CUPID CLUMPFINDING
ALGORITHMS
This chapter focuses on testing clump-finding algorithms, which have been widely used over the
past couple of decades to determine structure in molecular clouds and to identify dense cores which
may be star-forming. The determination of the basic properties of pre-stellar cores is crucial to
uncovering the process of early star formation. How does a cloud collapse to form dense clumps?
How many of these, and with what properties, then go on to form stars? CO is often used as
a tracer of denser gas as its J=(3→2) lines have critical densities of around 104-105 cm−3, and
although the more common isotopes suffer from optical depth effects, in general the rarer isotopes
such as C18O do not. In clouds of average density 1000 cm−3, clearly density enhancements are
required to provide the conditions for the observed CO emission. We investigate the performance
of 4 different popular clump-finding routines on both synthetic data cubes and on C18O data from
two clouds mapped as part of the GBS and presented in Chapter 4.
Dense clumps can be traced by thermal dust emission or via particular molecular lines that
trace the colder, denser material in GMCs. In the past it was possible to analyse data sets by eye in
order to pick out dense cores, however this process is heavily dependent on the individual carrying
out the analysis and, with the quantity of data now available, has become painstaking. This is
particularly true in the case of 3D emission line data which includes velocity information as well
as positional, and where emission is blended in crowded regions. We also require a consistent
method in order to compare the structure of similar regions in terms of the filling factor and
orientation of dense regions and the sizes and physical properties of cores which may go on to be
star-forming.
93
94
While we have moved far from the idea of a star-forming cloud as an homogeneous region of
gas denser than the surrounding ISM, a detailed understanding of GMC structure is still elusive.
The importance of achieving a better picture of the physical make-up of these regions to our overall
grasp of the star formation process has led to much recent work, both in observational studies of
GMCs and in their modelling. One of the main leaps forward over the past couple of decades
has been the realisation that turbulence is a driving factor in the formation of molecular cloud
structure. We see long filaments housing denser knots which in turn fragment to form sub-parsec
scale cores (e.g.Molinari et al. (2010) with Herschel). The structure seen in molecular clouds
is often described as scale-free, in that it does not appear to have a characteristic size. There is
debate, however, over the issue of completely scale-free structure and this obviously breaks down
at small scales when gravity becomes dominant (Ossenkopfet al. (2001); Sanchezet al. (2010)).
Hydrodynamical models including turbulence do seem to be able to well reproduce a scale-free
structure (Klessen & Burkert(2000); Klessenet al.(2000). Aside from modelling, straight forward
analysis of observations is paramount. To this end, algorithms designed to categorise emission in
an unbiased way have flourished. There are many different types with many applications across
astrophysics and cosmology. Each algorithm has its advantages and its downsides, so choosing
which to use and then interpreting the results sensibly is a particularly difficult task and requires a
very good understanding of the data you are analysing and with what particular goal.
The earliest algorithm designed to categorise emission in this way was calledGAUSSCLUMPS
(Stutzki & Guesten(1990)), which is described in detail below but works by fitting a series of
Gaussian profiles to a 2D or 3D emission map, removing these from the data and then repeat-
ing the process on the residual map. This was superseded byWilliams et al. (1994) with the
CLUMPFIND algorithm, after which followed several other, similar programmes such asFELLWALKER
andREINHOLD, developed in Hawaii (seeBerry et al. (2007)). All these programs work to identify
isolated, dense regions in data sets but achieve their goal in slightly different ways. Together, the
four algorithms mentioned make up theCUPID ‘findclumps’ routine (described later;Berry et al.
(2007)).
Flux-fitting routines can be used to compare the structure of similar regions, however there
is much controversy linked to their use for other means since outputs depend heavily on user
defined input parameters. A common use of these codes in the past has been the derivation of
clump mass functions (CMFs), a measure of how many cores of each mass are to be found in a
particular region (e.g.Buckleet al. (2010); Motte et al. (2001); Motte et al. (1998) and others).
The slope of the CMF is usually found to be similar to the IMF (the stellar initial mass function)
95
and has often been cited as evidence that the shape of the IMF is determined during the pre-stellar
phase rather than later (Testi & Sargent(1998)). Because of the heavily input-dependent nature
of the CLUMPFIND output catalogue and the dependence on the noise across the input maps, it is
important to be aware of just how reliable or otherwise the CMFs may be. For example, the user
can define parameters such as the lowest intensity emission to be considered, and others relating
to how each code splits clumps into smaller sub-clumps. Some algorithms also have trouble in
regions of crowded emission because they cannot distinguish two clumps with very similar peak
positions from just one peak at the same location.
Several studies have been undertaken to determine biases in the use of these codes.Pineda
et al. (2009) investigated how theCLUMPFIND routine worked to determine the CMFs for both
13CO (3D cubes with velocity information) and 850 micron emission (2D cubes for which only
spatial information is available) in the Perseus molecular cloud. They found that, while varying
the lower threshold of emission allowed to form part of a clump had little effect on the derived
clump numbers and CMF, the levels used to contour the data had a profound effect in the 3D case.
The authors attribute this to the fact that the emission in the13CO maps was crowded rather than
sparse as in the 2D case. Other studies test the algorithms using synthetic data. The input clumps
are much more easily identified in the case of isolated emission than for crowded maps.Curtis &
Richer(2010) use bothCLUMPFIND andGAUSSCLUMPSto fit 850 micron data in four different regions
of the Perseus molecular cloud. They compare results and find several differences between the
clump populations identified by the two algorithms.GAUSSCLUMPStends to find larger numbers
of smaller clumps with shallower mass vs. radius relations. The authors go on to investigate
the clump mass distributions from both output catalogues and find them to be different when
separating starless and protostellar core distributions. One recent method of categorising emission
in GMCs is to use Dendrograms (Rosolowskyet al. (2008)). These link isophotes or structures
on different scales allowing an appreciation of how larger structures are broken up into smaller
regions or how small structures link together. Typically, a data set (which may be 2D or 3D) is
contoured from the highest level of emission downwards, and at each level objects are identified.
The brightest peaks will be found in the highest contour level and defined there as separate objects.
As lower contour levels are considered, these peaks will slowly merge where a contour surrounds
two or more peaks. The Dendrogram retains information about which structures merge and at what
contour level. This is an important distinction from the more traditional flux fitting algorithms
which generally divide emission and associate it with separate intensity peaks, making it more
difficult to extract information about the larger structure. The latter are, however, useful when the
5.1. Description of the Algorithms 96
aim is simply to identify small or isolated structures and to statistically study their properties.
We test all four algorithms from theCUPID clumpfinding package, first on crowded and sparse
synthetic 3D data cubes and then on a selection of real HARP data from the GBS (although this
was not successful in the case ofREINHOLD andGAUSSCLUMPS, which struggle to identify clumps
in the real data). Ultimately, we aim to gain a better understanding of the performance of the
codes and to determine which of these, and with which selection of input parameters, might be
best suited to the study of our HARP CO data.
5.1 Description of the Algorithms
The following provides a short description of the fourCUPID clumpfinding algorithms and their
use. Running the algorithms (either on 3D line data or 2D continuum data) involves a simple set
of commands in which various user defined inputs are specified. After running the algorithms,
the user is left with a mask ndf (extensible n-dimensional data format, a standard file format used
to store n-dimensional arrays of numbers such as spectral data cubes) with the same dimensions
as the input ndf containing information about which pixels have been attributed to an emission
peak and which have not. Information about the properties of these identified clumps is contained
in an output catalogue (in FIT format). It is possible to overlay this mask on the original image,
or another with the same dimensions, in order to visualise the position, shape and sizes of the
emission peaks. The output catalogue contains information about the volume and effective radii
of the‘clumps’ as well as the sum and peak intensity values which are useful in the determination
of clump masses and CMFs. In our runs we ignore clumps that touch the edge of the array to
avoid biasing the CMF with extra low mass clumps. We set the minimum number of pixels in
each clump to 16 for all runs (the default for the codes) and the beam size to 2.77 pixels (equal
to that of the HARP CO data which we investigate later). All algorithms (with the exception of
GAUSSCLUMPS) reduce clump sizes in quadrature by the beam size after clump-finding to account
for the smearing effect on emission.GAUSSCLUMPSbehaves slightly differently, in that rather than
reducing clump sizes after performing the main clump-finding, clump sizes are measured using the
standard deviation of pixel intensities inside the clump and clumps smaller than the input fwhm
(width of the line at half of the maximum intensity) beam size or velocity resolution are simply
rejected. ForCLUMPFIND, FELLWALKER andREINHOLD, theVeloResparameter, which describes the
velocity resolution of the instrument, can be set so that the size of the clump along the velocity
axis is again reduced to account for the velocity resolution. ForGAUSSCLUMPSthe clump size is
5.1. Description of the Algorithms 97
constrained to being at least as large as the instrument resolution but no correction is made. Our
HARP data has one channel per pixel so, in effect, the velocity resolution of the instrument is the
same as that of the map and no correction should be required. Input parameters not investigated
here were set to their default values (there are many input parameters for each algorithm, and an
explanation of their function and default values are listed in theCUPID on-line documentation).
5.1.1 CLUMPFIND
The CLUMPFIND algorithm works by contouring the data from the peak of emission in the map
down to a user-specified level (the value of the parameterTlow). The code steps through the
contours, linking pixels at the same contour level that appear to be neighbours (the exact method
the code uses to decide which pixels are linked can also be changed, but as a default, in the 3D
case, it considers all pixels in a 3×3 cube around the central one as a neighbour). Pixels within
a particular contour level are attributed to clumps if they are linked to pixels at higher levels, or
are designated as peaks to new clumps if not. Often emission in a closed contour at one level will
surround two peaks at higher levels. In this caseCLUMPFIND uses a friends-of-friends algorithm to
locate the nearest peak to a pixel and it is allocated to the appropriate clump in this way. In this
work we investigate how sensitive outputs are to the parametersTlowandDeltaTwhich determine
the minimum level of emission allocated to clumps and the spacings between levels used in the
contouring process.
5.1.2 FELLWALKER
FELLWALKER considers, in turn, every pixel above a minimum emission threshold (specified by the
parameterNoise) in the 3-dimensional array. From each starting point it follows the steepest gra-
dient to the next pixel by locating the neighbouring one with the highest data value. Neighbouring
pixels in the 3D case are those in a 3×3 cube surrounding a central pixel. The algorithm continues
this process until it a) meets a pixel already assigned to a clump in which case all the pixels en-
countered so far are allocated to the same clump or b) locates a peak. In the latter case, to ensure
that the peak is not merely a noise spike in the data, surrounding pixels are checked. The size of the
area considered is controlled by the input parameterMaxJump.For all clumps below the specified
threshold level plus two times the rms noise in the data, pixels on a single walk are not allocated to
a clump until the gradient over four steps reaches a value equal to that of the parameterFlatSlope.
This avoids large, flat sections with low levels of emission being included in clumps (flat sections
5.1. Description of the Algorithms 98
are excluded until a higher level of emission is reached). To discourage slight mounds and troughs
near to a peak being separated into distinct clumps, the algorithm finally merges all nearby pairs
of clumps for which the dip between falls below a value specified by the parameterMinDip. We
investigate various values for the parametersNoise, MinDip andFlatSlope.
5.1.3 REINHOLD
TheREINHOLD algorithm looks at 1D profiles across a data cube, initially parallel to the first pixel
axis, then the second and finally the third. Diagonal profiles are also included. The pixel with the
highest data value in the profile is designated as a peak (so long as it is above the level specified
by theNoiseparameter and spans more than a given number of pixels in all directions) and the
profile is followed down in both directions until it either reaches the edge of the map, another pixel
already associated with a peak, the data value of the next two pixels are below the threshold level or
the gradient over 3 consecutive pixels is less than that specified by theFlatSlopeparameter. Peak
pixel designations will only be retained at the end of the run if none of the other profiles running
through them contain an additional peak at higher intensity. After this initial stage one is left with
a map of the edge pixels which should take the form of shells (or rings in the 2D case) surrounding
peaks. These shells will often be badly affected by noise, with holes in the shells or extra pixels
designated as edges. To rectify this a series of cleaning routines are applied which first dilate and
then erode the edges. The dilation involves marking all pixels in a 3×3 cube around every edge
pixel as a new edge pixel. The new edges are then shrunk down again by evaluating whether an
edge pixel is now surrounded by ample additional edge pixels. If the number of neighbouring edge
pixels is below a value specified by the parameterCatThresh, then the original pixel is no longer
designated as an edge. One can control the number of times that this erosion is applied. After
the cleaning, clumps are then filled in the following manner to produce a catalogue containing
identifiers for each pixel belonging to a clump; starting from each peak, a profile through the peak
and parallel to the first pixel axis is followed away from the peak pixel in both direction. All pixels
encountered are allocated an identifier corresponding to the particular peak until an edge pixel is
reached. The process is repeated for profiles parallel to the second pixel axis and through every
pixel in the first profile. The same is done for the third pixel axis through every pixel identified as
part of the clump in the second pass. If the first profile covers a small part of the clump then this
may result in clump pixels being missed so the process is repeated, the first profile investigated
this time being parallel to the second rather than the first pixel axis. This is repeated, first using a
profile parallel to the third pixel axis, before the algorithm is terminated. Some leaking can result
5.1. Description of the Algorithms 99
from holes in the clump walls during the filling process which is combated to some extent via the
use of a final cleaning routine. This replaces every pixel with the most common value in a 3×3
cube. As for the identification of edge pixels, this can be repeated a number of times (achieved
by increasing the value of the parameterFixClumpsIterations). We investigate the response to
changing the value of theNoiseparameter,FlatSlope, MinLenwhich decides the number of pixels
spanned by a significant peak, andCaIterationswhich controls the number of times the erosion is
carried out after clump edges have been identified. We also experiment with changing the number
of times the algorithm applies the final cleaning in an attempt to decrease the effect of leaking
where this is seen in the output arrays.
5.1.4 GAUSSCLUMPS
Stutzki & Guesten(1990) introduced theGAUSSCLUMPSroutine in order to determine the properties
of small scale clumps of emission in CS and C18O observations of the M17 SW cloud core.
Some small modifications to the code have been made since the original version. We describe
the CUPID routine but note that it is based heavily on work from the 1990 paper. As mentioned,
GAUSSCLUMPSworks by fitting clumps as a series of Gaussian profiles with varying properties.
Unlike the other three algorithms it allows clumps to overlap, so that emission from a particular
pixel can be assigned to more than one clump. This is useful when considering crowded regions
where clumps lie very close together. The algorithm fits its first profile to the highest intensity
point in the map, calculating by least squares how well an original guess at the profile fits the
actual emission and then changing the parameters of the profile until a best fit is found (when
changes to the parameters describing the profile are small). The first profile is then subtracted
from the map and the same process carried out on the highest intensity peak in the residual map.
Clumps continue to be fit until either a maximum number of clumps have been identified (defined
by the user with the parameterMaxClumps), the total data sum in the fitted Gaussians matches or
exceeds the total data sum in the original map, 10 clumps are fitted with peaks below a user defined
threshold level (the number of low intensity clumps allowed before termination is again defined
by the user) or the algorithm fails to fit a Gaussian profile to a number of consecutive clumps
(defined by the parameterMaxSkip). Pixels under consideration are weighted via a function that
is, as a default, around 2 times the width of the original guess at the width of the clump. This way
emphasis is on the small scale emission rather than large scale and the code will not, for example,
fit a Gaussian to the entire region. Several stiffness parameters ensure that the peak and centre
of the fits remain near to the originals and that points in the profile at all times have lower values
5.2. Method 100
than those in the real data. This is achieved via an exponential in the chi-squared term used to
fit the profiles which rises rapidly if the data value is larger than that of the original data. This
way, should two peaks lie close together they will not be fit by a single Gaussian. The code was
tested (by Stutzki& Gusten) on Monte-Carlo simulated data and reproduced fairly well the mass
functions of the clumps in the original data. However, in crowded regions the derived slopes of
the mass functions where slightly shallower than the inputs and when run on circular rather than
Gaussian clumps,GAUSSCLUMPStended to find smaller, false clumps near to the edges of the input
clumps.
5.2 Method
We first tested the response of the fourCUPID algorithms on four sets of noise-added synthetic
data, two sparsely populated with clumps and two more crowded. The data cubes were created
using the‘makeclumps’ programme, also part of theCUPID package, and have the same dimensions
as the HARP CO data for NGC 2024. Clumps have a Gaussian emission profile along all three
axes, the sizes, peak intensity and orientation of the clumps are randomly selected from a normal
distribution for which we choose the mean and width to be roughly similar to the GBS HARP data
sets. The sparse cube contains 50 clumps and the crowded 1000 clumps, the latter resulting in a
complex overlapping structure more similar to the real data. We ran the algorithms on 4 different
synthetic cubes. For the first two, clump properties were sampled from a normal distribution so
that we produced crowded and sparse cubes with mean peak intensities of 6 K and a fwhm for the
distribution of peaks of 3 K, mean sizes along axis one and two (the two spacial axis) of 7 pixels
(corresponding to a clump radius of 0.03 pc at the distance of NGC 2024) with a fwhm of 3 pixels.
Along the third (velocity) axis the clumps had a mean radius of 1 kms−1 (6 pixels) and a fwhm of
3 pixels. We also produced sparse and crowded cubes for which peak intensities and sizes were
the same for all clumps (equal to the mean values used for the first two cubes). We add noise at
a level of 0.23 K equal to that estimated in NGC 2024 C18O maps (in spectra from four separate
positions).
We tested the influence of user defined inputs on the behaviour of all four algorithms. For each
algorithm, there are several of these, all with suggested default values. We chose those that we
deemed to be the most important or most likely to affect the results. The parameters we tested,
their names, the behaviour they control and the values we used for each run are listed in Table 5.1.
Following the work on synthetic cubes we ran the algorithms again, with the same selection
5.2. Method 101
Table 5.1: Parameters Investigated
Clumpfind.Tlow Minimum data value of pixel to
be included in a clump
2,3,4,5,10 and 20×rms
Clumpfind.DeltaT Contour spacings used in initial
contouring of data
2,3,4,5 and 10×rms
Fellwalker.Noise Minimum data value of pixel to
be included in a clump
2,3,4,5 and 10×rms
Fellwalker.MinDip Minimum dip between clumps
before merging
3,4,5 and 10×rms
Fellwalker.FlatSlope Minimum gradient (over 3 pix-
els) that needs to be reached be-
fore pixels are included in clump
0.5,1,2,3,4 and 10
Reinhold.Noise Minimum data value of pixel to
be included in a clump
2,3,4,5,10 and 20×rms
Reinhold.MinLen Minimum length of clump along
any one axis
2,3,5,6,10 and 20 pixels
Reinhold.FlatSlope Minimum gradient (over 3 pix-
els) that needs to be reached be-
fore pixels are included in clump
0.5,1,2,3,4,5,6 and 10
Reinhold.CaIterations Number of times to apply ero-
sion to edges of clumps after di-
lation
1,2,3,5,6 and 8
Gaussclumps.Thresh Minimum peak value for the fit-
ted clumps
3,5,10 and 20×rms
Gaussclumps.MaxNF Number of times a the algorithm
attempts to fit a particular clump
50,75,100 and 300 times
5.3. Results 102
of input parameters, on C18O HARP maps for Taurus and NGC 2024, taken as part of the JCMT
GBS (see maps Chapter 4 for HARP images). We chose these clouds as representative of opposite
ends of the spectrum in terms of temperature and structure, NGC 2024 being much hotter and
more turbulent. We expect the structure of Taurus to be more like that of a sparsely populated
cube and NGC 2024 more like a crowded cube, but clearly the observed emission will be much
more complicated, not contained within separate Gaussian clumps as for the synthetic data.
Before clump-finding on the HARP maps, we binned the data in velocity to 0.15 kms−1. This
value is smaller than the maximum expected line width in the clouds due to thermal broadening
and so cores should be resolved. We also chose to convert the data to SNR (signal to noise ratio)
cubes in order that more weight be given to peaks with higher signal to noise. We ranCLUMPFIND
on both the original NGC 2024 data and an SNR cube with the same input parameters and found
that the run on the SNR cube did seem to be more sensitive to real structure in the maps, although
lowering the threshold intensity for the run on the original data cubes did increase the number of
clumps identified among those visible in the maps, a lot more noise (e.g. around the edges of the
map) was also attributed to clumps. To make the SNR cubes we used the‘makesnr’ command
available as part ofCUPID which divides pixels in the array by the square root of the variance
component. Spurious values (e.g. very large SNR values) are marked bad and are no longer
considered.
After locating clumps in the SNR cubes, we used the‘extractclumps’ command to find their
properties in the original data cube. This routine uses the clump perimeters identified after clump-
finding on the SNR data. However, the output clump properties are now based on the data within
the clump boundary in the original cube. Sizes and peak positions of these new clumps may
therefore vary from the first run, which results in the rejection of some clumps due to the fact that
their diameters may now be smaller than the beam width of the observations.
We outline the results of the parameter testing for each algorithm in turn (sections 5.3.1, 5.3.2,
5.3.3 and 5.3.4) before summarising their overall performance in section 5.4.
5.3 Results
Tables 5.2, 5.3, and 5.4 list the number of clumps identified for all runs and all algorithms on the
sparse, crowded, uniform and data cubes as well as extra runs for very crowded (5000 clumps)
synthetic cubes.
5.3. Results 103
Tabl
e5.
2:C
lum
pnu
mbe
rs-CL
UM
PF
IND
Tlo
wD
elta
TN
clum
ps
(sa)
Ncl
umps
(c)
Ncl
umps
(us)
Ncl
umps
(uc)
Ncl
umps
(vc)
Ncl
umps
(Tau
rus)
Ncl
umps
(NG
C20
24)
2×rm
s2×
rms
125
1930
109
1698
2964
223
931
3×rm
s2×
rms
8214
5979
1415
2474
5241
4
4×rm
s2×
rms
5512
6580
1447
2206
3128
3
5×rm
s2×
rms
4610
9178
1337
1955
1821
9
10×
rms
2×rm
s21
626
7212
9711
990
111
20×
rms
2×rm
s6
160
213
738
20
36
3×rm
s3×
rms
6611
5965
1186
1886
5531
6
3×rm
s4×
rms
5510
0162
1062
1639
3027
4
3×rm
s5×
rms
5489
767
1000
1451
2518
8
3×rm
s10×
rms
3965
658
843
984
172
a-‘s
’ref
ers
toru
nson
asp
arse
synt
hetic
cube
,‘c
’to
acr
owde
dcu
be,‘u
s’to
aun
iform
spar
secu
be,
‘uc’
toa
unifo
rmcr
owde
dcu
be
and‘v
c’to
ave
rycr
owde
dcu
be.
5.3. Results 104
Tabl
e5.
3:C
lum
pnu
mbe
rs-FE
LLW
ALK
ER
Noi
seM
inD
ipF
latS
lope
Ncl
umps
(s)
Ncl
umps
(c)
Ncl
umps
(us)
Ncl
umps
(uc)
Ncl
umps
(vc)
Ncl
umps
(Tau
rus)
Ncl
umps
(NG
C20
24)
2×rm
s2×
rms
1×rm
s40
563
4671
381
017
85
3×rm
s2×
rms
1×rm
s34
538
4772
478
711
67
4×rm
s2×
rms
1×rm
s30
515
4772
675
96
59
5×rm
s2×
rms
1×rm
s26
487
4772
674
35
54
10×
rms
2×rm
s1×
rms
1436
247
726
577
031
3×rm
s3×
rms
1×rm
s34
515
4769
473
32
58
3×rm
s4×
rms
1×rm
s34
496
4766
370
01
45
3×rm
s5×
rms
1×rm
s34
471
4662
365
41
42
3×rm
s10×
rms
1×rm
s33
367
4647
945
51
16
3×rm
s2×
rms
0.5×
rms
3453
847
724
788
1167
3×rm
s2×
rms
2×rm
s34
537
4772
578
411
69
3×rm
s2×
rms
3×rm
s33
541
4772
979
111
69
3×rm
s2×
rms
4×rm
s33
545
4772
879
011
71
3×rm
s2×
rms
10×
rms
3354
547
730
795
1172
5.3. Results 105
Tabl
e5.
4:C
lum
pnu
mbe
rs-RE
INH
OLD
Noi
seM
inLe
n
(pix
)
Fla
tSlo
peC
aIte
ratio
nsN
clum
ps(s
)N
clum
ps
(c)
Ncl
umps
(us)
Ncl
umps
(uc)
Ncl
umps
(vc)
Ncl
umps
(Tau
rus)
Ncl
umps
(NG
C20
24)
2×rm
s4
1×rm
s1
2044
843
674
650
03
3×rm
s4
1×rm
s1
2043
945
677
645
03
4×rm
s4
1×rm
s1
1742
142
639
624
02
5×rm
s4
1×rm
s1
1438
236
559
586
01
10×
rms
41×
rms
110
226
3240
640
30
0
20×
rms
41×
rms
13
641
4812
50
0
3×rm
s2
1×rm
s1
1942
944
652
625
02
3×rm
s3
1×rm
s1
1943
044
662
636
03
3×rm
s5
1×rm
s1
2145
347
706
662
03
3×rm
s6
1×rm
s1
2344
747
718
649
01
3×rm
s10
1×rm
s1
377
163
112
02
3×rm
s20
1×rm
s1
00
00
00
0
3×rm
s4
0.5×
rms
113
392
4360
358
80
3
3×rm
s4
2×rm
s1
2039
243
571
521
04
3×rm
s4
3×rm
s1
816
26
105
254
03
3×rm
s4
4×rm
s1
456
016
930
5
3×rm
s4
5×rm
s1
214
04
300
3
3×rm
s4
6×rm
s1
27
00
70
2
3×rm
s4
10×
rms
10
00
00
00
3×rm
s4
1×rm
s2
4469
750
906
1176
028
3×rm
s4
1×rm
s3
2395
2710
239
10
23
3×rm
s4
1×rm
s5
202
272
20
4
3×rm
s4
1×rm
s6
202
272
20
0
3×rm
s4
1×rm
s8
202
272
20
0
5.3. Results 106
Tabl
e5.
5:C
lum
pnu
mbe
rs-GA
US
SC
LUM
PS
Thr
esh
Max
NF
Ncl
umps
(s)
Ncl
umps
(c)
Ncl
umps
(us)
Ncl
umps
(uc)
Ncl
umps
(Tau
rus
SN
R)
Ncl
umps
(NG
C20
24
SN
R)
3×rm
s10
076
1547
8414
8353
109
5×rm
s10
076
1547
8414
8353
109
10×
rms
100
5285
957
870
5510
9
20×
rms
100
3147
5773
89
82
3×rm
s50
6513
0172
1371
1310
9
3×rm
s75
7419
7582
1575
9310
8
3×rm
s30
078
1459
8317
6273
109
5.3. Results 107
5.3.1 CLUMPFIND Results
We ran theCLUMPFIND routine, varying theTlow parameter which controls the minimum level of
emission (or data value) that is included in a clump andDeltaT, the contour level spacing (refer
to Table 5.1 for a description of the parameters). As expected, asTlow is increased, fewer clumps
are identified due to weaker peaks either falling below the threshold or the associated clumps
shrinking to such an extent that they contain too few pixels (the default value for the minimum
number of pixels in any one clump is 16). Figures 5.3-5.10 show the positions of clumps located
by CLUMPFIND at different values ofTlow andDeltaT as well as the positions of clumps in the
synthetic cubes (yellow). In synthetic cubes a single Gaussian clump does tend to be divided by
CLUMPFIND into two or more in the noise added cube. This is evident even at high values ofTlow
and so is likely due to noise spikes on top of a particular clump being identified as a second, nearby
clump. Noiseless cubes do not demonstrate this splitting. On occasions, higher thresholds can lead
to the identification of more clumps. This is only a small effect and is probably a result of clumps
being split at the higher contour level due to a small dip between two peaks which could lead to
both smaller clumps being rejected. IncreasingDeltaTcan reduce this division of clumps, but at
higher levels will miss finer structure in the emission. In Figures 5.15-5.22 we plot the sums (the
addition of intensity values for all pixels in the clump) and radii of the detected clumps asTlow
andDeltaTchange (as well as those in the synthetic cubes - shown in yellow).
On the Taurus and NGC 2024 HARP data, increasingTlow again has the effect of decreasing
the number of clumps found (see Figures 5.11-5.14 for positions of located clumps and 5.23-5.26
for their sums and radii with varyingTlow and DeltaT). At a Tlow of 2×rms the algorithm is
clearly allocating some of the noise to clumps. For Orion, in particular, clumps are found all over
the map (and in the original cube clumps are more often found where noise levels are higher, again
suggesting that many of these are due to noise spikes in the data). In addition, some striping is
evident which is probably an artifact of noise. This effect disappears at 4×rms. C18O emission in
Orion is very inhomogeneous and is located not in isolated regions but compressed into filaments
of emission. We see cores very near to each other which could either be due to coincident clumps
or due to noise splitting (which does likely occur as evident from runs on synthetic cubes.) Taurus
clump-finding locates isolated clumps and there is no apparent splitting for any value ofTlow.
Strangely, some cores are identified at aTlow of 3 and 5 that are not at aTlow of 4. This could
occur as a result of an undulation in a clump peak. The lowest contour forCLUMPFIND is always at
the threshold level, and contours placed at intervals ofDeltaTabove this, so that for four different
5.3. Results 108
values for the lowest contour the highest could miss the peaks entirely, the second hit one of the
two smaller peaks, the third hit both peaks and the lowest dissect a part of the clump where the
two peaks have merged. It is conceivable that the third contour could detect no clumps if the lower
peak were smaller. Pixels are shared out between the two peaks (according to a friends-of-friends
algorithm). In this way the larger peak could be assigned fewer pixels than it was actually due
and hence both clumps be rejected. In generalCLUMPFIND appears to overestimate peak values
very slightly for most of the clumps, badly overestimating at lower clump indices and producing
a large range of peak values at high clump indices (figure 5.1). This is probably an artifact of the
correction for beam size with both reduced the size of the clumps and increases its peak value. The
fact that this probably affects the brightest clumps to a larger extent could be due to the fact that
they tend to lie closer to the highest contour level than the small clumps to the contour level above.
CLUMPFIND assigns an index as it moves through the contour levels and detects more clumps so that
clumps with low indices will be those identified first, in the highest contour levels. Conversely,
apart from those with low indices, values for the sums of the clumps are underestimated (Figure
5.2). This is particularly clear for clumps with high indices. It is likely that the underestimated
sums (the addition of data, or intensity, values in all pixels lying within the clump radius) are due
to splitting of clumps for which the peak values are similar.
Figure 5.1: Peak values for synthetic uniform
clump catalogue andCLUMPFIND output
Figure 5.2: Sums for synthetic uniform clump
catalogue andCLUMPFIND output
5.3. Results 109
Figure 5.3:CLUMPFIND, clump positions - sparse cube, changing Tlow
Figure 5.4:CLUMPFIND, clump positions - crowded cube, changing Tlow
5.3. Results 110
Figure 5.5: CLUMPFIND, clump positions - uni-
form sparse cube, changing Tlow
Figure 5.6: CLUMPFIND, clump positions - uni-
form crowded cube, changing Tlow
Figure 5.7:CLUMPFIND, clump positions - sparse
cube, changing DeltaT
Figure 5.8: CLUMPFIND, clump positions -
crowded cube, changing DeltaT
Figure 5.9: CLUMPFIND, clump positions - uni-
form sparse cube, changing DeltaT
Figure 5.10:CLUMPFIND, clump positions - uni-
form crowded cube, changing DeltaT
5.3. Results 111
Figure 5.11:CLUMPFIND, clump positions - Tau-
rus, changing Tlow
Figure 5.12:CLUMPFIND, clump positions - Tau-
rus, changing DeltaT
Figure 5.13:CLUMPFIND, clump positions - NGC
2024, changing Tlow
Figure 5.14:CLUMPFIND, clump positions - NGC
2024, changing DeltaT
5.3. Results 112
Figure 5.15:CLUMPFIND, data sums - sparse cube, changing Tlow
Figure 5.16:CLUMPFIND, data sums - crowded cube, changing Tlow
5.3. Results 113
Figure 5.17: CLUMPFIND, data sums - uniform
sparse cube, changing Tlow
Figure 5.18: CLUMPFIND, data sums - uniform
crowded cube, changing Tlow
Figure 5.19:CLUMPFIND, data sums - sparse cube,
changing DeltaT
Figure 5.20: CLUMPFIND, data sums - crowded
cube, changing DeltaT
Figure 5.21: CLUMPFIND, data sums - uniform
sparse cube, changing DeltaT
Figure 5.22: CLUMPFIND, data sums - uniform
crowded cube, changing DeltaT
5.3. Results 114
Figure 5.23: CLUMPFIND, data sums - Taurus,
changing Tlow
Figure 5.24: CLUMPFIND, data sums - Taurus,
changing DeltaT
Figure 5.25:CLUMPFIND, data sums - NGC 2024,
changing DeltaT
Figure 5.26:CLUMPFIND, data sums - NGC 2024,
changing DeltaT
5.3. Results 115
In order to see how well each algorithm replicates the distribution of clumps (the CMFs) for
variations of the input parameters, we simulate CMFs using the sums of data values from clumps
in the synthetic cubes and calculating masses as if for emission from C18O (codes to do this were
provided by J.Roberts). These are not actual masses in any sense (rather the mass real clumps
would have should their C18O peak emission be the same as that of the synthetic clumps) but the
aim is to see how well CMFs derived from theCLUMPFIND outputs represent those of the synthetic
cubes. For Taurus and NGC 2024 we calculate LTE masses (mass of the clump assuming LTE,
see Appendix A) using the same technique, adjusting to suit the temperatures and distances of the
respective clouds. CMFs fromCLUMPFIND reflect the tendency of this algorithm to divide clumps
in a noise-added cube. From Figures 5.27-5.30, it is evident that the lower end of the CMF is
extended particularly for low values ofTlowwhere the algorithm is also attributing noise spikes to
clumps. For the uniform cubes (Figures 5.28 and 5.30),CLUMPFIND detects a range of masses and,
where onlyTlow is varying, actually reproduces a mass function very similar to those of the non-
uniform cubes. There is a visible peak or hump in the CMF where the actual input masses lie but
the CMF could easily be mis-interpreted, particularly in the sparse case where this is less evident.
High values ofDeltaT (larger contour spacings) reproduce the synthetic mass functions slightly
better because splitting effects are less severe (Figures 5.31-5.34) but such high contour spacings
will miss clumps and fine-structure. For the uniform cubes (Figures 5.32 and 5.34), CMFs are still
not well reproduced; however, they are shallower due to less splitting and probably some merging
of adjacent clumps.
5.3. Results 116
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cubealpha = 0.97
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=2*rmsalpha = 1.01
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=4*rmsalpha = 0.83
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - Tlow=10*rmsalpha = 0.93
Figure 5.27:CLUMPFIND, clump mass function - sparse cube, changing Tlow
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=2*rmsalpha = 0.84
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=4*rmsalpha = 0.64
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - Tlow=10*rmsalpha = 1.16
Figure 5.28:CLUMPFIND, clump mass function - sparse uniform cube, changing Tlow
5.3. Results 117
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cubealpha = 0.83
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=2*rmsalpha = 1.44
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=4*rmsalpha = 1.38
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - Tlow=10*rmsalpha = 1.43
Figure 5.29:CLUMPFIND, clump mass function - crowded cube, changing Tlow
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind Tlow=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - Tlow=10*rms
Figure 5.30:CLUMPFIND, clump mass function - crowded uniform cube, changing Tlow
5.3. Results 118
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cubealpha = 0.97
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=2*rmsalpha = 0.85
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=4*rmsalpha = 0.78
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - DeltaT=10*rmsalpha = 0.87
Figure 5.31:CLUMPFIND, clump mass function - sparse cube, changing DeltaT
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=2*rmsalpha = 0.49
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=4*rmsalpha = 0.50
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - DeltaT=10*rmsalpha = 0.67
Figure 5.32:CLUMPFIND, clump mass function - sparse uniform cube, changing DeltaT
5.3. Results 119
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cubealpha = 0.83
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=2*rmsalpha = 1.45
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=4*rmsalpha = 1.12
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - DeltaT=10*rmsalpha = 0.79
Figure 5.33:CLUMPFIND, clump mass function - crowded cube, changing DeltaT
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=2*rmsalpha = 0.37
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind DeltaT=4*rmsalpha = 0.43
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Clumpfind - DeltaT=10*rmsalpha = 0.10
Figure 5.34:CLUMPFIND, clump mass function - crowded uniform cube, changing DeltaT
5.3. Results 120
To see whether or notCLUMPFIND could effectively find the peak mass of a CMF, we produced
several sparse and crowded maps for which we varied the mean peak height (keeping the distribu-
tion width the same). CMFs are shown in Figures 5.35 and 5.36 for the synthetic cubes and the
CLUMPFIND outputs respectively. The peak of theCLUMPFIND-derived CMF does appear to move to
the right (to higher masses) along with the actual peak mass of the synthetic cube.
5.3. Results 121
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=10K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=30K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=100K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=1000K
Figure 5.35: Clump mass function - synthetic cubes, changing mean clump peak (fwhm of distri-
bution 5K)
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
cf23w5 (crowded) - mean peak=10K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
cf23w5 (crowded) - mean peak=30K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
cf23w5 (crowded) - mean peak=100K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
cf23w5 (crowded) - mean peak=1000K
Figure 5.36:CLUMPFIND, clump mass function -CLUMPFIND output (Tlow=3×rms, DeltaT=2×rms,
changing mean clump peak of input cube
5.3. Results 122
5.3.2 FELLWALKER Results
We ran theFELLWALKER algorithm a total of 14 times, varying first theNoiseparameter which
controls the lower threshold level for inclusion in a clump (asTlow for CLUMPFIND), MinDip which
determines how big the dip between two adjacent clumps must be before the two are considered
separate, and finally theFlatSlopeparameter which decides how steep the path from pixel toward
the clump peak must be before pixels are included in a clump. Figures 5.39-5.50 show positions of
clumps from theFELLWALKER output catalogues for different input parameter values and different
synthetic cubes. Figures 5.56-5.67 show sums and radii for the same clumps. Synthetic clumps are
shown in yellow.FELLWALKER tends to underestimate clump numbers, very slightly in the case of
the sparse cubes where only three or four clumps are missed, and to a larger extent for the crowded
cubes, where the algorithm detects around 70% of the clumps.FELLWALKER does not seem to find
clumps where there are none in the original cubes and so is likely merging some clumps. This
is supported by the fact that in the crowded cubes, where clumps are more often located near to
one and other, the effect is worse. TheNoiseparameter has a very small effect on clump numbers
in the uniform and sparse non-uniform cubes but detects over 50% too few clumps for a crowded
non-uniform cube when a value for theNoiseparameter of 10×rms is used due to clumps below
the threshold being missed. Interestingly,FELLWALKER detects slightly more clumps whenNoiseis
increased in the uniform cubes. Thresholding does not, in these cases, cause weaker clumps to be
missed because all clumps have roughly similar peaks so these increased numbers must be due to
reduced splitting and the second peak on an original clump lying below the threshold.FELLWALKER
underestimates clump radii and masses when high values of theNoiseparameter are used due to
truncation of the clumps at a higher level (see Figures 5.56-5.59). For the non-uniform cubes it
reproduces these rather better thanCLUMPFIND whenNoiseis set to 2×rms. When high values of
the threshold are applied to the uniform cubes, output sums and radii exhibit an interesting effect
(Figures 5.58 and 5.59). For a sparse uniform input cube, the majority of the clumps are assigned
the same mass and radii which is much lower than the input. The offset is reduced at lower levels
of Noiseand comes closest to the input for a value of 2×rms. This is fairly intuitive since, if the
correct clumps are being detected, the truncation at a higher level will reduce output radii and sums
to roughly the same extent for all clumps. Merged clumps appear as isolated points on sum vs.
radius plots at higher values. The same effect is seen in the crowded uniform cube but the effect of
merging is more severe and occurs for all values ofNoise. Sums and radii are located on the plots
in groups, probably those that have not been merged, those that have been merged with one other
5.3. Results 123
clump, three others and so on.FELLWALKER appears to be a very robust algorithm but one must note
that in crowded environments it will not do so well at finding two clumps located close by and will
tend to merge these into one even when clumps have Gaussian profiles and are definitely distinct.
Plots of the peak and sum values derived byFELLWALKER from the crowded uniform cubes (Figures
5.37 and 5.38) show evidence of merging creating a population of clumps with higher sum values.
The peaks are overestimated in some cases (for clumps with lower indices, those identified first)
which could suggest their being detected at higher contour levels.
Figure 5.37: Peak values for synthetic uniform
clump catalogue andFELLWALKER output
Figure 5.38: Sums for synthetic uniform clump
catalogue andFELLWALKER output
Variation of theMinDip parameter has very little effect on the sparse cubes (both uniform
and non-uniform) but tends to decrease identified clump numbers when it is increased for the
crowded cubes. This suggests a false merging of nearby clumps for higher levels ofMinDip. Low
values of this parameter are probably more suited to the identification of real clumps in a crowded
environment. Again the effects of merging are seen in the sum vs. radius plots with different
values ofMinDip (Figures 5.43-5.46). The sparse cubes are reproduced well for all values but for
the crowded cubes these values are over-estimated and are clumped in the uniform cube suggesting
again that this is the effect of a merging of two adjacent clumps. Unfortunately, merging occurs at
all values ofMinDip. It is less severe, however, at 2×rms than at 10×rms.
5.3. Results 124
Figure 5.39:FELLWALKER, clump positions - sparse cube, changing Noise
Figure 5.40:FELLWALKER, clump positions - crowded cube, changing Noise
5.3. Results 125
Figure 5.41:FELLWALKER, clump positions - uni-
form sparse cube, changing Noise
Figure 5.42:FELLWALKER, clump positions - uni-
form crowded cube, changing Noise
Figure 5.43: FELLWALKER, clump positions -
sparse cube, changing MinDip
Figure 5.44: FELLWALKER, clump positions -
crowded cube, changing MinDip
Figure 5.45:FELLWALKER, clump positions - uni-
form sparse cube, changing MinDip
Figure 5.46:FELLWALKER, clump positions - uni-
form crowded cube, changing MinDip
5.3. Results 126
Figure 5.47: FELLWALKER, clump positions -
sparse cube, changing FlatSlope
Figure 5.48: FELLWALKER, clump positions -
crowded cube, changing FlatSlope
Figure 5.49:FELLWALKER, clump positions - uni-
form sparse cube, changing FlatSlope
Figure 5.50:FELLWALKER, clump positions - uni-
form crowded cube, changing FlatSlope
Figure 5.51:FELLWALKER, clump positions - Tau-
rus, changing Noise
Figure 5.52:FELLWALKER, clump positions - NGC
2024, changing Noise
5.3. Results 127
Figure 5.53:FELLWALKER, clump positions - Tau-
rus, changing MinDip
Figure 5.54:FELLWALKER, clump positions - NGC
2024, changing MinDip
Figure 5.55:FELLWALKER, clump positions - Tau-
rus, changing FlatSlope
5.3. Results 128
Figure 5.56:FELLWALKER, data sums - sparse cube, changing Noise
Figure 5.57:FELLWALKER, data sums - crowded cube, changing Noise
5.3. Results 129
Figure 5.58: FELLWALKER, data sums - uniform
sparse cube, changing Noise
Figure 5.59: FELLWALKER, data sums - uniform
crowded cube, changing Noise
Figure 5.60: FELLWALKER, data sums - sparse
cube, changing MinDip
Figure 5.61: FELLWALKER, data sums - crowded
cube, changing MinDip
Figure 5.62: FELLWALKER, data sums - uniform
sparse cube, changing MinDip
Figure 5.63: FELLWALKER, data sums - uniform
crowded cube, changing MinDip
5.3. Results 130
Figure 5.64: FELLWALKER, data sums - sparse
cube, changing FlatSlope
Figure 5.65: FELLWALKER, data sums - crowded
cube, changing FlatSlope
Figure 5.66: FELLWALKER, data sums - uniform
sparse cube, changing FlatSlope
Figure 5.67: FELLWALKER, data sums - uniform
crowded cube, changing FlatSlope
Figure 5.68: FELLWALKER, data sums - Taurus,
changing Noise
Figure 5.69: FELLWALKER, data sums - Taurus,
changing FlatSlope
5.3. Results 131
Figure 5.70:FELLWALKER, data sums - NGC 2024,
changing Noise
Figure 5.71:FELLWALKER, data sums - NGC 2024,
changing MinDip
Figure 5.72:FELLWALKER, data sums - NGC 2024,
changing FlatSlope
5.3. Results 132
The algorithm, at least when used on this kind of synthetic data, is extremely robust against
changes to theFlatSlopeparameter. Clump numbers, sums and radii all change very little with
its increase or decrease for all synthetic cubes (Figures 5.47-5.50 and 5.64-5.67).FlatSlopeonly
applies when the pixel considered has a low data value so perhaps this is unsurprising since the
data (particularly synthetic) are unlikely to contain slow, low level undulations or clumps have
very extended, associated, low level emission.
The algorithm behaves similarly on the real Taurus and NGC 2024 data as it does on the
synthetic cubes (see Figures 5.51-5.55 for positions of identified clumps and Figures 5.68-5.72 for
data sums and radii). No runs appear to be picking up noise around the edges or noisy sections
of the maps as didCLUMPFIND. FELLWALKER again detects fewer clumps, either tending not to split
regions as much or merging nearby clumps. High levels of theNoiseparameter again appear to
exclude weaker clumps, the same clumps being detected but fewer of them with a higher threshold.
Calculated radii are smaller withNoiseset to higher values however the masses do not appear to be
affected in the same way as the synthetic cubes. This could suggest a more peaked emission to the
clumps in the real data than the Gaussian profiles in the synthetic cubes. Higher values ofMinDip
than the default 2×rms manage to locate only 2 or fewer clumps in the Taurus data. Increasing
MinDip should result in more merging as increasing numbers of pairs will have intervening dips
below this value. Although they appear fairly far apart, some clumps listed in the output catalogue
are larger than their average separation. It is possible that clumps are merging for higher values of
MinDip. Radii and masses for the clumps at highMinDip are larger as would be expected in this
case. Alteration of theFlatslopeparameter again makes very little difference to theFELLWALKER
output catalogues, none in the case of Taurus. Four extra clumps are detected withFlatSlopeset to
4×rms than set to 0.5×rms in the NGC 2024 data cube. Perhaps in these cases a lower level bump
in the emission is missed when the algorithm is forced to begin including pixels in clumps only
when the slope is steeper. This could prevent segregation of the original clump and its rejection
due to size.
CMFs vary quite little with the input parameters in the case of all three tested. These are
plotted for different values of theNoiseparameter and for all synthetic cubes in Figures 5.72-5.84.
For synthetic cubes they do not, asCLUMPFIND, represent a spread of masses but masses located in
bins near to the actual mass of the input cubes (see for example Figures 5.74 and 5.76). There is a
little spread but this does not particularly worsen with the increase or decrease of any parameter.
Mass functions in the non-uniform cubes (e.g. Figures 5.73 and 5.75) miss the lower mass end
due to merging which also slightly decreases the slope at the high mass end.
5.3. Results 133
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - Noise=10*rms
Figure 5.73:FELLWALKER, clump mass function - sparse cube, changing Noise
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - Noise=10*rms
Figure 5.74:FELLWALKER, clump mass function - uniform sparse cube, changing Noise
5.3. Results 134
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - Noise=10*rms
Figure 5.75:FELLWALKER, clump mass function - crowded cube, changing Noise
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - Noise=10*rms
Figure 5.76:FELLWALKER, clump mass function - uniform crowded cube, changing Noise
5.3. Results 135
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - MinDip=10*rms
Figure 5.77:FELLWALKER, clump mass function - sparse cube, changing MinDip
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - MinDip=10*rms
Figure 5.78:FELLWALKER, clump mass function - uniform sparse cube, changing MinDip
5.3. Results 136
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - MinDip=10*rms
Figure 5.79:FELLWALKER, clump mass function - crowded cube, changing MinDip
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker MinDip=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - MinDip=10*rms
Figure 5.80:FELLWALKER, clump mass function - uniform crowded cube, changing MinDip
5.3. Results 137
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - FlatSlope=10*rms
Figure 5.81:FELLWALKER, clump mass function - sparse cube, changing FlatSlope
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - FlatSlope=10*rms
Figure 5.82:FELLWALKER, clump mass function - uniform sparse cube, changing FlatSlope
5.3. Results 138
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - FlatSlope=10*rms
Figure 5.83:FELLWALKER, clump mass function - crowded cube, changing FlatSlope
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Fellwalker - FlatSlope=10*rms
Figure 5.84:FELLWALKER, clump mass function - uniform crowded cube, changing FlatSlope
5.3. Results 139
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=10K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=30K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=100K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
synthetic crowded cube - mean peak=1000K
Figure 5.85: Clump mass function - synthetic cubes, changing mean clump peak (fwhm of distri-
bution 5K)
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
fw_2_3_1 on crowded cube - peak=10K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
fw_2_3_1 on crowded cube - peak=30K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
fw_2_3_1 on crowded cube - peak=100K
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
fw_2_3_1 on crowded cube - peak=1000K
Figure 5.86:FELLWALKER, clump mass function -FELLWALKER output changing mean clump peak
of input cube
5.3. Results 140
We again tested the algorithms ability to reproduce CMFs from synthetic cubes with different
mean peak values for the clumps (Figures 5.85 and 5.86).FELLWALKER tends to overestimate the
masses in some cases but does well at representing the CMFs in others. The performance of the
algorithm could have more to do with the distribution of clumps in a cube (hence the capacity for
merging) than other parameters.
5.3.3 REINHOLD Results
RIENHOLD underestimates clump numbers and severely underestimates clump radii and in most
cases clump sum values. This is so in the case of uniform and non-uniform, sparse and crowded
cubes. Figures 5.87 and 5.88 show clump peaks and sums for a uniform crowded synthetic cube
and those identified in the same cube withREINHOLD. See Figures 5.77-5.92 for clump positions
and Figures 5.93-5.108 for sums and radii. Changing the lower threshold (Noise) does not seem to
change the distribution of radii and masses output by the code for a non-uniform cube very much.
Probably, sizes are so underestimated in any case that the clumps are not being truncated any
differently. On uniform synthetic cubes, however, larger values forNoisedo lead to different sums
and radii. The output clumps are still too small but they are underestimated to a larger extent for
higherNoise. From plots of the positions of identified clumps, the algorithm fails to identify quite
a few clumps at all values of this parameter, particularly in the non-uniform cubes. The algorithm
occasionally manages to locate a clump when a higherNoiseis input than for lower values. This
could simply be due to the shape of the clump at different threshold levels, which could allow
the filling routine to perform better or differently resulting in the identification of a larger clump
where the edges lie at higher pixel values.
Figure 5.87: Peak values for synthetic uniform
clump catalogue andREINHOLD output
Figure 5.88: Sums for synthetic uniform clump
catalogue andREINHOLD output
5.3. Results 141
The parameterMinLen, which controls the minimum number of pixels spanned by a clump on
any one of the three axis, makes a big difference to the output clump numbers, though not their
masses and radii to such an extent. In general the number of clumps identified seems to increase up
to a value of around 5 and then decrease rapidly. The initial increase in clump numbers is puzzling
as one would expect this parameter simply to lead to the exclusion of smaller or elongated clumps.
The effect could be complicated though, since the code considers single profiles of pixel values
separately and the shape of the clump will have a large influence on what happens when its edges
are eroded and dilated or when the clump is filled. Very large values ofMinLendo appear to lead
to ‘leakages’ at the filling stage, probably because many more profiles are being rejected leading
to holes in clump edges.
5.3. Results 142
Figure 5.89:REINHOLD, clump positions - sparse cube, changing Noise
Figure 5.90:REINHOLD, clump positions - crowded cube, changing Noise
5.3. Results 143
Figure 5.91: REINHOLD, clump positions - uni-
form cube, changing Noise
Figure 5.92: REINHOLD, clump positions - uni-
form crowded cube, changing Noise
Figure 5.93:REINHOLD, clump positions - sparse
cube, changing MinLen
Figure 5.94: REINHOLD, clump positions -
crowded cube, changing MinLen
Figure 5.95: REINHOLD, clump positions - uni-
form sparse cube, changing MinLen
Figure 5.96: REINHOLD, clump positions - uni-
form crowded cube, changing MinLen
5.3. Results 144
Figure 5.97:REINHOLD, clump positions - sparse
cube, changing FlatSlope
Figure 5.98: REINHOLD, clump positions -
crowded cube, changing FlatSlope
Figure 5.99: REINHOLD, clump positions - uni-
form sparse cube, changing FlatSlope
Figure 5.100:REINHOLD, clump positions - uni-
form crowded cube, changing FlatSlope
Figure 5.101:REINHOLD, clump positions - sparse
cube, changing CaIterations
Figure 5.102: REINHOLD, clump positions -
crowded cube, changing CaIterations
5.3. Results 145
Figure 5.103:REINHOLD, clump positions - uni-
form sparse cube, changing CaIterations
Figure 5.104:REINHOLD, clump positions - uni-
form crowded cube, changing CaIterations
5.3. Results 146
Figure 5.105:REINHOLD, data sums - sparse cube, changing Noise
Figure 5.106:REINHOLD, data sums - crowded cube, changing Noise
5.3. Results 147
Figure 5.107: REINHOLD, data sums - uniform
sparse cube, changing Noise
Figure 5.108: REINHOLD, data sums - uniform
crowded cube, changing Noise
Figure 5.109:REINHOLD, data sums - sparse cube,
changing MinLen
Figure 5.110: REINHOLD, data sums - crowded
cube, changing MinLen
Figure 5.111: REINHOLD, data sums - uniform
sparse cube, changing MinLen
Figure 5.112: REINHOLD, data sums - uniform
crowded cube, changing MinLen
5.3. Results 148
Figure 5.113:REINHOLD, data sums - sparse cube,
changing FlatSlope
Figure 5.114: REINHOLD, data sums - crowded
cube, changing FlatSlope
Figure 5.115: REINHOLD, data sums - uniform
sparse cube, changing FlatSlope
Figure 5.116: REINHOLD, data sums - uniform
crowded cube, changing FlatSlope
Figure 5.117:REINHOLD, data sums - sparse cube,
changing CaIterations
Figure 5.118: REINHOLD, data sums - crowded
cube, changing CaIterations
5.3. Results 149
Figure 5.119: REINHOLD, data sums - uniform
sparse cube, changing CaIterations
Figure 5.120: REINHOLD, data sums - uniform
crowded cube, changing CaIterations
In contrast toFELLWALKER, theFlatSlopeparameter hugely affects the output when theREIN-
HOLD algorithm is run. Almost no clumps are identified at a value of 5×rms. The parameter in this
case works quite differently in the sense that, while forFELLWALKER it controls where a clump is
allowed to begin (and only below a certain data value), here it controls where a clump ends. If the
gradient over two adjacent pixels falls below this value the clump is truncated. Where data values
vary a lot over consecutive pixels (as they likely will due to noise effects), peaks will be truncated
very quickly and rejected due to size.
We ran the algorithm again eroding the clump edges once, twice and five times (controlled
by the parameterCaIterations). Running the erosion routine any more than once resulted first in
extreme leakages during clump filling and later in failure to identify clumps at all, probably due to
edges being completely eroded. It is possible that when working with less noisy data this routine
could be more useful.
REINHOLD completely failed when used on the Taurus and NGC 2024 HARP maps. For Taurus
it did not identify any clumps at all for any combination of input parameters, and for NGC 2024
only very few except at middling values ofCaIterationswhich, on inspection, produced extremely
strange shaped clumps with protrusions caused by leaking.
CMFs are not reproduced too badly by the algorithm where sufficient clumps are identified.
See Figures 5.121-5.132 for CMFs derived from synthetic cubes andREINHOLD runs on the same
cubes with input parameter values changed (we do not produce CMFs for runs for which we varied
theCaIterationsparameter as these suffer very badly from the leaking that occurs during the clump
filling process). For crowded cubes, the high mass end of the CMF is steeper than for the input
5.3. Results 150
cube with slightly more low mass clumps being identified (although this is a very small effect - see
Figure 5.123 for example). On uniform cubes, distributions strongly peaked at masses just lower
than the input clumps are recovered (Figure 5.124). CMFs are similar for increasing values of the
Noiseparameter until very few clumps are recovered at 10×rms (Figures 5.121-5.124). The same
is true forMinLen andFlatSlope(Figures 5.125-5.132) in that when very high values are used,
few clumps are identified.
5.3. Results 151
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cubealpha = 0.97
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=2*rmsalpha = 0.67
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=4*rmsalpha = 0.67
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=10*rmsalpha = 0.42
Figure 5.121:REINHOLD, clump mass function - sparse cube, changing Noise
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=10*rms
Figure 5.122:REINHOLD, clump mass function - uniform sparse cube, changing Noise
5.3. Results 152
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cubealpha = 0.99
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=2*rmsalpha = 1.89
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=4*rmsalpha = 1.85
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=10*rmsalpha = 1.54
Figure 5.123:REINHOLD, clump mass function - crowded cube, changing Noise
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=4*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - Noise=10*rms
Figure 5.124:REINHOLD, clump mass function - uniform crowded cube, changing Noise
5.3. Results 153
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cubealpha = 0.97
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=2*rmsalpha = 0.68
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=5*rmsalpha = 0.69
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=10*rms
Figure 5.125:REINHOLD, clump mass function - sparse cube, changing MinLen
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Uniform Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=6*rms
Figure 5.126:REINHOLD, clump mass function - uniform sparse cube, changing MinLen
5.3. Results 154
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cubealpha = 0.99
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=2*rmsalpha = 1.84
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=5*rmsalpha = 1.85
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=10*rms
Figure 5.127:REINHOLD, clump mass function - crowded cube, changing MinLen
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - MinLen=10*rms
Figure 5.128:REINHOLD, clump mass function - uniform crowded cube, changing MinLen
5.3. Results 155
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Sparse Cubealpha = 0.97
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=0.5*rmsalpha = 0.70
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=5*rms
Figure 5.129:REINHOLD, clump mass function - sparse cube, changing FlatSlope
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Sparse Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=2*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=3*rms
Figure 5.130:REINHOLD, clump mass function - uniform sparse cube, changing FlatSlope
5.3. Results 156
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Crowded Cubealpha = 0.99
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=0.5*rmsalpha = 2.03
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=3*rmsalpha = 1.17
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=5*rmsalpha = 0.47
Figure 5.131:REINHOLD, clump mass function - crowded cube, changing FlatSlope
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Uniform Crowded Cube
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=0.5*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=3*rms
-2 -1 0 1 2log[M/Msun]
-2
-1
0
1
2
3
4
5
log[
dN/d
M]
Reinhold - FlatSlope=5*rms
Figure 5.132:REINHOLD, clump mass function - uniform crowded cube, changing FlatSlope
5.3. Results 157
5.3.4 GAUSSCLUMPS Results
In the case ofGAUSSCLUMPSwe tested theThreshandMaxNFparameters, which control the mini-
mum peak height of the fitted Gaussians and the maximum number of attempted fits allowed for a
single clump. Figures 5.133 and 5.134 show the peak and data sums determined by the algorithm
in comparison to the input data for a crowded uniform data set. Figures 5.135-5.142 show the
positions of identified clumps for different choices of the input parameters alongside those of the
original synthetic cubes and Figures 5.143-5.150 show the data sums and radii for the equivalent
clumps. IncreasingThreshresulted in the identification of fewer clumps which appeared, in most
cases, to be due not to the identification of spurious clumps but to the splitting of clumps. This
splitting is probably a result of noise spikes on top of clumps that were already being fit. These
would remain in the residual map and fit later as a separate clump. A population of small, weak
clumps are found for threshold levels of 3×rms which disappear when higher peak thresholds are
used (Figures 5.143-5.146). In all cases, however,GAUSSCLUMPSfails to identify small but strongly
emitting regions (e.g. clumps that have low radii but high sum values). This is probably due to
the problem of fitting Gaussians to clumps that do not necessarily share this profile. Although the
input cubes are Gaussian, the addition of a noise component will change the shape of the clumps
and the residuals, which may be fit byGAUSSCLUMPS. When a very high threshold level is used
(20×rms) the algorithm appears to perform well for the uniform synthetic sets but less so for the
non-uniform data for which many of the real, smaller clumps are missed.
Figure 5.133: Peak values for synthetic uniform
clump catalogue andGAUSSCLUMPSoutput
Figure 5.134: Sums for synthetic uniform clump
catalogue andGAUSSCLUMPSoutput
5.3. Results 158
Figure 5.135:GAUSSCLUMPS, clump positions - sparse cube, changing Thresh
Figure 5.136:GAUSSCLUMPS, clump positions - crowded cube, changing Thresh
5.3. Results 159
Figure 5.137: GAUSSCLUMPS, clump positions -
sparse uniform cube, changing Thresh
Figure 5.138: GAUSSCLUMPS, clump positions -
crowded uniform cube, changing Thresh
Figure 5.139: GAUSSCLUMPS, clump positions -
sparse cube, changing MaxNF
Figure 5.140: GAUSSCLUMPS, clump positions -
crowded cube, changing MaxNF
Figure 5.141: GAUSSCLUMPS, clump positions -
sparse uniform cube, changing MaxNF
Figure 5.142: GAUSSCLUMPS, clump positions -
crowded uniform cube, changing MaxNF
5.3. Results 160
Figure 5.143:GAUSSCLUMPS, clump data sums - sparse cube, changing Thresh
Figure 5.144:GAUSSCLUMPS, clump data sums - crowded cube, changing Thresh
5.3. Results 161
Figure 5.145:GAUSSCLUMPS, clump data sums -
sparse uniform cube, changing Thresh
Figure 5.146:GAUSSCLUMPS, clump data sums -
crowded uniform cube, changing Thresh
Figure 5.147:GAUSSCLUMPS, clump data sums -
sparse cube, changing MaxNF
Figure 5.148:GAUSSCLUMPS, clump data sums -
crowded cube, changing MaxNF
Figure 5.149:GAUSSCLUMPS, clump data sums -
sparse uniform cube, changing MaxNF
Figure 5.150:GAUSSCLUMPS, clump data sums -
crowded uniform cube, changing MaxNF
5.3. Results 162
The MaxNF parameter appears to make very little difference in the output cubes (Figures
5.139-5.142 and 5.147-5.150). A slight increase in the number of clumps identified is seen as
the number of fitting attempts is increased. The extra clumps that are found, however, appear
to be smaller and are likely caused by the algorithm fitting to noise spikes on the original input
clumps. There is evidence of a small number of clumps having overestimated fluxes and sizes for
the uniform synthetic cubes in all runs (Figures 5.149 and 5.150). Looking closely at the output
catalogues and masks for these clumps this appears to be due to an overestimate of the clump
size along all three axis. Peak heights are also slightly overestimated. Underestimates are often
due to splitting of clumps and appear to affect the resulting sum data values more than the radii.
GAUSSCLUMPSmay be fitting rather wide, low-level Gaussians to residuals on pre-identified clumps.
BecauseGAUSSCLUMPS, unlike the other three algorithms tested, does not produce an output
catalogue containing unique identifiers for each pixel within a clump, the‘extractclumps’ com-
mand cannot be used. Clump-finding on the SNR data is thus not possible. We carried out several
runs on the original data but even with the selection of input parameters that would be expected
to return the most clumps (a lower threshold for the clump peaks of 2×rms and aMaxNFof 300)
we found only 2 clumps in the Orion data and none in the Taurus data. This is probably caused by
the difficulty of fitting Gaussian profiles to emission that may be far from this in reality. The two
clumps we did find in Orion (which were also detected with aThreshvalue of 3×rms andMaxNF
100) were large, and together covered the brightest region of the map.
CMFs did not appear to be strongly influenced by the alteration of theMaxNFparameter (Fig-
ures 5.155-5.158). Peak threshold levels of around 10×rms could reproduce the input functions
quite well for the non-uniform cubes but failed for uniform cubes where, similarly toCLUMPFIND
but still more evident, they produced output functions with a range of masses and a peak where the
real input masses lay (Figures 5.151-5.154). The large number of false or split low mass clumps
identified is clear.
5.3. Results 163
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Sparse cubealpha = 0.84
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=3*rmsalpha = 1.05
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=10*rmsalpha = 0.98
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=20*rmsalpha = 1.06
Figure 5.151:GAUSSCLUMPS, clump mass function - sparse cube, changing Thresh
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Sparse uniform cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=3*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=10*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=20*rms
Figure 5.152:GAUSSCLUMPS, clump mass function - sparse uniform cube, changing Thresh
5.3. Results 164
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Crowded cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=3*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=10*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=20*rms
Figure 5.153:GAUSSCLUMPS, clump mass function - crowded cube, changing Thresh
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Crowded uniform cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=3*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=10*rms
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps Thresh=20*rms
Figure 5.154:GAUSSCLUMPS, clump mass function - uniform crowded cube, changing Thresh
5.3. Results 165
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Sparse cubealpha = 0.84
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=50alpha = 0.99
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=75alpha = 1.04
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=300alpha = 1.04
Figure 5.155:GAUSSCLUMPS, clump mass function - sparse cube, changing MaxNF
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Sparse uniform cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=50
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=75
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=300
Figure 5.156:GAUSSCLUMPS, clump mass function - uniform sparse cube, changing MaxNF
5.3. Results 166
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Crowded cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=50
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=75
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=300
Figure 5.157:GAUSSCLUMPS, clump mass function - crowded cube, changing MaxNF
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Crowded uniform cube
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=50
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=75
-3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Gaussclumps MaxNF=300
Figure 5.158:GAUSSCLUMPS, clump mass function - uniform crowded cube, changing MaxNF
5.4. Summary and Comparison 167
5.4 Summary and Comparison
Overall, CLUMPFIND has a tendency to divide single clumps quite often due to noise spikes near
to clump peaks. As a result it underestimates average clump radii and masses. CMFs are skewed
more towards the lower masses than are the input distributions and one sees a large spread in output
clump masses even for a uniform input distribution. The algorithm is quite sensitive to the two
input parameters tested and one clearly needs to use a threshold noise level of 4×rms when dealing
with cubes such as the HARP Taurus and NGC 2024 C18O maps to avoid attributing a lot of noise
to clumps.FELLWALKER will merge rather than split clumps and will tend to miss smaller clumps
and fine detail in the emission structure. However, it does quite well at matching clump sizes,
masses, numbers and CMFs, at least when the clumps are Gaussian in profile and does not appear
to be particularly affected by noise in the maps. The algorithm is also more robust to changes in
the input parameters than the others.REINHOLD badly underestimates clump sizes in all cases and
suffers from problems with its cleaning and filling routines.GAUSSCLUMPS, while fairly insensitive
to changes in the two input parameters we tested, splits clumps as doesCLUMPFIND and has real
trouble fitting clumps when used on real, noisy data that probably contains highly non-Gaussian
clump profiles.
In order to aid comparison of the four algorithms, we include Tables 5.6, 5.7, 5.8 and 5.9,
which list input clump numbers, mean radii and masses, and the output values after runs with
each algorithm and for each combination of input parameters. Obviously this is only a very rough
comparison as we only compare with one input map (the sparse map). Results may differ for a
crowded cube. It is also difficult to pick out one best algorithm or one best set of input parameters
solely from the information in this table, as different inputs effect the output values of different
properties differently, and there are other factors to consider, such as leaking in the case ofREIN-
HOLD or performance on real data. Despite this, we try to give a qualitative idea of which may
be the best choices of input parameters. It is evident from Table 5.6 thatCLUMPFIND tends to un-
derestimate mean clump masses and radii. Mean masses, radii and clump numbers have a wide
range of values depending on the input parameters used. It appears that higher values ofTlowand
values of between 5 and 10×rms forDeltaTgive better matches to the input cube. The algorithm,
however, tends to underestimate masses and radii in general and the higher mean mass and radii
for higher values of the input parameters is due to merging or to missing lower intensity clumps.
FELLWALKER does the best of the four algorithms at reproducing mean masses for the cubes. What
is more, these do not vary much with the alteration of any of the input parameters that we investi-
5.4. Summary and Comparison 168
gate. Clump numbers and radii are always slightly underestimated. But, as long as a lower value of
the threshold parameterNoiseis used this effect is not too extreme (these properties, like the mean
masses, do not vary significantly when different values ofMinDip andFlatSlopeare used. Again
these results point toFELLWALKER as an extremely robust algorithm against changes to the user
defined inputs. TheREINHOLD algorithm underestimates mean radii, masses and clump numbers
despite varying the user defined input parameters. Higher values of theCaIterationsparameter
appear from Table 5.8 to give a better fit, however it is clear upon inspection of the output masks
that running the erosion routine any more than once or twice results in the appearance of holes in
the clump edges defined by theREINHOLD and prominence-like shapes emerging during the filling
process. Setting theNoiseparameter to around 4×rms or 5×rms gives the best fit to the mean
masses in the input cube, however clump numbers are best fit using a lower value for this param-
eter. The parameterMinDip makes little difference to the output mean masses, radii and clump
numbers unless a very high value is used (around 10×rms), in which case clumps are merged by
the algorithm into only a few, much larger condensations. A value of around 2 for the parameter
FlatSlopeappears to give the best fit to the mean radii, masses and clump numbers, and at higher
values, clump numbers are severely underestimated.GAUSSCLUMPStends to overestimate clump
numbers and underestimate masses and, in most cases, radii. The best fit to the mean masses,
radii and clump numbers appears to be for rather high values of theThreshparameter, controlling
the minimum level of emission for inclusion within a clump. At values at or above 10×rms how-
ever, many of the weaker, smaller clumps will be missed. Lower values for the parameterMaxNF
appear preferable.
5.4. Summary and Comparison 169
Tabl
e5.
6:C
LUM
PF
IND
perf
orm
ance
Tlo
w
(×rm
s)
Del
taT
(×rm
s)
Inpu
tm
ean
mas
s(M
)
Out
put
mea
nm
ass
(M
)
Inpu
tm
ean
radi
us(p
c)
Out
put
mea
n
radi
us(p
c)
Inpu
t
clum
p
num
bers
Out
put
clum
p
num
bers
22
9.99
3.06
0.02
70.
016
4312
5
23
4.11
0.01
682
24
5.43
0.01
755
25
5.65
0.01
646
210
7.23
0.01
621
220
6.41
0.01
46
23
4.11
0.01
682
33
5.12
0.01
766
43
6.15
0.01
855
53
6.30
0.01
754
103
8.60
0.01
939
5.4. Summary and Comparison 170
Tabl
e5.
7:F
ELL
WA
LKE
Rpe
rfor
man
ce
Noi
se
(×rm
s)
Min
Dip
(×rm
s)
Fla
tSlo
pe
(×rm
s)
Inpu
tm
ean
mas
s(M
)
Out
put
mea
nm
ass
(M
)
Inpu
tm
ean
radi
us(p
c)
Out
put
mea
n
radi
us(p
c)
Inpu
t
clum
p
num
bers
Out
put
clum
p
num
bers
22
19.
999.
330.
027
0.02
543
40
32
19.
820.
023
34
42
19.
830.
022
30
52
110
.18
0.02
126
102
110
.40
0.01
814
33
19.
820.
023
34
34
19.
880.
023
34
35
19.
880.
023
34
310
110
.19
0.02
333
32
0.5
9.83
0.02
334
32
19.
820.
023
34
32
29.
780.
023
34
32
39.
960.
023
33
32
49.
920.
023
33
32
109.
860.
023
33
5.4. Summary and Comparison 171
Tabl
e5.
8:R
EIN
HO
LDpe
rfor
man
ce
Noi
se
(×rm
s)
Min
Len
(pix
els)
Fla
tSlo
pe
(×rm
s)
CaI
tera
tions
Inpu
tm
ean
mas
s(M
)
Out
put
mea
nm
ass
(M
)
Inpu
tm
ean
radi
us(p
c)
Out
put
mea
nra
dius
(pc)
Inpu
tcl
ump
num
bers
Out
put
clum
p
num
bers
24
11
9.99
7.96
0.02
70.
016
4320
34
11
7.88
0.01
520
44
11
8.24
0.01
617
54
11
8.62
0.01
614
104
11
7.37
0.01
410
204
11
4.95
0.01
03
32
11
7.90
0.01
519
33
11
7.96
0.01
519
35
11
7.67
0.01
521
36
11
7.44
0.01
623
310
11
20.3
60.
031
3
34
0.5
18.
920.
018
13
34
11
7.88
0.01
520
34
21
9.24
0.01
920
34
31
10.8
10.
020
8
34
41
10.8
90.
020
4
34
51
11.9
00.
021
2
34
61
10.2
30.
019
2
34
11
7.88
0.01
520
34
12
6.81
0.01
744
34
13
8.37
0.01
723
34
15
9.38
0.01
720
34
16
9.38
0.01
720
34
18
9.38
0.01
720
5.4. Summary and Comparison 172
Tabl
e5.
9:G
AU
SS
CLU
MP
Spe
rfor
man
ce
Thr
esh
(×rm
s)
Max
NF
Inpu
tm
ean
mas
s(M
)
Out
put
mea
nm
ass
(M
)
Inpu
tm
ean
radi
us(p
c)
Out
put
mea
n
radi
us(p
c)
Inpu
t
clum
p
num
bers
Out
put
clum
p
num
bers
210
09.
995.
400.
027
0.02
243
76
310
05.
400.
022
76
510
05.
400.
022
76
1010
07.
730.
026
52
2010
011
.89
0.03
131
350
6.27
0.02
465
375
5.53
0.02
274
310
05.
400.
022
76
330
05.
250.
022
78
5.4. Summary and Comparison 173
It is clear from the tables, as from the plots, thatCLUMPFIND andREINHOLD both underestimate
clump radii and masses. ForCLUMPFIND this is a result of splitting due to noise (as evidenced by
overestimated clump numbers).GAUSSCLUMPSoverestimates clump numbers and underestimates
masses (again this may point to splitting of clumps asGAUSSCLUMPSmay try to fit residuals left
after fitting previous clumps). From the table it appears to give a rather accurate estimated of the
radius as compared to the other algorithms.FELLWALKER is the only algorithm that occasionally
seems to overestimate clump masses. It has a tendency to merge clumps that are close together
in the input map. The output catalogues, however, are the closest to the input data and the code
seems to provide similar results no matter what the input parameters.FELLWALKER also manages to
reproduce CMFs well which is important as these are often used as a diagnostic of star formation
processes in molecular clouds.CLUMPFIND worryingly produces very similar CMFs for uniform
cubes with clumps of one mass as those with a spread in the masses. The other codes do better
in this respect and show a definite peak in masses at the correct mass range for uniform input
cubes.GAUSSCLUMPSworks reasonably well on synthetic cubes with Gaussian clumps, however it
has problems fitting real data in which clumps are non-Gaussian and have a range of flux distribu-
tions. REINHOLD suffers from leakages and also struggles to fit to real data. After considering the
performance of the four algorithms on both synthetic and real data, looking at how well they repro-
duce properties of the input cubes and commonly used diagnostics such as CMFs, and considering
sensitivity to user defined input parameters, we conclude the theFELLWALKER algorithm is the best
choice for use on our GBS HARP data, and that the choice of value for the input parameters should
matter little to the resulting clump catalogue so long as the input value for theNoiseparameter is
not set too high (above around 4×rms clumps will be missed, however set this parameter too low
and one risks detecting noise in the data as clumps). The next chapter details the results of our
clumpfinding study on the HARP data, during which we try to bear in mind problems with the
code discovered in this study such as merging of nearby clumps and the resulting overestimation
of clump masses.
CHAPTER 6
PROPERTIES OF CO CLUMPS IN THE GOULD
BELT CLOUDS
Following the work outlined in Chapter 5, in which the performance of 4 different clump decom-
position algorithms were tested, the most suitable is chosen and used to investigate the structure
of CO emission in 5 star-forming regions within the Gould belt, namely NGC 2024 and 2071 in
Orion, Ophiuchus, Serpens and Taurus (L1495). These represent a range of physical conditions,
are nearby allowing for high resolution mapping, and consistent CO data is available for all of
them so that a good statistical comparison should be possible (see Chapter 4 for a description of
the data).
It has been common over the past couple of decades to study star-forming regions in either the
dust continuum or high density molecular tracers, using algorithms such asCLUMPFIND (Williams
et al. (1994)) to decompose maps into discrete regions of strong emission. The initial mass func-
tion (IMF) of stellar objects appears to be fairly universal (Scalo(1986), Kroupa & Boily (2002)),
following what is known as the Salpeter relation, the differential mass function having a slope of
-2.3. The clump mass function (CMF) for dense cores seems to follow a similar relation, which
has lead many authors to conclude that the IMF is set early on during the star formation process
(Testi & Sargent(1998); Walshet al. (2007); Andre et al. (2010)). While there are plenty of pa-
pers focusing on the decomposition of CO data, these are generally in the J=(1→0) lines which
have lower critical densities than the (3→2) lines mapped for the GBS. Most other decomposition
studies seem to deal with either the 2D dust continuum or other molecular tracers such as HCO+.
In the GBS first look paper on Orion B,Buckleet al. (2010) useCLUMPFIND to identify small,
dense condensations in13CO (3→2). They find 1561 clumps in NGC 2024 and 1399 in NGC
174
175
2071 with average radii of 0.018 pc (NGC 2024) and 0.075 (NGC 2071), and LTE masses of 0.52
M (NGC 2024) and 0.22 M (NGC 2071). The authors went on to calculate virial masses for
the clumps, for which the mean values were 5.1 M in NGC 2024 and 3.4 M in NGC 2071 (see
Appendix A for a derivation of LTE and virial masses). The LTE mass for all clumps was smaller
than the virial mass, suggestive of condensations that are not gravitationally bound and therefore
unlikely to be star-forming. The authors do mention, however, that there are many uncertainties in
the mass calculations which could affect this result. Calculations of the CMFs (fitting above 0.02
M only) result in slopes, for single power law fits, of -1.3 for NGC 2024 and -1.7 for NGC 2071.
The authors also fit a broken power law (with a turnover at around 2 M). In this case the CMF for
the NGC 2024 condensations has a slope of -1 at the low mass end and -2.6 at the high mass end.
For NGC 2071, the low and high mass slopes have values of -0.06 and 2.3 respectively. Other
decomposition studies in Orion B include the paper byIkedaet al. (2009) who study H13CO+
cores and find a wider mass range for NGC 2024 than NGC 2071 (up to 13 M for the former and
5 M for the latter). They identify condensations with mean radius 0.1 pc, velocity width 0.53
kms−1, mass 8.4 M and virial ratios of around 1 suggesting clumps on the verge of being or just
being gravitationally bound.Motte et al. (2001) andJohnstoneet al. (2001) both study the dust
continuum emission in Orion B and find that the CMF mirrors the IMF above 1 M. Krameret
al. (1998) used a Gaussian clump decomposition algorithm to study (1→0) and (2→1) transitions
of 13CO, 12CO and C18O. They find slopes for the CMFs of -1.6 to -1.8 with no evidence of a
turnover near to the Jean’s mass.
Theρ Ophiuchus molecular cloud core has also been widely studied using clump decomposi-
tion methods, although again, so far as we are aware, not in the (3→2) transitions of CO.Friesen
et al. (2009) describe the NH3 condensations in this region, finding that the smaller NH3 clumps
from their sample tend to coincide better with sub-mm dust clumps than larger ones. They also
find some evidence of NH3 depletion in the denser regions.Motte et al. (1998), using the 1.3mm
emission, identify 58 starless cores in a 480 square degree region in the same cloud. Most of these
appeared to be gravitationally bound. Calculations of the CMF yielded slopes of -1.5 for<0.5 M
and -2.5 for higher masses.Stamatelloset al. (2007) calculate masses for the mm cores inρ Oph.
They use new dust temperatures which result in the break in a power law fit to the CMF occurring
at 1 M rather than at 0.5M as derived by previous authors. Again they calculate slopes of -1.5
for the low mass end and -2.5 for the high mass end.
Reid & Wilson(2006) investigate the CMFs of sub-mm clumps in 11 high and low mass star-
forming regions, including Orion B andρ Oph. They discuss the suitability of the most commonly
176
used broken power law fit in contrast to a log-normal functional fit to the CMF. They find that in
regions where the mean clump mass is less than a few M (as is the case forρ Oph but not Orion
B), a log-normal form provides a more satisfactory fit to the CMF with a double power law fitting
better for higher mass distributions. They comment that the change is relatively subtle so that
the form of the CMF does not correlate strongly with the overall mass of the clumps. They also
caution that a distribution of masses can appear artificially curved when plotted in the differential
form. They find a fairly consistent slope for the CMF, in all regions, of around -2.4 at the high
mass end.Tachiharaet al. (2002) achieve similar results by using C18O (1→0) emission to study
dense clumps in 8 regions, includingρ Oph and Taurus. They find 179 clumps in total across all
their fields, 136 starless, 36 star-forming and 7 cluster-forming. Star-forming cores appear to have
higher column densities and masses as well as lower velocity distributions which they claim is an
indication of turbulent decay. Their power law fits to the CMFs have slopes of 0.25 (2-10 M),
1.5 (10-55 M) and 2.6 for masses above 55 M.
Onishi et al. (1998) study clumps of C18O (1→0) emission in the Taurus molecular cloud.
They compare the locations of their cores with previous identifications of HCO+ cores and cold/warm
IRAS objects. They conclude that the more massive, sizeable C18O clumps with larger line widths
more often tend to coincide with cold IRAS sources or HCO+ clumps than smaller ones, or those
coincident with a warm IRAS source (possibly in a slightly later protostellar phase). The same
authors later look at H13CO+ clumps in the same region (Onishiet al.(2002)). They find 23 cores
and again calculate the CMF, the slope of which they find to be steeper than those of lower density
tracers.
In Serpens,Testi & Sargent(1998) identify 32 mm dust cores in a 5.5×5.5 square degree
region, 26 of which appear to be protostellar. Their fit to the CMF has a slope of -2.1.
Several further decomposition studies have been attempted in regions aside from those inves-
tigated in this chapter.Pinedaet al. (2006) use theCLUMPFIND algorithm on maps of12CO and
13CO emission in Perseus. They find very few bound clumps, which they attribute to either CO
freeze-out in the dense regions or to a sensitivity limit. Their CMF fits have slopes of around 1.2
below 10 M and 2.9 for the higher masses.Williams et al.(1994) carry out a similar study using
CO maps of the Rosette molecular cloud for which they find clumps of mean size around 1 pc. In
the case of13CO close to half of these appear to be bound. The filling factor for their clumps is
around 8% and they note an increasing velocity dispersion with increasing CO clump mass.Walsh
et al. (2007) determine that the slope of the CMF for their 93 N2H+ cores of masses 0.05-2.5 M
in NGC 1333 matches the slope of the IMF in the same region. One of the first results papers for
177
Herschel (Andreet al.(2010)) describes the identification of clumps in Aquila and Polaris at PACS
and SPIRE wavelengths (in the range 70-500 micron), extracted using the‘getsources’ algorithm
(fully described inMen’shchikovet al. (2012)). They find 350-500 prestellar cores of 0.01-0.1 pc
sizes in Aquila as well as 45-60 class 0 protostars. In Polaris they identify 300 unbound starless
cores and no protostars. The prestellar CMF in Aquila appears, once again, to resemble the stellar
IMF for the same region. The highest transition study of CO we could recover from the literature
was that ofKrameret al. (1998) for the (2→1) line of C18O in Sharpless 20140 for which they
derive a power law slope for the CMF of 1.65.
Having fully investigated all four algorithms in theCUPID package, testing them on both syn-
thetic and real data, and analysing the response of the codes to various user defined input param-
eters, we choose to runCUPID FELLWALKER on our data.FELLWALKER was able to best reproduce
various properties of the synthetic input parameters such as mean clump mass, mean radii and the
overall number of clumps in the catalogue. It also emerged as being fairly robust against changes
in the user defined input parameters when compared to the other three algorithms. We select this,
with values for theMinDip andNoiseparameters of 2*rms and 4*rms respectively to investigate
CO emission in our 5 regions. The selected input parameters appeared to be the most efficient in
detecting clumps without mis-identifying noise (see chapter 5, table 5.1 for a description of the
role of these parameters).
We ran the algorithm in total 15 different times (for five regions, each with available12CO,
13CO and C18O data). For each we trimmed off the noisier regions at the edges of the maps before
binning to a velocity resolution of 0.15 kms−1. This value was chosen as smaller than the estimated
line width of a CO clump in Taurus due to thermal motions alone (given by√
kT/mHmCO, where
k is Boltzmann’s constant,T is the temperature of the gas, andmH andmCO are the masses of a
hydrogen and CO particle respectively). Taurus has the lowest temperatures of all the regions so
it is assumed that line widths in this cloud will in general be narrower than for the other four. The
Serpens data was taken during the science verification stage so higher resolution12CO images
were not available. For this map we did not bin the data since the initial velocity resolution of the
maps was around 0.42 kms−1 rather than 0.1 kms−1 as for the other maps. We tested the result
of different velocity bins on the resultingFELLWALKER output catalogues and found little difference
for Serpens in the13CO and C18O data. In terms of clump numbers, when data was binned to a
velocity resolution of 0.42 kms−1, 18 C18O and 3113CO clumps were found as opposed to 16
and 31 in the data binned to 0.1 kms−1. We estimated the noise in the data (usingSPLAT, part
of theSTARLINK software collection,Warren-Smith & Wallace(1993)) at 3 positions on each map
178
for comparison with theCUPID estimate. TheCUPID estimate tended to be slightly bigger, however
this was not a large effect. For consistency, we chose to use theCUPID estimated noise during the
algorithm runs.
Some problems with the available data maps for Ophiuchus meant that it was impossible to
produce signal to noise ratio cubes. Since time was short and this problem was not resolved,
we chose to run the clump decomposition on the original data cubes for all clouds to preserve
consistency (trimming noisy regions carefully first). We ranFELLWALKER on a signal to noise cube
for another cloud (NGC 2024) in order to compare results from the two runs. Results of the snr runs
(in which we run the algorithms on the signal to noise cubes rather than the original data) for NGC
2024 are shown in Table 6.1 where we list the numbers of clumps identified in each isotopologue
and for each cloud. Clump numbers are, in general, a little higher for the snr runs particularly for
the noisier12CO data. Clump-finding on an snr cube is probably slightly more sensitive to weak
emission so we may be missing a few more of the less massive or smaller clumps in our runs.
We experimented with theCUPID ‘findback’ command (Berry et al. (2007)) which removes
emission on scales above a specified value. The algorithm works via a series of routines designed
to smooth out small-scale structure, leaving a background spectrum which can then be removed
from the original cube. The first step replaces all pixels within a box (the size of which is specified
by the user and defines the smallest scale structure to be retained) with the minimum value within
that box. The process is repeated on the filtered data, this time replacing each pixel with the
maximum value in a box of the same size. Finally, pixels are replaced by the average value in
the box which leaves a fairly good estimate of the background including structure on scales larger
than the box size. We removed emission on scales larger than 0.1 pc from the NGC 2024 C18O
map and ranFELLWALKER with the same input parameters as for the other runs. The result was
the identification of fewer clumps (27 rather than 50). The positions of the clumps appear to
correspond mainly with clumps identified in the original data set (see Figure 6.1). Radii and LTE
masses of the clumps in the data set on which‘findback’ had been run were smaller (Figures 6.2
and 6.3). Probably some clumps of emission in the original data set were larger than the 0.1 pc
cut-off and so were not identified in the second set. Running‘findback’ on the12CO data rather
than the C18O had different results. More clumps were identified in the map on which we had
run ‘findback’ and these did not seem to match positions of clumps from the original map (Figure
6.4). Radii and LTE masses were again smaller (Figures 6.5 and 6.6). We eventually chose not
to use‘findback’ previous to our clump-finding runs because time was too short to investigate
the effects of this parameter further and results so far seemed inconsistent between the different
6.1. Results - The CO Clumps 179
isotopologues.
Figure 6.1: Positions of clumps identified in the
original C18O maps and C18O maps with large-
scale emission removed.
Figure 6.2: Radius vs. LTE mass for clumps
identified in the original C18O maps and C18O
maps with large-scale emission removed.
Figure 6.3: LTE mass vs. Virial mass for clumps
identified in the original C18O maps and C18O
maps with large-scale emission removed.
Figure 6.4: Positions of clumps identified in the
original 12CO maps and12CO maps with large-
scale emission removed.
6.1 Results - The CO Clumps
After running FELLWALKER on all the available maps we used the output catalogues to look for
trends in various properties of the identified clumps. LTE masses were derived using the following
6.1. Results - The CO Clumps 180
Figure 6.5: Radius vs. LTE mass for clumps
identified in the original12CO maps and12CO
maps with large-scale emission removed.
Figure 6.6: LTE mass vs. Virial mass for clumps
identified in the original12CO maps and12CO
maps with large-scale emission removed.
equation (to find the mass of13CO):
M(13CO)M
= 1.15× 10−7 Tex
exp−31.8Tex
S1
ηmbdvL2
pix
1X13CO
, (6.1)
which follows from the column density calculation outlined in Appendix A (some more details of
the mass calculation are also given), accounting for the entire volume of the clump and the mass
of helium and converting to units ofM. Tex is the excitation temperature of the gas,S the sum
of values of the antenna temperature for all pixels in the clump,X13CO the fractional abundance of
13CO with respect to molecular hydrogen,Lpix the length of a single pixel in pc, dv the velocity
width of the clump, andηmb the main beam efficiency of the telescope. For the other isotopologues
the constants in this equation will be slightly different due to molecular considerations but the form
is the same. Virial masses of clumps are given by (see Appendix A for details)
Mvir
M=
5Rδ2v,3D
3γG, (6.2)
whereγ is a factor which depends on the assumed density distribution of the clumps and equal to
5/2 if an r2 density distribution is assumed,R is the radius of the clumps,G is the gravitational
constant andδv,3D the 3D velocity dispersion of the clump (see Appendix A) given by:
δ2v,3D = 3[δ2
CO +kT
mH(1µ− 1
mCO)], (6.3)
6.1. Results - The CO Clumps 181
which can be used for any isotopologue of CO takingδCO as the size of the clump along the
velocity axis. mH is the mass of a hydrogen atom,µ the mean molecular mass of the material
and mCO the atomic mass of a CO molecule (C18O, 13CO or 12CO). As a measure of T, the
kinetic temperature of the gas, we use the average excitation temperatures derived using the12CO
emission at the centres of SCUBA dust cores in the clouds. This may give an underestimate as
the dense cores are likely to be cooler than more diffuse, gaseous regions. We can be more sure,
however, that12CO will be optically thick in these regions giving an accurate measure of the gas
temperature. As a test we experimented with using different temperatures to determine the LTE
masses of clumps in one of the clouds (Serpens). Masses are altered very little by changes in the
assumed excitation temperature above around 20 K, however below this the exponential function
in the equation to determine LTE mass rises sharply so that below 20 K (which is also near to the
CO freeze-out temperature,Nakagawa(1980)) an underestimate in the excitation temperature will
lead to an overestimate of masses. Plots for Serpens of LTE vs. Virial masses for theFELLWALKER
identified clumps are shown in Figures 6.7 and 6.8 using an excitation temperature of 15 K (left)
and 10 K (right). The difference is still not too large, although at 10 K masses are larger and more
of the clumps appear bound.
Figure 6.7: LTE mass vs. Virial mass of CO
clumps in Serpens assuming an excitation tem-
perature of 15 K.
Figure 6.8: LTE mass vs. Virial mass of CO
clumps in Serpens assuming an excitation tem-
perature of 10 K.
6.1. Results - The CO Clumps 182
Table 6.1: Number of Clumps Identified withFELLWALKER
Cloud Isotopologue Nclumps Noise (K)
NGC 2024 12CO 268 0.31
NGC 2024 13CO 203 0.15
NGC 2024 C18O 50 0.20
NGC 2024(snr) 12CO 325 -
NGC 2024(snr) 13CO 207 -
NGC 2024(snr) C18O 58 -
NGC 2071 12CO 230 0.29
NGC 2071 13CO 126 0.14
NGC 2071 C18O 59 0.17
Ophiuchus 12CO 201 1.45
Ophiuchus 13CO 296 0.28
Ophiuchus C18O 153 0.22
Serpens 12CO 65 0.09a
Serpens 13CO 33 0.20
Serpens C18O 16 0.23
Taurus 12CO 170 0.06
Taurus 13CO 38 0.20
Taurus C18O 2 0.25
a - in channels of 0.42kms−1
Table 6.1 lists the numbers of clumps identified withFELLWALKER in all 3 isotopologues and for
all 5 clouds. Map areas for the clouds are different and it is important to take these into account
when comparing clump numbers. NGC 2071 is mapped over an area of around 4.2 pc2, NGC
2024 over 3.5 pc2, Serpens over 1.7 pc2 and Taurus and Ophiuchus over just 0.4 pc2.
6.1.1 Clump Positions and Ellipticities
13CO and12CO emission appears to be fairly widespread across the maps (Figures 6.9-6.13), with
C18O clumps located in regions of strongest12CO emission, e.g. in the filaments around CO
cavities in NGC 2024 and NGC 2071. For Ophiuchus, however, clumps are spread fairly evenly
across the entire map in all isotopologues. We looked for correlations between the isotopologue
6.1. Results - The CO Clumps 183
and ellipticity of the clumps (measured by the ratio of clump sizes in the two spatial directions) and
plot the results in Figures 6.14-6.18. For none of the clouds does this parameter appear to show
any correlation. Clump ellipticities are fairly similar for all clouds ranging from about 0.33-3 with
some more extreme values in Taurus12CO and13CO clumps. High ellipticity could indicate a
more filamentary structure rather than a compact pre-stellar core, however it is surprising that we
did not see more elongated clumps in Orion where dust emission also reveals filaments.
Figure 6.9: CO clump positions for NGC 2024Figure 6.10: CO clump positions for NGC 2071
Figure 6.11: CO clump positions for Ophiuchus Figure 6.12: CO clump positions for Serpens
6.1. Results - The CO Clumps 184
Figure 6.13: CO clump positions for Taurus
Figure 6.14: Ellipticity of the CO clumps in NGC
2024
Figure 6.15: Ellipticity of the CO clumps in NGC
2071
6.1.2 Clump Masses
In Figures 6.19-6.23 we plot the radii of the CO clumps against their LTE masses for all 5 clouds
(plotting codes are adapted from scripts written by J.Roberts) and in Table 6.2 we list the means,
standard deviations and ranges (the difference between LTE masses of the highest mass clump in
the sample and that of lowest mass clump) of our calculated LTE masses as well as the gradient and
intercept of least squares fits to the radius versus mass plots and the goodness of fit or R2 (goodness
of fit) value for our least squares fit. Errors on the gradient and intercept use standard equations
assuming equal error on all the points (the mass and radii of the CO clumps). This may not be
the case if for smaller clumps, masses are more affected by noise. There will also be uncertainties
introduced during the mass calculations so that the errors quoted are probably underestimates.
Errors in the LTE masses are hard to quantify, given the large number of variables, each with their
own uncertainties, in equation 6.1. What is more, the sum of emission from pixels associated with
6.1. Results - The CO Clumps 185
Figure 6.16: Ellipticity of the CO clumps in
Ophiuchus
Figure 6.17: Ellipticity of the CO clumps in Ser-
pens
Figure 6.18: Ellipticity of the CO clumps in Tau-
rus
a clump depends on the performance of the clumpfinding algorithm used to detect the clumps.
The choice of Tex (for which we assume an average value for each cloud based on calculations of
12CO temperatures in the centers of dust cores) will introduce uncertainties. Values of Tex may
be overestimated as12CO likely traces a more diffuse gas than the C18O emission used to detect
clumps. Below values for Tex of around 20 K, an overestimate could lead to an underestimate of
the LTE mass for the clump. Errors will be largest for Taurus and Serpens, as for these clouds the
average values of Tex we calculate are lower than for the other clouds. Both the abundance ratio
of 13CO to hydrogen and the main beam efficiency will suffer from uncertainties as the first will,
in reality, vary among regions and the second is a simplification, failing to account properly for
the error pattern of the beam. Values for the radii of the clumps are the geometric mean of the
fellwalker-derived sizes along perpendicular axis. Depending on the orientation of the clump, and
6.1. Results - The CO Clumps 186
the performance of the algorithm on clumps with differing intensity profiles, this will vary. As
an average value for many clumps within each cloud, this method of calculating the masses and
radii should allow a decent comparison, however one must be careful when dealing with absolute
values in these cases and the positions of the clumps on radii versus mass plots will involve large
uncertainties.
In all plots12CO clumps are coloured black,13CO red and C18O blue. Radii are similar for the
3 isotopologues, however the C18O clumps appear to be more massive than13CO clumps, which
are in turn more massive than the12CO clumps of a similar size. This is a result of the fact that, due
to the higher optical depth of the more common isotopologues, the12CO and13CO tend to trace
lower density, more diffuse emission (in the surrounding regions or envelopes) than the C18O,
which will be more likely to trace the core material. Alternatively, the assumption of LTE may be
inaccurate in the more diffuse regions which are likely to be traced by the common isotopologues
rather than the optically thin C18O. The assumed excitation temperature for the LTE calculations
may also be incorrect for some of the clumps which, although for Orion is unlikely to have much
of an effect, for the clouds at lower temperatures a small difference in the assumed Tex will have
a larger impact on the LTE masses derived. However, we show in the previous section that this
is still not a very large effect. For all isotopologues and in all clouds there is a clear correlation
between the radii and masses for the clumps. The slope of this correlation is similar for all clouds
and all isotopologues (ranging from 1.86 to 2.95).Buckleet al. (2010) derived a gradient of 2.6
for the13CO clumps in NGC 2024 (found usingCLUMPFIND) and 1.7 in NGC 2071. We find values
of 2.95±0.14 in NGC 2024 and 2.44±0.11 in NGC 2071, slightly steeper slopes but consistent
considering the different choice of algorithm used and errors involved.Krameret al.(1996) derive
a slope of 2.2 for the southern region of Orion B in13CO. Results are all consistent with Larson’s
well known law (Larson(1981)) which suggests a slope for the log-log plots of mass versus radius
of around 2.
6.1. Results - The CO Clumps 187
Figure 6.19: Radius vs LTE mass for CO clumps
in NGC 2024
Figure 6.20: Radius vs LTE mass for CO clumps
in NGC 2071
Figure 6.21: Radius vs LTE mass for CO clumps
in Ophiuchus
Figure 6.22: Radius vs LTE mass for CO clumps
in Serpens
Figure 6.23: Radius vs LTE mass for CO clumps
in Taurus
6.1. Results - The CO Clumps 188
Tabl
e6.
2:LT
Em
asse
s
Clo
udIs
otop
olog
ueN
clum
psM
ean
clum
p
LTE
mas
s
(M
)
Sta
ndar
d
devi
atio
nof
LTE
mas
s
Ran
ge(M
)in
terc
ept
offit
toM
LTE
vs.
Rad
plot
s
grad
ient
offit
toM
LTE
vs.
Rad
plot
s
R2
NG
C20
2412C
O26
80.
230.
330.
0003
-1.9
2.26±
0.17
2.49±
0.13
0.60
NG
C20
2413C
O20
35.
3514
.13
0.00
5-18
14.
37±
0.20
2.95±
0.14
0.70
NG
C20
24C
18O
5026
.14
48.5
20.
38-2
284.
55±
0.25
2.47±
0.17
0.82
NG
C20
7112C
O23
00.
160.
230.
001-
1.7
1.91±
0.11
2.30±
0.09
0.80
NG
C20
7113C
O12
64.
746.
960.
07-5
53.
50±
0.15
2.44±
0.11
0.79
NG
C20
71C
18O
5910
.28
10.9
30.
1-52
3.40±
0.23
1.89±
0.16
0.71
Oph
iuch
us12C
O20
10.
016
0.01
80.
0003
-0.0
781.
88±
0.13
2.26±
0.07
0.83
Oph
iuch
us13C
O29
60.
220.
400.
0018
-3.5
73.
59±
0.15
2.47±
0.08
0.77
Oph
iuch
usC
18O
153
1.07
2.02
0.01
7-18
.83
4.04±
0.20
2.34±
0.11
0.75
Ser
pens
12C
O65
0.02
0.02
6.12
(-5)
-0.0
961.
48±
0.29
2.23±
0.19
0.69
Ser
pens
13C
O33
0.59
0.97
0.00
6-5.
22.
14±
0.23
1.95±
0.16
0.83
Ser
pens
C18O
161.
321.
980.
03-8
3.23±
0.74
2.25±
0.46
0.63
Taur
us12C
O17
00.
005
0.00
79.
38(-
6)-0
.04
2.58±
0.31
2.91±
0.16
0.65
Taur
us13C
O38
0.09
0.18
0.00
18-0
.78
1.74±
0.36
1.86±
0.19
0.72
Taur
usC
18O
20.
580.
340.
2-0.
9-
--
6.1. Results - The CO Clumps 189
The most massive clumps, on average, and for all isotopologues are in NGC 2024. The NGC
2071 clumps are slightly less massive, followed by the clumps in Serpens, then Ophiuchus and
Taurus in which the average clump mass is the lowest. The range in masses of the clumps are
generally larger for clouds with more massive clumps (e.g. the largest ranges are found in NGC
2024, consistent with Buckleet al.(2010) who found larger masses and a wider mass range in
13CO clumps in NGC 2024 than in NGC 2071), however Ophiuchus, which contains smaller mass
clumps on average than Serpens exhibits a larger range in masses for the C18O clumps.
6.1.3 Clump virial masses - how bound are the clumps?
Figure 6.24: LTE mass vs. virial mass for CO
clumps in NGC 2024
Figure 6.25: LTE mass vs virial mass for CO
clumps in NGC 2071
Figure 6.26: LTE mass vs. virial mass for CO
clumps in Ophiuchus
Figure 6.27: LTE mass vs virial mass for CO
clumps in Serpens
6.1. Results - The CO Clumps 190
Figure 6.28: LTE mass vs. virial mass for CO
clumps in Taurus
Figures 6.24-6.28 show plots of clump LTE masses versus Virial masses. The dotted line
marks the point at which clumps become gravitationally bound (their LTE mass is higher than
their virial mass). In all clouds, according to our mass calculations, all of the identified12CO
and13CO clumps are unbound. In both regions in Orion B more than half of the C18O clumps
are bound, one of the two identified C18O clumps in Taurus may be just bound, in Ophiuchus
the large majority of the C18O clumps are unbound with some bound clumps, and in Serpens,
none of the C18O clumps appear bound which could suggest that star-formation is more likely to
be ongoing in Orion, and to some extent Ophiuchus than in the other two clouds. The fact that,
even using the most optically thin isotope available, clumps in Serpens appear unbound could be
a consequence of the turbulent nature of the southern, less evolved region. It may be an indication
that star formation has ceased in the more quiescent parts and that, in the south, star formation is
unlikely to occur perhaps due to conditions there.
6.1.4 Investigating the CO Clump Mass Functions
Figures 6.29-6.33 show the clump mass functions for identified clumps in all three isotopologues
along with power law fits to the data. In some cases a broken power law was required to achieve
a better fit and in some cases a single value for the slope sufficed. There is evidence in Figure
6.30 (particularly for C18O clumps) of a steepening again in the CMF at very high masses. We fit
the differential mass function which describes the number of clumps in a particular mass bin. The
6.1. Results - The CO Clumps 191
equation is as follows with -α equal to the slope of the CMF:
dN
dM= M−α (6.4)
values ofα from our fits are listed in Table 6.3. Only NGC 2071 shows possible evidence of a
further turnover in the slope at around 10 M but only for the two highest mass bins. We do
not attempt to fit the high mass slope but note that other authors have found evidence of a break
in the CMF power law at high masses in similar regions using different molecular transitions to
trace the mass. Most CMFs are best fit with a single power law with the exception of12CO and
13CO clumps in Orion B and13CO and C18O clumps in Ophiuchus. Turnovers occur at 0.05 M
for 12CO in Orion B, 1 M for 13CO in Orion B, 0.3 M for C18O in Ophiuchus and at around
0.1 M for 13CO in Ophiuchus. These turnovers and shallower slopes at the low mass end for
Orion and Ophiuchus may suggest some disruption of the lowest mass cores due to turbulence or
tidal forces in these regions of clustered star-formation. Offsets in mass are evident between the
different isotopologues with CMFs for12CO clumps shifted to lower masses relative to the13CO
clump CMFs and likewise for the13CO relative to the C18O. Again this is most likely due to the
fact that the more common isotopologues trace more diffuse gas than C18O. Slopes are shallower
at the lower mass end of the CMF (few very low mass clumps identified) which is consistent with
other studies. Some authors have suggested that this could be due to a completeness limit with
lower mass clumps being overlooked due to resolution or noise in the data. At the higher masses,
slopes are shallower in Serpens and Taurus in general (aside from the C18O clumps in Orion).
This is a possible consequence of the lower number of identified clumps in these clouds, which
could result in a shallowing at lower masses being missed. Steeper and shallower regions of the
CMF would then be fit as one power law with a middling gradient. These clouds probably do
contain fewer high mass clumps in general. A shallower slope at the high mass end of the CMF
for Serpens and Taurus could also be due to a lower level of fragmentation for the highest mass
clumps in regions where cores are more isolated and levels of turbulence are lower. Our CMF fits
are shallower than those derived by other authors for higher mass tracers but consistent in most
cases with those deduced from CO lines.
Errors in the slope of the CMF will arise not just from the least squares fit for the power law but
also during the clump identification and the calculation of masses so it is very hard to accurately
estimate the uncertainty in alpha. Considering this, our values of alpha for the higher mass end
of the CMFs are very similar for the clouds and the different isotopes and are generally consistent
6.1. Results - The CO Clumps 192
Table 6.3: Values of alpha from clump mass distributions
Cloud α(12CO) α(13CO) α(C18O)
NGC 2024 0.52(<-1.3)/1.71(>-1.3)a 0.58(<0)/1.74(>0) 0.75
NGC 2071 0.11(<-1.3)/1.84(>-1.3) 0.42(<0)/1.65(>0) 0.83
Taurus 1.48 0.96 -
Serpens 0.93 1.03 0.97
Ophiuchus 1.28 1.76 0.34(<-0.5)/1.72(>-0.5)
a - We fit the slope with a broken power law of slope 0.52 for masses less than∼ 0.05 M and
1.71 at higher masses.
with previous studies (e.g.Krameret al. (1998) who found power law slopes of 1.6-1.8 with CO
isotopes in similar regions).
6.1. Results - The CO Clumps 193
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2024 12COalpha(<-1.3) = 0.52alpha(>-1.3) = 1.71
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2024 13COalpha(<0) = 0.58alpha(>0) = 1.74
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2024 C18Oalpha = 0.75
Figure 6.29: Clump mass functions for CO clumps in NGC 2024
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2071 12COalpha(<-1.3) = 0.11alpha(>-1.3) = 1.84
-3 -2 -1 0 1 2 3log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2071 13COalpha(<0) = 0.42alpha(>0) = 1.65
-3 -2 -1 0 1 2 3log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
ngc 2071 C18Oalpha = 0.83
Figure 6.30: Clump mass functions for CO clumps in NGC 2071
6.1. Results - The CO Clumps 194
-5 -4 -3 -2 -1 0 1log[M/Msun]
0
1
2
3
4
5
6
7
log[
dN/d
M]
Ophiuchus 12COalpha(>-2) = 1.28
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Ophiuchus 13COalpha(>-1) = 1.76
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Ophiuchus C18Oalpha(<-0.5) = 0.34alpha(>-0.5) = 1.72
Figure 6.31: Clump mass functions for CO clumps in Ophiuchus
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Serpens 12COalpha = 0.93
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Serpens 13COalpha = 1.03
-4 -3 -2 -1 0 1 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Serpens C18Oalpha = 0.97
Figure 6.32: Clump mass functions for CO clumps in Serpens
6.1. Results - The CO Clumps 195
-6 -4 -2 0 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Taurus 12COalpha = 1.48
-6 -4 -2 0 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Taurus 13COalpha = 0.96
-6 -4 -2 0 2log[M/Msun]
-2
0
2
4
6
log[
dN/d
M]
Taurus C18O
Figure 6.33: Clump mass functions for CO clumps in Taurus
6.2. Matches with SCUBA Cores 196
6.2 Matches with SCUBA Cores
We used the catalogues of protostellar and starless cores fromSadavoyet al. (2010) to determine
whether CO clumps in each cloud and for each isotopologue tended to coincide with dust cores.
One would expect the C18O emission to follow the dust emission fairly well (being optically thin)
if we fail to account for freeze-out of CO onto dust grains in the dense cores. To determine whether
a clump and a core are coincident, we used the positions of the peaks along the two spatial axes
defining a match as a case where the two peaks lay within 0.01 pc of one and other. This distance
is fairly arbitrary, chosen as a rough average of the radii of our CO clumps. For comparison, we
also matched cores using the radius of the dust core as the maximum separation for the CO and
dust peaks (as determined by Sadavoyet al.2010 using theCLUMPFIND algorithm). The dust cores
were generally larger than 0.01 pc so we defined many more matches using the second method,
but the general trends remained the same. From this point on we plot and discuss only matches
defined using the first method. Table 6.4 lists the number of matches (with a separation of 0.01
pc) as a proportion of the total number of CO clumps for each cloud. Figures 6.34-6.41 plot the
radius versus LTE mass of our12CO clumps and LTE mass versus virial mass. We colour-code the
matches with protostellar dust cores in red and starless dust cores in yellow. Figures 6.42-6.51 and
Figures 6.52-6.59 are identical but for the populations of13CO and C18O respectively. Figures
6.60-6.69 illustrate properties of the SCUBA identified dust cores (radii, peak flux, core mass and
extinction), again matches with CO cores are indicated. We use red for matching protostars, blue
for matching starless cores and black where there is no match. Symbols indicate whether the
match is with a12CO,13CO or a C18O clump.
For the starless cores in Orion and Serpens, C18O clumps do appear to correlate better with
the positions of the dust cores than for the other 2 isotopologues, although this is not the case
for Ophiuchus or Taurus. The Ophiuchus data, however, was much noisier than the other maps
and CO clumps were located across the whole region rather than in obvious cores or filaments as
for the other clouds. In Taurus we found only one match between a13CO clump and a starless
SCUBA core. 12CO clumps did not match well with either starless dust cores or protostellar in
any of the clouds. This is probably due to the higher optical depth of this isotopologue in denser
regions and the fact that it tends to trace the more diffuse gas. Surprisingly few C18O clumps are
found to be coincident with dust cores (roughly 15% in Orion and Serpens and less in Ophiuchus
and Taurus). It is possible that the peaks of the C18O and dust emission are offset due to CO
depletion at the positions of the core peaks. In an attempt to look for some relationship between
6.2. Matches with SCUBA Cores 197
Table 6.4: Number of matches with SCUBA cores
Cloud Isotopologue match(sless)/tot match(proto)/tot Nsless Nproto
NGC 2024 12CO 0.01 0 25 3
NGC 2024 13CO 0.06 0 - -
NGC 2024 C18O 0.16 0 - -
NGC 2071 12CO 0.01 0.02 28 11
NGC 2071 13CO 0.04 0.04 - -
NGC 2071 C18O 0.17 0.03 - -
Ophiuchus 12CO 0.05 0.01 42 11
Ophiuchus 13CO 0.02 0 - -
Ophiuchus C18O 0.03 0.01 - -
Serpens 12CO 0.02 0.02 4 11
Serpens 13CO 0.03 0.02 - -
Serpens C18O 0.13 0.06 - -
Taurus 12CO 0 - 19 0
Taurus 13CO 0.03 - - -
Taurus C18O 0 - - -
the CO clumps that did match with SCUBA cores we plotted a few important clump properties,
colouring the matched cores according to whether the match was with a protostar or a starless core.
We also looked at properties of the SCUBA clumps for each cloud, again colour-coding those that
coincided with one of our identified CO clumps.
6.2. Matches with SCUBA Cores 198
Figure 6.34:12CO matches with SCUBA cores
in NGC 2024.
Figure 6.35:12CO matches with SCUBA cores
in NGC 2024.
Figure 6.36:12CO matches with SCUBA cores
in NGC 2071.
Figure 6.37:12CO matches with SCUBA cores
in NGC 2071.
Figure 6.38:12CO matches with SCUBA cores
in Ophiuchus.
Figure 6.39:12CO matches with SCUBA cores
in Ophiuchus.
6.2. Matches with SCUBA Cores 199
Figure 6.40:12CO matches with SCUBA cores
in Serpens.
Figure 6.41:12CO matches with SCUBA cores
in Serpens.
Figure 6.42:13CO matches with SCUBA cores
in NGC 2024.
Figure 6.43:13CO matches with SCUBA cores
in NGC 2024.
Figure 6.44:13CO matches with SCUBA cores
in NGC 2071.
Figure 6.45:13CO matches with SCUBA cores
in NGC 2071.
6.2. Matches with SCUBA Cores 200
Figure 6.46:13CO matches with SCUBA cores
in Ophiuchus.
Figure 6.47:13CO matches with SCUBA cores
in Ophiuchus.
Figure 6.48:13CO matches with SCUBA cores
in Serpens.
Figure 6.49:13CO matches with SCUBA cores
in Serpens.
Figure 6.50:13CO matches with SCUBA cores
in Taurus.
Figure 6.51:13CO matches with SCUBA cores
in Taurus.
6.2. Matches with SCUBA Cores 201
Figure 6.52: C18O matches with SCUBA cores
in NGC 2024.
Figure 6.53: C18O matches with SCUBA cores
in NGC 2024.
Figure 6.54: C18O matches with SCUBA cores
in NGC 2071.
Figure 6.55: C18O matches with SCUBA cores
in NGC 2071.
Figure 6.56: C18O matches with SCUBA cores
in Ophiuchus.
Figure 6.57: C18O matches with SCUBA cores
in Ophiuchus.
6.2. Matches with SCUBA Cores 202
Figure 6.58: C18O matches with SCUBA cores
in Serpens.
Figure 6.59: C18O matches with SCUBA cores
in Serpens.
6.2. Matches with SCUBA Cores 203
6.2.1 Properties of the SCUBA Dust Cores
There is some evidence in NGC 2024, Serpens and somewhat in NGC 2071 that the largest, most
massive protostellar cores tend to coincide with at least one CO clump (Figures 6.60, 6.62 and
6.66). At the protostellar stage, after freezing-out onto dust grains in an earlier stage or star-
formation, much of the CO could have been released back into the gas phase with a rise in the
temperature of the envelope, causing the CO and dust to appear coincident. The same cannot be
said for the starless cores, in fact it appears that it is the less massive and smaller cores that are
more often coincident with stronger CO emission. This is an interesting result, and could perhaps
be related to CO depletion in the more massive starless cores. We do not see these trends in Taurus
and Ophiuchus. Taurus contains only one core coincident with a CO clump so it is impossible
to say much regarding this cloud. Ophiuchus has quite uneven noise over the map so that the
identification of CO clumps could be affected by artifacts in the data. We runFELLWALKER again
with the noise parameter set to 10×rms and 15×rms rather than 4×rms. We should detect CO
clumps more reliably at these levels. We find 13212CO clumps with the noise parameter set to
10×rms, 27613CO clumps and 87 C18O clumps. With the noise parameter set to 15×rms we
find 56, 114 and 31 clumps in the12CO, 13CO and C18O data respectively. We reproduce Figure
6.64 using results from the two new runs. Despite raising the minimum level of emission for core
identification, we still do not see the largest cores matching with the CO for this cloud, although
the matching protostars are some of the most massive (if not the largest as for the other clouds).
Figure 6.60: SCUBA cores in NGC 2024,
coloured to illustrate a match with a CO clump.
Figure 6.61: SCUBA cores in NGC 2024,
coloured to illustrate a match with a CO clump.
6.2. Matches with SCUBA Cores 204
Figure 6.62: SCUBA cores in NGC 2071,
coloured to illustrate a match with a CO clump.
Figure 6.63: SCUBA cores in NGC 2071,
coloured to illustrate a match with a CO clump.
Figure 6.64: SCUBA cores in Ophiuchus,
coloured to illustrate a match with a CO clump.
Figure 6.65: SCUBA cores in Ophiuchus,
coloured to illustrate a match with a CO clump.
Figure 6.66: SCUBA cores in Serpens, coloured
to illustrate a match with a CO clump.
Figure 6.67: SCUBA cores in Serpens, coloured
to illustrate a match with a CO clump.
6.2. Matches with SCUBA Cores 205
Figure 6.68: SCUBA cores in Taurus, coloured
to illustrate a match with a CO clump.
Figure 6.69: SCUBA cores in Taurus, coloured
to illustrate a match with a CO clump.
Figure 6.70: SCUBA cores in Ophiuchus,
coloured to illustrate a match with a CO clump.
Here we set the noise parameter to 10*rms when
running the FELLWALKER algorithm to locate
CO clumps.
Figure 6.71: SCUBA cores in Ophiuchus,
coloured to illustrate a match with a CO clump.
Here we set the noise parameter to 15*rms when
running the FELLWALKER algorithm to locate
CO clumps.
6.3. Summary 206
6.3 Summary
We investigate the properties of CO clumps in five nearby star-forming clouds using the J=(3→2)
transitions of three different isotopologues of CO. Clumps are identified using the flux fitting
algorithmFELLWALKER and we use the resulting output catalogues to derive LTE and virial masses,
radii, ellipticities, distributions and CMFs for the clumps. Finally we look at how well CO clumps
and dust cores coincide spatially and correlations between clumps or cores that did coincide and
their physical properties. The main results are as follows;
• More and smaller clumps are found in the more common isotopes of CO. This is a possible
result of higher optical depth which reduces the apparent mass of the clumps identified and
could result in a double peaked profile in the CO lines and identification of 2 clumps around
a dense core.
• We find more clumps in Orion B than in the other three clouds and clumps there tend to be
more massive. C18O clumps in NGC 2024 reach masses of 230 M, those in NGC 2071
reach 50 M, Ophiuchus 20 M, Serpens 8 M and in Taurus clumps are just 1 M at their
most massive.
• There are no obvious correlations between the ellipticity of the clumps and the isotopologue
in which they were identified or the parent cloud.
• The radii of the clumps correlate well with clump LTE masses for all clouds and for all
isotopologues. Power law fits to plots of mass versus radius have exponents ranging from
1.86 to 2.95, consistent with Larson’s law.
• None of the12CO or13CO clumps appeared to be gravitationally bound since these isotopes
tend to trace the more diffuse gas. Over half of the C18O clumps in NGC 2024 and 2071
were bound according to our mass calculations, but very few for Ophiuchus and Taurus (the
latter only housing two C18O clumps). None of the CO clumps in Serpens appeared to be
bound, however errors in the mass calculations could effect these results, and the velocity
resolution for the Serpens data is much lower than for the other clouds.
• Power law fits to the clump CMFs show a turnover in some cases at very low masses,
possibly an effect of lower sensitivity in this range. At the higher mass end, slopes appear
to be consistent across the clouds and for different isotopes (although the CMF is shifted
6.3. Summary 207
according to the mean masses of the cores which is different from cloud to cloud). C18O
cores in Orion B, however do have quite shallow CMFs compared to the other clouds.
• 12CO clumps are rarely coincident with dust cores according to our definition of a match.
C18O clumps coincide better with the starless cores in Orion and Serpens but still only
around 15% of the clumps in a cloud are within 0.01 pc of a dust peak.
• The largest, most massive protostellar cores seem to correlate with CO clumps where it is
the less massive starless cores that are coincident with the CO. This could be a consequence
of CO freeze-out in the core centers for the more massive starless cores. We investigate CO
freeze-out in SCUBA identified starless and protostellar cores in the following chapter.
CHAPTER 7
DEPLETION IN THE GOULD BELT CLOUDS
The work presented in this chapter is based on the paper by Christie et al. (2012) in collaboration
with S.Viti, J.Yates and 15 co-authors.
This chapter presents a statistical comparison of CO depletion in 5 star-forming clouds within
the Gould Belt. We use the early GBS spectral data from HARP together with catalogues of dust
cores collated bySadavoyet al. (2010) from SCUBA dust emission maps to study depletion in
NGC 2024 and NGC 2071 in Orion, L1495 in Taurus, the Ophiuchus main cloud core (L1688),
and the Serpens main cluster, which represent a range of physical conditions. We compare the
depletions using a consistent methodology that allows meaningful comparisons between these
regions to be made. We discuss how depletion factors are calculated, compare LTE methods with
the use ofRADEX and discuss how depletion varies in a region and between regions.
7.1 Introduction
In dense, cold, star-forming cores, molecules in the gas phase freeze-out onto dust grains, forming
icy mantles on grain surfaces. The extent to which this freeze-out (or depletion) occurs for a
particular molecule depends on a complicated chemistry that varies non-linearly with time and
physical environment. The strong dependence of depletion on the age and make-up of a core
could make it a useful probe of core history.
Depletion is difficult to quantify observationally. It is common to use gas phase emission from
molecules such as CO to infer the fraction of the species that is in the solid phase. This requires
a comparison of gas phase molecular line emission with continuum emission from dust. Several
208
7.1. Introduction 209
assumptions are made about the state of the emitting gas and dust, and the possible destruction
of the molecule by other means is often ignored. This method has been successful, and studies
show significant depletion in star-forming cores (seeCaselliet al. (1999), Bacmannet al. (2002),
Redmanet al. (2002), Savvaet al. (2003), Thomas & Fuller(2008), Duarte-Cabralet al. (2010),
Ford & Shirley(2011)).
In addition to studies of the gas phase, one can directly observe molecules in the solid state
using, e.g., the absorption of IR emission from background sources (see reviews byvan Dishoeck
(2004), Oberget al. (2011)). Several authors have attempted to model cores including freeze-
out reactions to replicate observed line strengths and profiles. These models require accurate
depletion and desorption rate estimates from laboratory experiments that are very difficult to make.
Desorption can occur as a result of several processes including direct photodesorption (species in
the mantle are excited by incoming UV photons and the subsequent release of energy results
in desorption), and hits by cosmic rays which cause local heating of the grain surface, again
leading to the desorption of species in the mantle. As well as direct hits, cosmic rays will ionise
or excite molecules as they pass through the dense gas in a molecular core. UV photons are
produced as a result of these excitations and these, in turn, can impart energy to the grain surface by
dissociation of molecules in the mantle (particularly water).Shenet al. (2004) discuss cosmic ray
photodesorption in a dark cloud environment. The formation of hydrogen molecules on grains will
also cause local heating of the surface. The relative importance of these as desorption mechanisms
in the dark cloud environment are discussed inRobertset al. (2007). It is worth noting that,
despite recent experiments (Munoz Caroet al. (2010), Oberget al. (2009b)) rates of non-thermal
desorption as a function of density and mantle composition, required for chemical codes, have
not yet been accurately determined. Even with these uncertainties, modeling provides strong
arguments for depletion of molecules in dense cores. In many cases where multiple observations
of different species are available it is impossible to reproduce observationally derived abundances
and ratios between abundances without substantial freeze-out, suggesting that this is an important
contributor to the chemistry of star-forming regions (e.g.Taylor & Williams (1996), Aikawaet al.
(2001), Viti et al. (2003)).
To study how the depletion of CO relates to environment, one requires line data from the CO
isotopologues as well as continuum data from dust, from a variety of sources. The JCMT Gould
Belt Survey data from HARP and SCUBA-2 (described in Chapter 4) provides just this and we
make use of the HARP CO maps as well as catalogues of objects identified in SCUBA dust maps
to quantify freeze-out in the following study.
7.2. A depletion factor for the dust cores - LTE analysis 210
7.2 A depletion factor for the dust cores - LTE analysis
Our sample of dust cores is taken directly from the catalogue produced by Sadavoyet al. (2010)
using the SCUBA 850 micron dust emission maps taken as part of the GBS. These authors used the
clump identification algorithm‘clumpfind′ (Williams et al.(1994)) to pick out localized regions of
strong emission. Clumpfind first identifies closed contours at the highest level of emission in the
map as peaks, then contours in flux down to a minimum level that is specified by the user. The area
inside the minimum contour, and including a peak, is defined as the clump and integrated emission
as well as peak values are outputted. We compared peak fluxes at the centre of each core from the
Sadavoyet al. catalogue with our CO data at the same position. We refer to the identified regions
as ‘cores’ since their sizes are generally less than 0.1 pc and they contain typically a few solar
masses of material. A typical starless core has a density of around 105 cm−3 and temperature 10
K (di Francescoet al. (2007)). Since CO freezes-out below∼20 K (15-17 K;Nakagawa(1980)),
and the amount of freeze-out should directly scale with the density of the surrounding material
(Rawlingset al. (1992)), the high densities and low temperatures observed in the centres of these
cores are expected to result in significant depletion of CO onto dust grains. Hence, we derive
hydrogen column densities from both the dust and C18O data and use the ratio between the two as
a measure of depletion in the core centres. In doing this we make several assumptions about the
state of the gas and dust (which we discuss in detail later). However, because this is a statistical
study of many cores in several different clouds, differences in the depletion mechanism between
different clouds and cores should still be evident even with some sources of error. To achieve the
best possible measure of depletion, C18O is preferred to either13CO or 12CO because it is more
optically thin, and thus more representative of the whole column of gas, than either of the other
2 isotopologues. To derive a column density from the dust emission, we assume that emission
from dust arises from an opacity modulated black body curve at a temperature of 10 K for the
starless cores and 20 K for those coincident with a YSO candidate identified by Spitzer (i.e., the
protostellar cores). We discuss the implications of assuming fixed dust temperatures for the cores
in section 7.6. To infer the total column density of the dust from the emission at 850 microns, we
use:
Fν =∫
ΩBν(T, ν)κνNH2µmpdΩ (7.1)
where Fν is the peak flux per beam at frequencyν, Bν is the black body function at the same
frequency and temperature T,κν is the dust emissivity per unit mass of gas and dust at the same
frequency,NH2 is the column density of molecular hydrogen,µ is the mean molecular mass, mp is
7.2. A depletion factor for the dust cores - LTE analysis 211
the mass of a proton andΩ is the beam size of the relevant telescope. We assume a dust emissivity
of 1.97 cm2 g−1 (Ossenkopf & Henning(1994), assuming grains in a gas volume density of 106
cm−3 with thin ice mantles). The equation above assumes an emitting area larger than the beam
size of the relevant telescope. The beam size of the JCMT is generally smaller than clumpfind
derived diameters for the dust cores so we do not consider beam dilution effects to be a problem
and assume a beam filling factor of 1 in all cases.
It is common practice to directly infer hydrogen column density from the visual extinction at a
particular point. The Sadavoy catalogue includes a value for the extinction at the centre of the dust
cores. Using a direct linear relation between visual extinction and hydrogen density, assuming all
hydrogen to be in its molecular form (Nakai & Kuno(1995))
NH2/cm−2 = 1.87× 1021Aν/mags (7.2)
we estimate the dust column density. The visual extinction in this case was estimated from maps
produced by Sylvian Bontemps (not yet published). These are higher resolution that the COM-
PLETE survey but make use of 2MASS data. Resolutions for the maps vary from cloud to cloud
and are around 106 arcseconds in the case of Serpens (by private communication with S.Sadavoy).
This is a much lower resolution than achievable with SCUBA and will lead to a lower estimate for
the core dust column density since core densities probably peak in the centre and then drop out-
wards. Even so we calculated depletion factors using this method, again for cores in Serpens. The
results of this method and our original plots are shown in Figure 7.1. As expected, dust column
densities and thus depletion factors are lower using the visual extinction method. The much lower
spread in dust column densities is likely a consequence of the lower resolution of the extinction
maps. Protostellar dust column densities are less affected, however we select to adopt our original
method rather than use the visual extinction to derive depletion factors.
The hydrogen column densities from the C18O maps were first derived assuming LTE and
optically thin emission. Critical densities of the CO lines (some 104 cm−3) are generally lower
than the typical core density of around 105 cm−3 so material should be thermalised. Buckleet al.
(2010) calculated optical depths for the three CO isotopologue lines in Orion B and, by comparing
13CO and C18O peaks, showed that the C18O line is optically thin across the whole of the imaged
region, so our assumption of low optical depth in the C18O lines is likely to be valid even in the
denser dust cores (in section 7.6 we consider the implications of optical depth effects on our de-
pletion results). Accordingly, the Boltzmann and Planck equations give
7.2. A depletion factor for the dust cores - LTE analysis 212
Figure 7.1: H2 Column density in Serpens vs. Fdep (left, with H2 column densities calculated
using visual extinction measurements and right, using the dust thermal emission at 850 microns).
Crosses represent the protostars and diamonds the starless cores.
N(C18O) =(5.21× 1012)× Tex(12CO)×
∫Tmbdv
e−31.6
Tex(12CO)
(7.3)
where N(C18O) is the column density of C18O (cm−2), Tex(12CO) is the excitation temperature of
the line (from the12CO line profile), and Tmb is the main beam temperature (see Appendix A for
a full derivation of this equation).
We then assumed an N(C18O)/N(H2) ratio of 1.7×10−7 (Frerkinget al. (1982)) to convert
from C18O to hydrogen column density. We discuss the implications of this assumption in section
7.6.
We used the peak temperature of the12CO line to estimate the gas kinetic temperature, and
hence the line excitation temperature in LTE (Appendix A), using:
Tex(12CO) =16.59K
ln(1 + 16.6Tmax(12CO)+0.036
), (7.4)
again following from the Boltzmann and Planck equations describing LTE, assuming an optically
thick line. Tmax is the peak temperature of the12CO line at the centre of the dust core. We adopt
a main beam efficiency of 0.61 (Buckleet al. 2010). More detail on the derivation of Equation
7.3 can be found inPinedaet al. (2008). The 0.036 term results from the removal of the cosmic
microwave background at 2.7 K.
The use of Equation 7.3 requires that the12CO line be optically thick and not self-absorbed
at its peak. In the case of the12CO maps, lines are often self-absorbed and so cannot be used to
7.2. A depletion factor for the dust cores - LTE analysis 213
estimate an accurate gas temperature in all cases. If we assume the13CO line to be optically thick,
it can be used in place of the12CO line, in a modified form of Equation 3, to estimate the excitation
temperature in cores where the latter is obviously self-absorbed. We used the13CO line to estimate
the temperature if the13CO line peak was higher than the12CO in the line centre, otherwise the
12CO line was considered to be sufficiently accurate. The13CO lines, however, were also self-
absorbed. In these cases, we used the peak line temperature (i.e., the height of the peaks at the line
edge rather than at the centre) as the best possible first estimate of the gas temperature and note
that these will probably be slightly underestimated in several cases. It is difficult, looking at the
profiles of the 3 lines together, to disentangle the effects of self-absorption from the possibility of
there being several CO condensations lying along the line of sight. The position of the C18O peak
can help but again in many cases it does not peak at the frequency where the13CO and12CO lines
dip, which would definitely point to self-absorption in the latter 2 isotopologues. Of the 186 cores,
in total roughly 60% have a clear double peak in the12CO line. For 70% of these, the C18O line
peaks in the dip of the12CO line. The rest of the profiles (making up roughly 20% of the total) are
more complicated with the C18O line peaking nearer in frequency to one of the12CO line peaks
or itself showing a double profile. For consistency, we adopted the approach detailed above, using
the 12CO and13CO to find a kinetic temperature, even when self-absorbed. In section 7.6 we
discuss the implications of using12CO and13CO, which probably trace hotter gas than the dust,
to derive excitation temperatures for the central regions of the cores.
The integrated intensity of the C18O emission was found by fitting a Gaussian profile to the
line using DIPSO (part of the Starlink software package;Warren-Smith & Wallace(1993)). In
cases where the C18O exhibited 2 or more peaks, the separate peaks were considered to be due to
distinct cores along the line of sight and we included emission from all lines in the sum. In doing
this we assume that emission from dust derives from all cores along the line of sight and we find an
average measure of the depletion factor. Such cores will not, in reality, contain equal amounts of
dust, but since it is not possible to disentangle the dust emission from different cores along the line
of sight we are unable to estimate the level of depletion in individual cores. Using the hydrogen
column density calculated from the dust data and the hydrogen column density calculated from
the C18O, we derived a depletion factor - Fdep - given by:
Fdep =N(H2)dust
N(H2)CO
(7.5)
where N(H2)dust and N(H2)CO are the hydrogen column densities calculated from the dust and
the C18O respectively.
7.3. Results of the LTE analysis 214
Figure 7.2: H2 Column density derived from dust emission vs. Fdep for Orion NGC 2024 (left)
and NGC 2071 (right). Squares represent starless cores and crosses protostellar cores.
Figure 7.3: H2 Column density derived from dust emission vs. Fdep for Serpens (left - dashed line
shows the line of best fit of a linear regression on protostellar cores) and Taurus (right - solid line
shows the line of best fit of a linear regression on starless cores).
The more CO is depleted onto dust grains, the lower the hydrogen column density derived
from the CO gas phase emission and hence the higher the value of Fdep. In section 7.6, we discuss
the uncertainties in the derived depletion factors.
7.3 Results of the LTE analysis
Figures 7.2-7.4 show depletion factors versus dust column density for all 5 regions and Figures
7.5-7.7 show depletion factors versus position within each cloud. The results will be discussed in
detail for each source. We present a more general analysis in section 7.5.
7.3. Results of the LTE analysis 215
Figure 7.4: H2 Column density derived from dust emission vs. Fdep for Ophiuchus.
Figure 7.5: Depletion factor vs. position in cloud for Orion NGC 2024 (left) and NGC 2071
(right). Squares represent starless cores and crosses protostellar cores.
Figure 7.6: Ophiuchus (left) and Serpens (right).
7.3. Results of the LTE analysis 216
Figure 7.7: Taurus (left) and Taurus with south east region (right).
7.3.1 Serpens
Graveset al. (2010) presented a detailed analysis of Serpens using C17O and C18O data from
IRAM alongside HARP C18O and SCUBA 850 micron maps from the JCMT archive. TheirRADEX
calculations of CO column density for 8 positions spread over the cluster revealed an average
discrepancy of roughly a factor of 2.5 between the H2 densities derived from the dust and those
from the CO emission in the NW. This implies some freeze-out of CO. We find higher levels of
depletion than these authors in the regions covered by their IRAM data. Bearing in mind that we
are looking at only the densest cores in each region, these values are not inconsistent.
The largest depletions we find in Serpens are measured for the protostars located in the NW
sub-cluster (see Figure 7.6, right plot). In the SE sub-cluster, depletion factors drop steadily from
north to south for both the protostellar and starless cores. If the SE sub-cluster formed from 2
colliding filaments (as suggested in Duarte-Cabral et al. 2011, who modeled the cloud using SPH
simulations) then perhaps star formation occurred there more rapidly. In this scenario, the NW
sub-cluster could have undergone a slower collapse followed by a burst of star formation. The
SE sources cover a larger spread of ages which supports this view. Also, the SE shows higher
temperatures, rising towards the interacting region between the two sub-clusters, probably leading
to a release of molecules from dust grains into the gas phase. Note that freeze-out timescales are
short compared to the lifetimes of these clouds.Jones & Williams(1985) estimated a value of
3×109/n years where n is the volume density in cm−3. For densities of up to 106 cm−3, such
7.3. Results of the LTE analysis 217
as those seen in pre-stellar cores, this timescale is much shorter than the lifetime of a typical
molecular cloud region (∼103 years as opposed to∼106 years for the cloud lifetime,Larson
(1994)). The slower collapse of the NW sub-cluster inferred here would allow more time for
freeze-out to occur, hence higher depletion factors in the NW.
Serpens is the only cloud for which protostellar depletion factors are larger on average than
those of the starless cores, however there are only 4 starless cores in the sample.
7.3.2 Orion
Despite the observation ofBuckleet al. (2010) that C18O emission in NGC 2071 seemed to cor-
relate less well with the dust emission than in NGC 2024, in general we find higher levels of
depletion in the NGC 2024 cores than in the NGC 2071 cores.Savvaet al.(2003) found depletion
factors of around 10 for cores in Orion B. They made use of both C18O and C17O lines, calculating
optical depths for each core and using published dust temperatures for each rather than assuming
a single temperature for all cores. We do not study exactly the same cores but these values are
in rough agreement with average depletions that we calculate for NGC 2024 and NGC 2071.?
studied CO depletion in infrared dark clouds, thought to be the earliest evolutionary stage of high
mass star formation. They used the C18O J=(3→2) line to determine CO column densities assum-
ing LTE, and ammonia lines to determine the temperatures used in these calculations. They found
much higher values for the CO depletion factors than previous studies (5-78 with a mean of 32).
Thomas & Fuller(2008) looked at CO depletion around 84 high mass sources and found low de-
pletions with a maximum Fdep of 10. Again, these values are consistent with our average depletion
factors for NGC 2024 and NGC 2071, but our sample contains cores for which we measure much
higher depletions, maybe due to an over-estimate of the excitation temperature for some cores in
these clouds. It is a surprise to find such high depletion factors in high mass star-forming regions
such as NGC 2024 and NGC 2071 because one might expect the hot, turbulent environment to
lead to desorption of molecules from grains.
No cores are detected in the NGC 2071 cavity, but rather in the rest of the cloud where the
CO emission is stronger. In both NGC 2024 and NGC 2071, the locations in which the highly
depleted cores all lie display CO emission but in a more fragmented form (evident in the12CO
maps). This distribution suggests a clumpy medium where parts of the cloud are breaking up to
form denser regions conducive to star formation. The dusty regions around the CO cavities are
perhaps also active sites of star formation in these clouds. Cores in NGC 2024 show the largest
range in calculated depletion factors (difference between the highest depletion factor calculated for
7.3. Results of the LTE analysis 218
the cloud and the lowest). The region is hot and turbulent, possibly housing either a more diverse
set of objects in terms of their evolution, or cores whose envelopes are affected by surrounding
outflows. In both regions, protostellar cores are less depleted on average than starless cores.
7.3.3 Taurus
Ford & Shirley(2011) found very high values of the depletion factor (up to 1000) in Taurus by
fitting radiative transfer models to C18O observations but admitted finding difficulty in fitting all
results well. For a core in L1495, they derived values of around 4 with a fairly largeχ2 value for
the best fit model. We measure depletion factors around 4-10 times higher for cores in the vicinity,
although none of our dust peaks correspond to exactly the same position as those investigated by
these authors.Caselliet al. (1999) found depletion factors of around 10 for the core L1544, also
in Taurus.
The only SCUBA protostars identified in the regions observed in the rarer isotopologues of
CO are located in the ridge, coincident with two cores identified in HCO+ by Onishiet al.(2002).
In general, levels of depletion are high, but a clear divide is found between cores in the bowl and
the ridge, though there is a paucity of cores in the latter. In Figure 7.7 (right), the bowl comprises
the set of starless cores in the top left and the ridge, the three cores in the bottom right. Cores
in the bowl appear to be much more depleted. This difference could be connected with the lack
of outflow activity in the bowl which may be responsible for heating material around cores in the
ridge, or may suggest that they are at a more advanced stage of evolution. The two protostars in the
ridge are very near HH objects, which is evidence of outflows associated with each. The starless
core in the ridge also appears to show low levels of CO depletion, perhaps due to the proximity of
the active cores or to its age.
7.3.4 Ophiuchus
Redmanet al. (2002) measured a depletion factor of 10 or so in L1689B in Ophiuchus. That core
has a fairly low dust column density (compared to those in our sample) of a few times 1022 cm−2
so their result agrees well with ours for L1688.Bacmannet al. (2002) measured CO depletion
in a sample of nearby pre-stellar cores, some in Ophiuchus and Taurus, by means of C17O and
C18O lines. They noted a flattening of the emission profile towards the centres of the cores that
they attributed to freeze-out and estimated ratios of 4-15 between observed CO abundances and
those inferred from the dust emission. For this cloud, we find the lowest overall levels of depletion
7.4. Analysis of depletion data 219
in our sample. The sample of cores in Ophiuchus was the largest in number but values showed
little spread compared to the other clouds. The lowest levels of depletion are in the centre of the
imaged region near cores C, E and F with slightly higher values in the starless cores away from
the denser, more obscured regions (see Figure 7.6, left plot). As for the other clouds (with the
exception of Serpens), mean protostellar depletions are lower than starless core averages. Studies
of the ISM in Ophiuchus suggest that the dust grain size distribution there may be rather unusual,
having a population of very large dust grains as well as evidence for very small spinning dust
grains (Carrascoet al. (1973), Casassuset al. (2008)). If true, perhaps the reduced surface area
available for freeze-out due to the larger grains could partly explain the low levels of depletion
seen here.
7.4 Analysis of depletion data
7.4.1 Comparison of sources and previous results
We see a large range in Fdep from unity (no depletion) up to 112 in NGC 2024. Table 7.1 lists
average values of Fdep for both the protostellar and starless cores in all 5 regions. Overall, levels of
CO depletion are highest in Taurus and NGC 2024 and lowest in Ophiuchus. The fact that we see
the largest levels of depletion in Taurus and NGC 2024, the two most contrasting clouds in terms
of their physical conditions (one being cool and fairly quiescent and the other hot and turbulent) is
interesting. Core samples for both clouds are made up mainly of starless cores and for both there
is a large spread in derived depletion factors. In Orion, the depletion factors in cores track much
less well the core dust column densities. The majority of the cores are not very depleted, with a
couple of very highly depleted cores affecting the mean.
The highest values we find are large compared to most past studies of which we are aware,
however we cover many more sources in our study and the average depletion factors we find are in
fair agreement with previously derived values. Table 7.2 compares values from the literature with
ours for the same clouds. Even taking into account errors, which in most cases will cause us to
overestimate the depletion factor (see section 7.6), this possibility cannot completely explain the
extremely high depletions found in some cores. The JCMT beam for both the line and continuum
data at the wavelengths we use is small so we are looking at the very centres of the cores, where
one would expect to see higher depletion factors, rather than an average over a larger region. There
are only a few very highly depleted cores (around 6 with an Fdep higher than 40). All but one of
these are classified as starless and are probably older, more evolved cores for which molecules
7.4. Analysis of depletion data 220
Table 7.1: Depletion factor (Fdep) - mean, standard deviation and range. Brackets indicate the
number of cores in each sample.
Cloud Starless
mean
Fdep
Starless
Fdep sd
Starless
Fdep
range
Protostellar
mean Fdep
Protostellar
Fdep sd
Protostellar
Fdep
range
Protostellar
mean
Fdep at 15
K
Serpens 11(4) 2 5 12(11) 10 35 19
Taurus 25(23) 20 91 4(2) - - 6
Ophiuchus 7(58) 6 26 4(20) 3 12 6
NGC 2024 19(26) 22 115 8(3) - - 13
NGC 2071 13(28) 8 32 10(11) 12 46 16
have had more time to deplete.
7.4.2 Density versus depletion correlation
There is some evidence of correlation between the column densities of the cores and the depletion
factor in the case of starless cores in Taurus and protostellar cores in Serpens. A linear regression
analysis yields high values of the coefficient of determination (R2), an indicator of how well a
particular linear model fits the data (an R2 value of 0.8 indicates that 80% of the variance in the
data can be explained by a particular model, usually considered a good fit). Cores in Serpens and
starless cores in Taurus have linear fits with R2 values above 0.8. The best-fit lines for these clouds
are plotted in Figure 7.3. The correlations are different for the two clouds (see Table 7.3 for values
of the intercept and gradient in each case), the relation for Serpens being shallower. This could
indicate a difference in the behaviour of starless and protostellar cores. Our sample of cores in
Serpens is a more evolved population for which some heating of the core centre causes a release
of molecules into the gas phase. Results for Orion and Ophiuchus do not point to any correlation
between depletion and core column density or mass.
In Figure 7.8, depletion factors are plotted against dust column density for all cores in all
clouds in the sample. In the right hand plot, the slopes of the two significant correlations have
been added, representing the increase in depletion with core density for Serpens and Taurus. The
data is suggestive of perhaps containing two populations, one similar to the starless cores in Taurus
and one similar to the protostars in Serpens, whose depletions vary differently with core column
7.4. Analysis of depletion data 221
Table 7.2: A comparison with previous studies.
Paper reference Region Fdep Our mean star-
less Fdep
Our mean pro-
tostellar Fdep
Caselli et al. (1999) Taurus 10 25 4
Bacmann et al. (2002) 14
Ford & Yancy (2011) 4-1000
Bacmann et al. (2002) Ophiuchus 4.5-14 7 4
Redman et al.(2002) 10
Savva et al. (2003) Orion B 10 19/13a 8/10a
Duarte-Cabral et al. (2010) Serpens 2.5 11 12
a - values quoted for NGC 2024 (left) and NGC 2071 (right)
density. The protostellar cores do tend to exhibit a shallower slope. There are many fairly unde-
pleted starless cores at high densities, but it could be that some of these cores house undetected
protostars. This relation would have to be confirmed using SCUBA-2 or ALMA observations of
these regions for a much larger sample of cores.
Figure 7.8: Fdep vs. dust column density for all clouds. Trends are plotted for Serpens (dotted
line) and Taurus (solid line).
7.4. Analysis of depletion data 222
Table 7.3: Intercept, gradient and coefficient of determination (R2) values for the fits to density
vs. depletion plots for starless and protostellar cores in all clouds.
Cloud Intercept* Gradient* Coefficient
of Deter-
mination
(R2)
Ncores
Serpens 3.98 3.10(-23) 0.81 15
Serpens protostellar 1.49 3.48(-23) 0.91 11
Taurus -3.67 1.73(-22) 0.89 25
Taurus starless -2.33 1.70(-22) 0.88 23
Ophiuchus 4.13 1.64(-23) 0.14 78
Ophiuchus starless 4.34 2.01(-23) 0.10 58
Ophiuchus protostellar 2.59 1.20(-23) 0.58 20
NGC 2024 18.43 -6.16(-25) 0.00 29
NGC 2024 starless 12.56 4.76(-23) 0.08 26
NGC 2071 10.68 9.93(-24) 0.06 39
NGC 2071 starless 6.83 4.86(-23) 0.51 28
NGC 2071 protostellar 9.83 2.10(-24) 0.00 11
* - Units for the intercept and gradient are the same as for figures 7.3-7.5 (The intercept is
dimensionless and the gradient has units of cm3).
7.4.3 Protostellar versus starless core depletion
On average, CO appears to be more depleted in starless cores than protostellar cores (other than
in Serpens for which the sample of starless cores is very small). Levels of depletion should relate
to both the timescale of envelope accretion and the stage of evolution of the central radiation
source for protostellar cores since both affect the freeze-out timescale. For all clouds, except
Serpens, protostellar cores with high densities tend not to be very depleted in comparison with
dense starless cores in the same cloud.Jørgensenet al. (2005) looked at depletion profiles across
16 protostellar cores and found that the size of the depletion zone appeared to grow with envelope
mass in the early stages of evolution and then shrink as the central star began to heat the inner
regions. Perhaps we see here that higher mass protostars are in a more advanced stage of evolution
7.5. Uncertainties in the LTE derived depletion factor 223
where a substantial envelope has been formed (hence the higher dust column densities) and the
central star has begun to evaporate material from the grains in the centre. It would be useful
to model in more detail a selection of cores from each cloud to get a handle on ages, density
structures and a more accurate measure of depletion. It should be noted that, particularly in Orion,
there is a lot of diffuse emission at the frequencies used to identify protostars that may confuse
weak protostellar emission. Core classifications in Orion may not be definitive although they are
based on careful analysis of emission in several bands (seeSadavoyet al. (2010)).
7.5 Uncertainties in the LTE derived depletion factor
The calculation of column densities via LTE does of course have drawbacks. The temperatures
used to derive hydrogen column densities from the CO are uncertain since they are roughly cal-
culated, more than one rotational transition of a given molecule not being available. The CO
temperatures are derived from the12CO and13CO profiles which may well arise in hotter regions
of the cloud, being self-absorbed in the core centre. In such a case, the use of these lines would
result in an artificially high C18O temperature and low abundance being derived, leading to over-
estimates of the CO depletion. Furthermore, the exponential factor including Tex in Equation 2
for calculating CO column density rises rapidly below about 20 K, so the difference between as-
suming a temperature of 20 K and 10 K leads to a factor of around 2.5 difference in the derived
depletion factor.
As a test, calculations were performed as above, this time fixing the C18O excitation tempera-
tures to the assumed dust temperatures (10 K for starless cores and 20 K for the protostars). Since
temperatures derived from12CO and13CO are near 10-15 K in general, little difference to what
was shown in Figures 7.2-7.5 was seen. The only major discrepancy was in the case of NGC 2024,
for which several very high excitation temperatures are derived from the two more common iso-
topologues of CO. Here, protostellar depletion factors remain similar but the starless cores show
far lower levels of depletion in most cases. Figures 7.9 and 7.10 show depletion plots for NGC
2024 and Serpens using temperatures derived from the CO isotopologues themselves (left) and
setting C18O temperatures equal to dust temperatures (right - note the different scales on the y axis
for NGC 2024). Depletion factors may be particularly influenced by the temperature estimation in
this cloud since the isotopologues used to calculate temperatures will trace the hotter surrounding
regions (due to higher optical depth in the denser regions) which may be more diverse physically,
or contrast more with the dense core centres, than for the other regions due to the filamentary
7.5. Uncertainties in the LTE derived depletion factor 224
Figure 7.9: Orion NGC 2024 using CO derived temperatures to estimate Fdep (left) and using dust
temperatures (right). Squares represent starless cores and crosses protostellar cores.
Figure 7.10: Serpens using CO derived temperatures to estimate Fdep (left) and using dust tem-
peratures (right)
structure and outflow activity.
A major cause of error in our results may be the assumption of optically thin C18O in the
core centres. Higher optical depth in that line could lead to an underestimate of the CO gas phase
abundance and hence an overestimate of the depletion. We estimated C18O opacities very roughly
using Figure 12 fromCurtiset al. (2010) showing the variation of the C18O opacity with the ratio
of the13CO to C18O line peaks for X(13CO)/X(C18O) equal to 7.3, where X(13CO) and X(C18O)
are the abundances of the two molecules relative to hydrogen (Wilson & Rood(1994)). Using
the ratios of the peak13CO and C18O temperatures at the dust peaks we estimated C18O opacities
for the cores. Values were primarily very low and greater than 1 in only 25 of the 370 cores in
our sample. Correcting Equation 2 using our derived value of the optical depth made very little
difference to the resultant plots. Note, however, that the same method is used for all cores in
all clouds so that while derived individual values of Fdep may suffer from these uncertainties a
7.6. Evaluating Depletion Factors usingRADEX 225
comparison between regions should still be possible.
The calculation of molecular hydrogen column density from C18O emission requires the as-
sumption of a constant N(C18O)/N(H2) ratio. Published values vary by a factor of∼7 from 0.7×
10−7 (Tafalla & Santiago(2004)) to 4.8× 10−7 (Leeet al. (2003)). We adopt the value quoted
in Frerkinget al. (1982) and note that this choice may influence our calculated depletion factors
differently in different regions.
In our dust column density calculations we assume fixed dust temperatures of 10 K for the
starless cores and 20 K for the protostars. Using the higher temperature for the protostellar cores
results in lower densities being derived from the dust and so lower values of the depletion factor
for these cores. For the protostellar cores there will likely be some local heating of the dust near to
the core centres, so we adopt 20 K. Modeling work in the past has suggested that dust temperatures
for Class 0 and Class I sources may be closer to 15 K than the 20 K assumed here (Shirleyet al.
(2002), Young et al. (2003)), though with fairly significant spreads in derived temperatures (4.8
K for the former and 8 K for the latter). In addition,Larssonet al. (2000) studied the SEDs of 5
sub-millimeter sources in Serpens and derived dust temperatures of around 30 K for those sources.
Given these differences, it is somewhat unrealistic to define a single dust temperature for the cores.
As a test, we re-calculated depletion factors assuming a dust temperature for all the cores of 15 K.
In this instance, protostellar core depletion factors rise by a factor of only 1.6 compared to those
calculated assuming 20 K, so this is probably not a major effect compared to other assumptions
we make.
Depletion factors may be underestimated due to the larger beam size of the telescope at 850
microns relative to that of the spectral line data (22.9 arcseconds and 14 arcseconds respectively).
The SCUBA beam will sample a larger area around the dust cores so that the flux will be slightly
diluted compared to the CO maps which sample the more central regions of the cores. Although
both beams are smaller than the core diameters (fromCLUMPFIND), our assumption of an even
distribution of material across the cores will not be accurate.
7.6 Evaluating Depletion Factors usingRADEX
We usedRADEX (van der Taket al. (2007)), a radiative transfer code approximating an LVG (large
velocity gradient) approach, to calculate CO column densities and derive alternative depletion
factors. RADEX and LTE are both approximations. In LTE, the Boltzmann equation accurately
describes the level populations for any molecule, with the excitation temperature of all lines equal
7.6. Evaluating Depletion Factors usingRADEX 226
to the gas kinetic temperature.RADEX, on the other hand, takes into account both collisions and the
local radiation field. It does not, however, include any external radiation field. Using both methods
should allow us to probe the range of conditions in the clouds.Whiteet al.(1995) compared C18O
column densities in the Serpens molecular cloud calculated using LTE and LVG methods. They
found that, particularly for cooler, dense material, LTE methods tended to underestimate column
densities compared to LVG calculations by factors of around 4-8 at 10 K.
To solve the level populations,RADEX uses the escape probability method to describe the effect
of the radiation field.RADEX allows for the use of several different geometries which affect the
escape probability calculations. Here we used an homogeneous sphere having tested other geome-
tries and found the choice to make little difference to the results. For theRADEX calculations two
grids of models were run, one for the13CO data and one for the C18O data. For both, the column
density of the molecule and the gas kinetic temperature were left as free parameters. The dust
density was fixed using the 850 micron emission exactly as for the LTE calculations and converted
to a volume density using the clumpfind derived core sizes. We measured line widths from the
HARP 13CO and C18O spectra at the peak of the dust emission. We then assumed a canonical
ratio of 7.3 between the13CO and the C18O abundances (Wilson & Rood(1994)). The best fit
output to the observed line intensities of both13CO and C18O was selected by minimising the
value of the reducedχ2 parameter given by:
(I18obs − I18mod)2
(∆I18obs)2+
(I13obs − I13mod)2
(∆I13obs)2(7.6)
where Iobs and Imod are the observed and modelled peak line intensities. This method assumes
that13CO and C18O are tracing the same gas though this may not be the case.
7.6.1 LTE versusRADEX
Both theRADEX and LTE results are shown in Table 7.4 as well as some properties of the cores
from the Sadavoy et al. (2010) catalogue. We did not analyse all cores withRADEX but chose a few
to get some idea of how different the results fromRADEX and LTE would be and how effectively
RADEX could be used with the data available to evaluate depletion factors. We selected cores from
a variety of positions within the cloud, and with varying properties.
Table 7.4 lists an identifier for each core, its position, the (CLUMPFINDdefined) radius, dust
density, dust column density, temperature derived from the12CO lines in LTE, depletion derived
in LTE, gas kinetic temperature fromRADEX and the depletion factor calculated withRADEX. The
7.6. Evaluating Depletion Factors usingRADEX 227
Figure 7.11:RADEX versus LTE depletion factors. Left - all cores fitted withRADEX (starless cores
are squares, protostellar cores are crosses). Right - only cores with a good (χ2 less than 2), unique
RADEX fit.
final column lists the reducedχ2 value, intended to give an idea of how well the best fit model
and observed values agreed in each case. We consider values of this parameter below 2 to indicate
a good fit (with the gas kinetic temperature and the13CO and C18O column densities as free
parameters). Note again that a depletion factor of 1 indicates no depletion. There are three cores
for which values of Fdep are equal to 0 as calculated byRADEX indicating that the column density
of hydrogen calculated using the dust emission was a lot lower than that calculated using the gas
phase CO emission. In these cases, theRADEX kinetic temperature was higher than 25 K. If correct,
it is likely that the CO in these cases emanates from warmer regions outside of the dense cores.
Theχ2 values for these cores were also all high.
In most cases,RADEX and the LTE approximation yielded similar values for the depletion fac-
tor and gas kinetic temperature. There appears, however, to be a tendency towards lower depletion
estimates when usingRADEX rather than LTE. Several cores, particularly those in Taurus and NGC
2024, were very difficult to fit usingRADEX (either never finding a good fit, indicated by the high
values for the fit parameter in Table 7.4, or else finding equally good fits for several input combi-
nations, marked by an asterisk in the table). Other than six cores, four of which are in NGC 2024,
kinetic temperatures derived via the two methods agree to within 4-5 K on average. We note that
the maximum depletion factor we calculate for the cores in Serpens is similar to that found by
Duarte-Cabralet al. (2010).
Figure 7.11 shows LTE versusRADEX derived depletion factors. The left hand plot includes
the full sample of fitted cores (with starless cores as squares and protostellar cores as crosses).
The right hand plot shows only those for which we could find a fairly good, unique fit withRADEX
7.7. Summary 228
(χ2 less than 2). Looking at the right hand plot, it does appear that for several cores (two in
particular) LTE methods overestimate CO depletion (or underestimate column densities). The two
cores for which this effect is most prominent are the two densest cores in the sample. If LTE line
intensities reach a maximum for a given column density, and if the population is sub-thermal, a
higher column density of CO is required to reach the same line intensities. Where LTE depletions
are high may be a result of high optical depth in the C18O line, resulting in an underestimate of
CO gas column density in the LTE approximation. On the other hand, using the13CO line in the
RADEX models may lead to problems due to self-absorption in that line. Cores with very different
measured depletion factors from the two methods did tend to display double peaked13CO line
profiles or have higher intensities in the C18O line than the13CO, both possible indications of
some self-absorption. We also use core sizes from the code clumpfind to calculate dust volume
densities to input intoRADEX, which may introduce further uncertainty. The fact that we have only
one transition for each isotopologue of CO is likely the main cause of error when usingRADEX to
estimate column densities. It is encouraging that temperatures, depletions and general trends agree
to some extent in those cores for which we could achieve a good fit (a median discrepancy of 2 in
the depletion factor and 4 K in the temperature). To use this code to find depletion factors for all
cores and properly compare regions, we would need a good and unique fit for all cores. It would
be preferable to obtain data with several transitions for C18O rather than using two isotopologues.
7.7 Summary
We have used the C18O and dust emission in the dense cores of five local star-forming regions,
experimenting with both LTE and non-LTE methods, to statistically compare large-scale depletion
factors. We find that:
• Within each cloud, the highest levels of depletion are found in the more quiescent regions
(Serpens and Taurus) or fragmented regions around the edges of CO cavities (Orion).
• Cores in Ophiuchus (L1688) are the least depleted overall. This behaviour could be con-
nected to the anomalous grain size distribution inferred from observations of this cloud.
• There is a strong correlation between core density and depletion in both Serpens and Taurus.
• Starless cores are, on average, more depleted than protostellar cores (an overall mean deple-
tion factor of 13 rather than 7) and protostars may show a different trend with core density
7.7. Summary 229
to the starless cores. This could be due to the evaporation of material from dust grains after
heating by the IRAS source.
We note that while our study suffers from uncertainties due to temperature estimations and
the assumption of LTE, these are often systematic and should not affect comparison of depletion
factors among the different clouds. These factors do, however, affect the depletion factors derived
for individual cores. Multi-line observations of C18O as well as other isotopologues should help
to constrain better the CO column densities and temperatures and achieve more accurate measures
of the depletion factors.
7.7. Summary 230Ta
ble
7.4:
LTE
andR
AD
EX
resu
lts-
Taur
sere
fers
toth
eso
uth-
east
ern
regi
onof
L149
5(t
herid
ge).
Bra
cket
sin
dica
tepo
wer
sof
10.
Cor
eR
a(J
2000
)D
ec(J
2000
)R
ad(p
c)D
ensi
tyof
gasa
(cm−
3)
Col
umn
Den
sity
of
gasa
(cm−
2)
Tex
(LT
E)
F dep
(LT
E)
Tkin
(RA
DE
X)
F dep
(RA
DE
X)
Red
uced
χ2
Oph
p316
h26
m10
s4
-24
20”5
6’0.
027
4.0(
5)6.
74(2
2)35
K2
37K
18.
69
Oph
p4↑∗
16h
26m
27s
6-2
423
”57’
0.05
42.
7(6)
8.93
(23)
29K
1328
K0
267.
88
Oph
p10
16h
27m
00s
5-2
426
”38’
0.01
71.
7(5)
1.76
(22)
23K
128
K1
2.07
Oph
p13
16h
27m
07s
2-2
438
”08’
0.02
32.
3(5)
3.32
(22)
18K
114
K1
2.09
Oph
s18
16h
26m
36s
3-2
417
”56’
0.02
66.
2(5)
1.00
(23)
27K
322
K2
5.51
Oph
s42
16h
27m
58s
6-2
433
”43’
0.03
31.
0(6)
2.24
(23)
17K
2012
K14
0.09
Oph
s53
16h
27m
05s
0-2
439
”14’
0.02
91.
3(6)
2.24
(23)
18K
210
K3
0.43
Taur
sep1
04h
19m
42s
327
13”3
7’0.
024
4.8(
5)7.
15(2
2)12
K3
8K
20.
07
Taur
sep2
04h
19m
58s
427
10”0
0’0.
026
4.3(
5)6.
95(2
2)12
K5
12K
40.
17
Taur
ses1
04h
19m
50s
827
11”3
0’0.
019
5.6(
5)6.
56(2
2)9
K8
10K
160.
04
Taur
s904
h18
m33
s6
28
26”5
3’0.
008
2.5(
6)1.
24(2
3)10
K13
10K
70.
25
Taur
s18∗
04h
18m
38s
728
21”3
0’0.
009
5.6(
6)3.
11(2
3)11
K38
8K
40.
02
Taur
s21∗
04h
18m
41s
028
22”0
0’0.
006
9.1(
6)3.
35(2
3)11
K16
8K
90.
80
Taur
s22∗
04h
18m
42s
428
21”3
0’0.
006
1.8(
6)6.
56(2
2)11
K15
8K
20.
21
Taur
s24↑∗
04h
18m
43s
728
23”2
4’0.
012
4.5(
6)3.
35(2
3)11
K53
7K
11.
38
Ser
pp2
18h
29m
49s
801
16”3
9’0.
055
3.0(
6)1.
02(2
4)21
K37
13K
140.
06
Ser
pp3
18h
29m
51s
401
16”3
3’0.
038
7.8(
5)1.
82(2
3)20
K15
14K
90.
46
Ser
pp8
18h
30m
00s
201
10”2
1’0.
037
2.9(
5)6.
53(2
2)13
K3
10K
10.
45
Ser
pp9
18h
30m
00s
201
11”3
9’0.
053
6.2(
5)2.
02(2
3)17
K6
14K
51.
42
Ser
pp1
118
h30
m01
s8
01
15”0
9’0.
035
2.7(
5)5.
91(2
2)19
K5
26K
60.
19
Ser
ps2
18h
30m
02s
601
09”0
3’0.
028
8.4(
5)1.
45(2
3)11
K10
11K
50.
87
Ser
ps3
18h
30m
05s
001
15”1
5’0.
022
5.4(
5)7.
25(2
2)18
K13
64K
1011
.38
Ser
ps4
18h
30m
13s
401
16”1
5’0.
032
3.7(
5)7.
25(2
2)15
K12
31K
150.
03
NG
C20
24p1
td
05h
41m
43s
0-0
154
”20’
0.16
86.
9(4)
7.15
(22)
59K
1264
K0
28.4
4
NG
C20
24p2
td
05h
41m
44s
6-0
155
”38’
0.23
35.
7(4)
8.18
(22)
71K
1080
K0
147.
78
NG
C20
24p3
t05
h41
m49
s4
-01
59”3
8’0.
084
4.0(
4)2.
05(2
2)22
K4
24K
114
.21
NG
C20
24s2
905
h41
m33
s4
-01
49”5
0’0.
044
4.0(
5)1.
10(2
3)24
K4
80K
317
.57
NG
C20
24s3
1t05
h41
m36
s2
-01
56”3
2’0.
120
3.7(
5)2.
76(2
3)36
K21
80K
769
7.60
NG
C20
24s3
905
h42
m03
s1
-02
04”2
1’0.
064
2.0(
5)7.
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CHAPTER 8
CONCLUDING REMARKS AND PROPOSALS
FOR FUTURE WORK
There is strong evidence to support the fact that molecular clouds are clumpy on small scales,
however the capabilities of the telescopes used to image these clouds place constraints on the scales
at which we can observe the underlying structure. The work presented in this thesis describes the
application of two contrasting approaches to explore the clumpy nature of star-forming molecular
clouds. Particular emphasis is placed on the process of depletion, or freeze-out, of molecules onto
the surfaces of dust grains in these regions.
Chapters 2 and 3 describe how we can use chemical models to study the structure of clumpy
molecular clouds near to Herbig-Haro objects. The intense radiation from these shock fronts has
not yet dynamically affected pre-existing clumps but acts to liberate species from icy mantles on
dust grains and encourages a gas phase photochemistry, allowing the clumps to be observed in
emission from various molecules. We consider the effect of a moving radiation field source (a
more realistic description of a passing shock front than the static source used in previous mod-
els) and conclude that some molecules can remain enhanced for longer under the influence of a
moving field. This goes some way to explaining the high abundances observed near to HHOs.
We extend this work to the consideration of a molecular cloud as a conglomeration of transient
density enhancements and use the same chemical code to produce synthetic maps of parsec scale
areas around HHOs, which should be comparable with observations of the same regions. Various
properties of the clumps, as well as their sizes and filling factors can be explored in this way,
making it a unique probe of the underlying structure in star-forming clouds.
231
232
An alternative approach is adopted in Chapters 4, 5 and 6, for which we make use of data
from the JCMT Gould Belt Survey (GBS) to study the structure of CO emission in molecular
clouds (using three different isotopologues). In Chapter 4 we present the data analysed and in
Chapter 5 test clump decomposition (or flux fitting) algorithms. These have been widely used
to derive clump mass functions in nearby star-forming regions and have led to the idea that the
stellar mass function is established early on in the stars life, prior to the switch on of the protostar.
The algorithms are designed to divide maps into discrete regions of higher intensity emission. An
output catalogue is produced which allows us to study the properties of the clumps. We chose an
appropriate algorithm and apply this to GBS data in Chapter 6. Because we have consistent data
for several different nearby clouds we are able to make meaningful comparisons between them.
In matching CO clumps to previously identified pre and protostellar dust cores, we begin to see
possible signs of CO freeze-out. Massive protostars appear to coincide better with CO clumps
than do the massive starless cores which could suggest some depletion in the latter and a liberation
of mantles in the former due to heating by the nascent stellar object.
We consider the depletion of CO further in Chapter 7 by directly comparing the hydrogen
column density calculated using dust emission measurements with that inferred from the CO at
the centre of starless and protostellar dust cores. Although this is a straightforward method, and
requires us to make several assumptions about the state of the dust and gas, it proves a useful
means of comparing depletion in different regions and we find higher levels of depletion in the
more quiescent or filamentary regions within clouds.
The study of the structure of a dark molecular cloud prior to star formation, and the chemi-
cal processes occurring in these regions presents many challenges, but a better understanding of
both will be a crucial step in clarifying the processes involved in early star formation and the rela-
tionship between a stellar population and its surroundings. Chapter 3 highlights some molecules
that may be particularly enhanced, and display a particularly condensed structure, when a clumpy
molecular cloud is illuminated by the radiation from a passing HHO. With observational data it
may be possible to infer something about the age, physical properties, filling factor and chemistry
(including grain surface chemistry) of transient clumps in an inhomogeneous cloud and it would
be worthwhile to investigate this possibility further. We present more of a statistical study in the
final few Chapters of the thesis, however an interesting next step would be to carry out detailed
work on a few cores in the same regions. Proper radiative transfer modelling would allow us to ob-
tain a much more accurate measure of freeze-out. Molecular line profiles may also provide a clue
to depletion in that the wings might tend to represent the collapsing inner regions of a protostar or
233
starless core. The GBS spectra would provide excellent data with which to look for a connection
between the size of the line wings and the depletion in a core, and to determine whether this might
provide a viable probe.
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APPENDIX A
DETAILS OF CO COLUMN DENSITY AND
M ASS CALCULATIONS
A.1 Column Density Calculations
For an optically thin transition, the antenna temperature of a source will be proportional to the
column density in the upper level of the same transition. It is thus possible, in such a case and
assuming local thermodynamic equilibrium, to calculate the total column density of a molecule
from just one spectral line.
In the case of a linear rotor molecule such as CO, this is a fairly straightforward process. Here
I summarize the steps involved in deriving column densities from line emission in the case of a
simple, two-level system.
For CO and other linear rigid rotors, the energies of rotational states depend on the quantum
number J via
EJ =J(J + 1)hν10
2, (A.1)
where EJ is the energy of the state with quantum number J,ν10 is the frequency of the transition
from first excited state to ground and h is the Planck constant. This energy is related to the moment
of inertia of the molecule about the single rotational axis, which is assumed constant in the case
of no molecular distortions. The degenaracy of a level is given by gJ = (2J+1) and rotational
transitions with∆J 6= 1 are forbidden.
For the two level system considered here, transitions are from J+1→J and I use subscripts 2
and 1 to denote quantities relating to the upper and lower energy levels respectively. n2 and n1 thus
245
A.1. Column Density Calculations 246
represent the total number density in the first excited state and the ground state of the molecule.
Transitions between states can occur via spontaneous emission, stimulated emission and col-
lisional excitation or de-excitation. The first two processes are described by the Einstein A and B
coefficients. The following equation for the A21 includes a term representing the electric dipole
momentµe of the molecule and describes how it is coupled to the radiation field (the rate of
spontaneous emission from the upper level is then given by A21n2).
A21 =16π3µ2
e
3ε0hc3(
J + 12J + 3
)ν321, (A.2)
whereε0 is the permittivity of free space andν21 the frequency of the transition of interest. The
Einstein B21 and B12 coefficients represent stimulated emission from the upper level and absorp-
tion respectively. The rates of collisional excitation and de-excitiation are described by the coef-
ficientsγ12 andγ12 which relate to the collisional cross-section of the molecule and the average
particle velocity. In LTE the Boltzmann distribution applies and the rates of collisional excitation
and de-excitation into and from the upper level are described by
γ21
γ12=
g2
g1. (A.3)
We begin from the equation of radiative transfer, which describes how radiation is absorbed and
re-emitted on passing through a medium.
dIν
ds= −κνIν + εν , (A.4)
where Iν is the specific intensity of the radiation in units of Wm−2Hz−1sr−1 along a ray s, andκν
andεν are the absorption and emission coefficients given by
εν =hν21
4πA21nνφ(ν). (A.5)
and
κν =hν21
c(n1B12 − n2B21)φ(ν). (A.6)
Here,φ(ν) is the intrinsic line profile, normalised so that its integral over all frequencies is equal
to 1. Since the line width due to the bulk motion of the cloud is much greater than this intrinsic
line width, it is useful to write the above equations in terms of the number densities in the two
levels per unit velocity, n1(v) and n2(v).
εν =hc
4πA21n2(v) (A.7)
A.1. Column Density Calculations 247
and
κν =A21c
3
8πν321
(2J + 32J + 1
)[1− exp(hν21
kTex)]n1(v). (A.8)
If we ignore stimulated emission and absorption and assume equilibrium, so that the population of
each level stays constant, the rate of collisional excitation into the upper level is equal to the rate
of collisional de-excitation out of the level plus the rate of spontaneous emission out of the level.
A12n1 = A21n2 + ntotn2γ21 (A.9)
rearranging and substituting in equation A.3 we are left with the following expression
n2
n1=
(g2/g1)exp(−hν21/kTex)1 + (nc/ntot)
(A.10)
where nc (A21/γ21) is the critical density, at which the rate of spontaneous emission from the
upper level is equal to the rate of collisional de-excitation. At low densities, for which the density
is much lower than nc, the upper level will de-excite via spontaneous emission of a photon much
quicker than via collisions and the levels are said to be sub-thermally excited. This effect will be
more prominent for the upper levels in a molecule with many. Much above the critical density,
the level populations are thermalized, and the kinetic temperature (Tkin of the gas is equal to he
excitation temperature (Tex) of the various levels. It is the second situation that we consider here.
Integrating the equation of radiative transfer (A.4) above we get
Iν = I0e−τν + (1− e−τν )Sν , (A.11)
whereτν is the optical depth at frequencyν, and Sν the source function given by
Sν =εν
κν. (A.12)
The term involving I0 can be ignored in this case as it represents low level, background emission
due to the cosmic microwave background. At low optical depths equation A.11 can be written as
Iν = τνSν , (A.13)
since the term in brackets simplifies toτν for τν 1.
Assuming an homogenous medium (optical depth does not vary),τν is simply equal to kνL
(with L the length of the path traversed by the ray through the medium). Iν is also given by
Iν =2kTR
λ2, (A.14)
A.1. Column Density Calculations 248
where TR is the radiation temperature of the source, the temperature of a black-body emitting the
same intensity of radiation, also called the Rayleigh-Jeans temperature. Here, since we assume
that the source emits as a black-body this should be the same as the radiation brightness tem-
perature received at the telescope antenna once corrected for losses due to atmospheric effects,
and for the direction-dependant response of the antenna to radiation. Generally, a telescope effi-
ciency (νmb is used which merely increases the measured antenna temperature by a certain factor,
however ideally a proper consideration of the telescope response would be attempted.λ is the
wavelength of the radiation and k the Boltzmann constant. Combining these two equations, sub-
stituting in equation A.7, we are left with the following expression for the main beam temperature
Tmb (antenna temperature corrected for telescopic effects) in terms of the total column density in
the upper level N2 (from the product of the number density of the upper level and the path length).
Tmb =hA21λ
2c
8πkN2(ν). (A.15)
Integrating this equation over velocity and then over the solid angle of the source, assuming a
distance d gives
N tot2 = (
3ε0kd2
2π2µ2eν10
)2J + 1
(J + 1)2
∫∫Tmb(ν,Ω)dνdΩ. (A.16)
To get the total column density of the molecule we need an expression involving the partition func-
tion, which describes the relative populations of the different energy levels. In LTE the occupancy
of the upper level of interest is given by
N2
Ntot=
g2exp(−E2/kTex)Z
, (A.17)
where Z is the partition function given by
Z =∑
allstates
gJexp(−EJ/kTex). (A.18)
For C18O, the above calculations and substitution of relevant constants leaves us with the following
expression for the total CO column density (after taking into account the abundance of this isotope
relative to total CO abundance). It is this that we use in Chapter 7 to calculate CO column densities.
N(C18O) = 5.21× 1012cm−2 Tex/K
exp(−31.6K/Tex)(∫
Tmbdν
Kkms−1). (A.19)
A.2. Excitation Temperature from12CO 249
A.2 Excitation Temperature from 12CO
Working from equation A.5 (following the method ofPinedaet al. (2008)), assuming blackbody
emission for both the background and source, as well as optically thick12CO so that the optical
depthtau tends to infinity, and taking the radiation temperature of the source TR to be equal to
the main beam brightness temperature at the peak of the12CO (Tmax(12CO)), we are left with the
following equation
Tmax(12CO) = T0(1
exp( T0Tex−1)
− 1exp( T0
Tbg−1)). (A.20)
where T0=hν/k, with h and k the Planck and Boltzmann constants respectively, andν the fre-
quency of the observed spectral line. Tex is the excitation temperature of the transition (and of all
transitions of the molecule in LTE) and Tbg is the temperature of the cosmic background radiation
(2.7 K). Substituting in this value for the background temperature, as well as the correct value of
ν for the J=(3→2) line of 12CO, and rearranging leaves us with the equation for the excitation
temperature of12CO, used in Chapter 7 of this Thesis.
Tex(12CO) =16.59K
ln[1 + 16.59K/(Tmax(12CO) + 0.036K)]. (A.21)
A.3 LTE Mass
It is fairly straightforward to convert the above value for the column density of C18O into a mass by
integrating the main beam temperature over the clump to get the total number of C18O molecules,
multiplying by the fractional abundance of hydrogen relative to C18O to get the total number of
hydrogen molecules and then by the mass of a hydrogen molecule to get the total mass in the
clump. We also multiply by a factor of 1.4 to account for helium in the clump (whose number
density relative to H2 is around 0.2).
A.4 Virial Mass
For a core in virial equilibrium, and ignoring the effect of external masses on the gradient in the
graviational potential, we can use the virial theorem to calculate a virial mass directly from the CO
line width. The virial mass represents the minimum mass required for the core to be gravitationally
bound. The virial theorem states that for a system in virial equilibrium
2T + W = 0 (A.22)
A.4. Virial Mass 250
where W is the gravitational potential energy of the system and T the kinetic energy. These are
given by
T = Mδv2 (A.23)
and
W = −3γGM2
5R(A.24)
whereγ allows for different density distributions (and for an r−2, or inverse-square density profile
is equal to 5/3), M is the mass of the core, R the radius and G the gravitational constant.δv is
the three-dimensional velocity dispersion of the core, measured from the line width, which gives
the velocity dispersion along the line of sight. Assuming an homogeneous, spherical core the 3D
velocity dispersion is then given by
δv2 = 3[δ2CO +
kT
mH[1µ− 1
mCO]] (A.25)
for C18O, with corrections for the molecular weight of the observed species compared to the core
material as a whole. Here,δCO is the size of the clump along the velocity axis, k the Boltzmann
constant, T the kinetic temperature of the gas, mH the atomic mass of a hydrogen atom, mCO
the atomic mass of CO andµ the mean molecular mass of the material of interest. Combining
equations A.20, A.21 and A.22, we are left with the following for the virial mass of the core
Mvir =5Rδv
2
3γG(A.26)
For more details, seeBertoldi & McKee(1992), Williams et al.(1994) andMacLarenet al.(1988).
APPENDIX B
CO M APS FROM THE JCMT G OULD BELT
SURVEY
Here we present the data used in the final three chapters of this thesis, which was taken as part of
the JCMT (James Clark Maxwell Telescope) Gould Belt Survey (GBS). We show images of12CO,
13CO and C18O in the J=(3→2) lines for five regions covered by the survey. Reduction of the data
is outlined in the first look papers (Buckleet al. (2010); Graveset al. (2010); Daviset al. (2010);
White et al. in prep). I had no part in this process but made some small changes (e.g. binning and
trimming the maps) in order to facilitate our study.
251
B.1. NGC 2024 CO maps 252
B.1 NGC 2024 CO maps
Figure B.1: NGC 202412CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1 (top left) and 16
kms−1 (top right).
B.1. NGC 2024 CO maps 253
Figure B.2: NGC 202412CO integrated intensity map from HARP (in units of Kkms−1).
B.1. NGC 2024 CO maps 254
Figure B.3: NGC 202413CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1 (top left) and 16
kms−1 (top right).
B.1. NGC 2024 CO maps 255
Figure B.4: NGC 202413CO integrated intensity map from HARP (units of Kkms−1).
B.1. NGC 2024 CO maps 256
Figure B.5: NGC 2024 C18O channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 4 kms−1 (bottom left), 8 kms−1 (bottom right), 12 kms−1 (top left) and 16
kms−1 (top right).
B.1. NGC 2024 CO maps 257
Figure B.6: NGC 2024 C18O integrated intensity map from HARP (units of Kkms−1).
B.2. NGC 2071 CO maps 258
B.2 NGC 2071 CO maps
Figure B.7: NGC 207112CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5 kms−1 (top left) and 15
kms−1 (top right).
B.2. NGC 2071 CO maps 259
Figure B.8: NGC 207112CO integrated intensity map from HARP (units of Kkms−1).
B.2. NGC 2071 CO maps 260
Figure B.9: NGC 207113CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5 kms−1 (top left) and 15
kms−1 (top right).
B.2. NGC 2071 CO maps 261
Figure B.10: NGC 207113CO integrated intensity map from HARP (units of Kkms−1).
B.2. NGC 2071 CO maps 262
Figure B.11: NGC 2071 C18O channel map from HARP showing mean intensity (in Kelvin) in
channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5 kms−1 (top left) and 15
kms−1 (top right).
B.2. NGC 2071 CO maps 263
Figure B.12: NGC 2071 C18O integrated intensity map from HARP (units of Kkms−1).
B.3. Ophiuchus CO maps 264
B.3 Ophiuchus CO maps
Figure B.13: Ophiuchus12CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 2 kms−1, 4 kms−1, 6 kms−1 and 8 kms−1.
B.3. Ophiuchus CO maps 265
Figure B.14: Ophiuchus12CO integrated intensity map from HARP (units of Kkms−1).
B.3. Ophiuchus CO maps 266
Figure B.15: Ophiuchus13CO channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 2 kms−1 (bottom left), 4 kms−1 (bottom right), 6 kms−1 (top left) and 8 kms−1
(top right).
B.3. Ophiuchus CO maps 267
Figure B.16: Ophiuchus13CO integrated intensity map from HARP (units of Kkms−1).
B.3. Ophiuchus CO maps 268
Figure B.17: Ophiuchus C18O channel map from HARP showing mean intensity (in Kelvin) in
channels centred at 2 kms−1 (bottom left), 4 kms−1 (bottom right), 6 kms−1 (top left) and 8 kms−1
(top right).
B.3. Ophiuchus CO maps 269
Figure B.18: Ophiuchus C18O integrated intensity map from HARP (units of Kkms−1).
B.4. Serpens CO maps 270
B.4 Serpens CO maps
Figure B.19: Serpens12CO channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1 (top left) and 14 kms−1
(top right).
B.4. Serpens CO maps 271
Figure B.20: Serpens12CO integrated intensity map from HARP (units of Kkms−1).
B.4. Serpens CO maps 272
Figure B.21: Serpens13CO channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1 (top left) and 14 kms−1
(top right).
B.4. Serpens CO maps 273
Figure B.22: Serpens13CO integrated intensity map from HARP (units of Kkms−1).
B.4. Serpens CO maps 274
Figure B.23: Serpens C18O channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 8 kms−1 (bottom right), 11 kms−1 (top left) and 14 kms−1
(top right).
B.4. Serpens CO maps 275
Figure B.24: Serpens C18O integrated intensity map from HARP (units of Kkms−1).
B.5. Taurus CO maps 276
B.5 Taurus CO maps
Figure B.25: Taurus12CO channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1 (top left) and 8 kms−1
(top right).
B.5. Taurus CO maps 277
Figure B.26: Taurus12CO integrated intensity map from HARP (units of Kkms−1).
B.5. Taurus CO maps 278
Figure B.27: Taurus13CO channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1 (top left) and 8 kms−1
(top right).
B.5. Taurus CO maps 279
Figure B.28: Taurus13CO integrated intensity map from HARP (units of Kkms−1).
B.5. Taurus CO maps 280
Figure B.29: Taurus C18O channel map from HARP showing mean intensity (in Kelvin) in chan-
nels centred at 5 kms−1 (bottom left), 6 kms−1 (bottom right), 7 kms−1 (top left) and 8 kms−1
(top right).
B.5. Taurus CO maps 281
Figure B.30: Taurus C18O integrated intensity map from HARP (units of Kkms−1).
283
Figure C.1: CS column density maps at 10 years without HH field (top left), with 1000 G0 field at
10 years (top right) without HH field at 1000 years (middle left) and with 1000 G0 field at 1000
years (middle right). Without radiation field at 5000 years (bottom left) and with 1000 G0 field
at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.22×1015
cm−2.
284
Figure C.2: NH3 column density maps at 10 years without HH field (top left), with 1000 G0 field
at 10 years (middle right) without HH field at 1000 years (middle left) and with 1000 G0 field
at 1000 years (middle right). Without radiation field at 5000 years (bottom left) and with 1000
G0 field at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.73×1017 cm−2.
285
Figure C.3: HCN column density maps at 10 years without HH field (top left), with 1000 G0 field
at 10 years (middle right) without HH field at 1000 years (middle left) and with 1000 G0 field
at 1000 years (middle right). Without radiation field at 5000 years (bottom left) and with 1000
G0 field at 5000 years (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
1.05×1016 cm−2.
286
Figure C.4: CO column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field
at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years (top
right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 3.17×1018 cm−2.
287
Figure C.5: NH3 column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field
at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years (top
right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.73×1017 cm−2.
288
Figure C.6: H2CO column density maps at 10 years with 100 G0 field (top left), with 1000 G0field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years
(top right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 6.15×1015 cm−2.
289
Figure C.7: SO column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field
at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years (top
right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 2.45×1015 cm−2.
290
Figure C.8: HCN column density maps at 10 years with 100 G0 field (top left), with 1000 G0field at 10 years (2nd), with 100 G0 field at 1000 years (3rd) and with 100 G0 field at 1000 years
(top right). Maps at 5000 years for a 100 G0 static field (bottom left) and a 1000 G0 field (bottom
right). Minimum contour level of 1×1011 cm−2, maximum of 1.05×1016 cm−2.
291
Figure C.9: HCO+ column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 3.93×1013 cm−2.
292
Figure C.10: CO column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 3.17×1018 cm−2.
293
Figure C.11: CS maps at 10 years with 1000 G0 static field (top left), with 1000 G0 moving field
at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0 moving field at
1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left) and a 1000 G0moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 4.27×1015
cm−2.
294
Figure C.12: NH3 column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 2.73×1017 cm−2.
295
Figure C.13: H2CO column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 6.15×1015 cm−2.
296
Figure C.14: SO column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 2.45×1015 cm−2.
297
Figure C.15: HCN column density maps at 10 years with 1000 G0 static field (top left), with 1000
G0 moving field at 10 years (2nd), with 1000 G0 static field at 1000 years (3rd) and with 1000 G0
moving field at 1000 years (top right). Maps at 5000 years for a 1000 G0 static field (bottom left)
and a 1000 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum
of 1.09×1016 cm−2.
298
Figure C.16: HCO+ column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right). Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.76×1013 cm−2.
299
Figure C.17: CO column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.96×1018 cm−2.
300
Figure C.18: CS column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
3.41×1015 cm−2.
301
Figure C.19: NH3 column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.42×1017 cm−2.
302
Figure C.20: H2CO column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.30×1015 cm−2.
303
Figure C.21: SO column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
2.30×1015 cm−2.
304
Figure C.22: HCN column density maps at 10 years with 100 G0 static field (top left), with 100
G0 moving field at 10 years (2nd), with 100 G0 static field at 1000 years (3rd) and with 100 G0
moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)
and a 100 G0 moving field (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
7.72×1015 cm−2.
305
Figure C.23: CO column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 4.20×1018
cm−2.
306
Figure C.24: CS column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.74×1015
cm−2.
307
Figure C.25: N2H+ column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 1.08×1011
cm−2.
308
Figure C.26: CH3OH column density maps at 10 years with 1000 G0 static field and 200 cores
(top left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field
and 200 cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top
right). Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0
static field with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of
1.00×1017 cm−2.
309
Figure C.27: NH3 column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.93×1017
cm−2.
310
Figure C.28: H2CO column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 6.15×1015
cm−2.
311
Figure C.29: SO column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 3.81×1015
cm−2.
312
Figure C.30: HCN column density maps at 10 years with 1000 G0 static field and 200 cores (top
left), with 1000 G0 static field at 10 years and 400 cores (2nd), with 1000 G0 static field and 200
cores at 1000 years (3rd) and with 1000 G0 static field and 400 cores at 1000 years (top right).
Maps at 5000 years for a 1000 G0 static field with 200 cores (bottom left) and a 1000 G0 static field
with 400 cores (bottom right). Minimum contour level of 1×1011 cm−2, maximum of 1.36×1016
cm−2.