Structure and Depletion in Star Forming Clouds - UCL Discovery

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.

Extract from the student notebooks of Poincare (circa 1875).

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)




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)




LIST OF FIGURES 12

3.6 CH3OH column density maps at 10 years without HH field (top left), with 1000





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





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




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


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




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





3.15 N2H+ column density maps at 10 years with 100 G0 static field (top left), with





3.16 CH3OH column density maps at 10 years with 100 G0 static field (top left), with





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


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




6.38 12CO matches with SCUBA cores in Ophiuchus.. . . . . . . . . . . . . . . . 198


6.40 12CO matches with SCUBA cores in Serpens.. . . . . . . . . . . . . . . . . . 199










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




6.56 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




6.64 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.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)



B.6 NGC 2024 C18O integrated intensity map from HARP (units of Kkms−1). . . . 257


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






LIST OF FIGURES 23

B.11 NGC 2071 C18O channel map from HARP showing mean intensity (in Kelvin)



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)



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)



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


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



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



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



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



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



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





C.2 NH3 column density maps at 10 years without HH field (top left), with 1000





C.3 HCN column density maps at 10 years without HH field (top left), with 1000





C.4 CO column density maps at 10 years with 100 G0 field (top left), with 1000




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




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




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




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




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





C.10 CO column density maps at 10 years with 1000 G0 static field (top left), with





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


C.12 NH3 column density maps at 10 years with 1000 G0 static field (top left), with





C.13 H2CO column density maps at 10 years with 1000 G0 static field (top left), with





C.14 SO column density maps at 10 years with 1000 G0 static field (top left), with





C.15 HCN column density maps at 10 years with 1000 G0 static field (top left), with





C.16 HCO+ column density maps at 10 years with 100 G0 static field (top left), with





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).


C.18 CS column density maps at 10 years with 100 G0 static field (top left), with 100





C.19 NH3 column density maps at 10 years with 100 G0 static field (top left), with


(3rd) and with 100 G0 moving field at 1000 years (top right) . Maps at 5000



C.20 H2CO column density maps at 10 years with 100 G0 static field (top left), with





C.21 SO column density maps at 10 years with 100 G0 static field (top left), with 100





C.22 HCN column density maps at 10 years with 100 G0 static field (top left), with





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




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





C.25 N2H+ column density maps at 10 years with 1000 G0 static field and 200 cores






C.26 CH3OH column density maps at 10 years with 1000 G0 static field and 200 cores






C.27 NH3 column density maps at 10 years with 1000 G0 static field and 200 cores






LIST OF FIGURES 29

C.28 H2CO column density maps at 10 years with 1000 G0 static field and 200 cores






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





C.30 HCN column density maps at 10 years with 1000 G0 static field and 200 cores






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


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.


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


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


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


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.


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


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


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


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


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


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(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



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



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



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



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



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



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


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



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



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




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


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


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


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


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


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


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


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


crowded cube, changing Tlow

Figure 5.19:CLUMPFIND, data sums - sparse cube,

changing DeltaT

Figure 5.20: CLUMPFIND, data sums - crowded

cube, changing DeltaT


sparse cube, changing DeltaT


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]


-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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-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]


-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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


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]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


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.


clump catalogue andFELLWALKER output


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


form crowded cube, changing Noise

Figure 5.43: FELLWALKER, clump positions -

sparse cube, changing MinDip


crowded cube, changing MinDip


form sparse cube, changing MinDip


form crowded cube, changing MinDip

5.3. Results 126


sparse cube, changing FlatSlope


crowded cube, changing FlatSlope


form sparse cube, changing FlatSlope


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


rus, changing MinDip

Figure 5.54:FELLWALKER, clump positions - NGC

2024, changing MinDip


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


crowded cube, changing Noise

Figure 5.60: FELLWALKER, data sums - sparse

cube, changing MinDip

Figure 5.61: FELLWALKER, data sums - crowded

cube, changing MinDip


sparse cube, changing MinDip


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






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


changing MinDip


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]


-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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


-2 -1 0 1 2log[M/Msun]

-2

-1

0

1

2

3

4

5

log[

dN/d

M]


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]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


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]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


-3 -2 -1 0 1 2log[M/Msun]

-2

0

2

4

6

log[

dN/d

M]


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.


clump catalogue andREINHOLD output


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


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


form sparse cube, changing MinLen


form crowded cube, changing MinLen

5.3. Results 144






form sparse cube, changing FlatSlope

Figure 5.100:REINHOLD, clump positions - uni-

form crowded cube, changing FlatSlope


cube, changing CaIterations


crowded cube, changing CaIterations

5.3. Results 145


form sparse cube, changing CaIterations


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


crowded cube, changing Noise

Figure 5.109:REINHOLD, data sums - sparse cube,

changing MinLen

Figure 5.110: REINHOLD, data sums - crowded

cube, changing MinLen


sparse cube, changing MinLen


crowded cube, changing MinLen

5.3. Results 148


changing FlatSlope








changing CaIterations


cube, changing CaIterations

5.3. Results 149


sparse cube, changing CaIterations


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

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Figure 5.121:REINHOLD, clump mass function - sparse cube, changing Noise

-2 -1 0 1 2log[M/Msun]

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Sparse Cube

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Figure 5.122:REINHOLD, clump mass function - uniform sparse cube, changing Noise

5.3. Results 152

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Figure 5.123:REINHOLD, clump mass function - crowded cube, changing Noise

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Figure 5.124:REINHOLD, clump mass function - uniform crowded cube, changing Noise

5.3. Results 153

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Reinhold - MinLen=2*rmsalpha = 0.68

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Reinhold - MinLen=10*rms

Figure 5.125:REINHOLD, clump mass function - sparse cube, changing MinLen

-2 -1 0 1 2log[M/Msun]

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Sparse Uniform Cube

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Figure 5.126:REINHOLD, clump mass function - uniform sparse cube, changing MinLen

5.3. Results 154

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Figure 5.127:REINHOLD, clump mass function - crowded cube, changing MinLen

-2 -1 0 1 2log[M/Msun]

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Figure 5.128:REINHOLD, clump mass function - uniform crowded cube, changing MinLen

5.3. Results 155

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Reinhold - FlatSlope=0.5*rmsalpha = 0.70

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Figure 5.129:REINHOLD, clump mass function - sparse cube, changing FlatSlope

-2 -1 0 1 2log[M/Msun]

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Uniform Sparse Cube

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Figure 5.130:REINHOLD, clump mass function - uniform sparse cube, changing FlatSlope

5.3. Results 156

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Figure 5.131:REINHOLD, clump mass function - crowded cube, changing FlatSlope

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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.


clump catalogue andGAUSSCLUMPSoutput


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


crowded uniform cube, changing Thresh


sparse cube, changing MaxNF


crowded cube, changing MaxNF


sparse uniform cube, changing MaxNF


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


crowded uniform cube, changing Thresh


sparse cube, changing MaxNF


crowded cube, changing MaxNF


sparse uniform cube, changing MaxNF


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

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Figure 5.151:GAUSSCLUMPS, clump mass function - sparse cube, changing Thresh

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Figure 5.152:GAUSSCLUMPS, clump mass function - sparse uniform cube, changing Thresh

5.3. Results 164

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Figure 5.153:GAUSSCLUMPS, clump mass function - crowded cube, changing Thresh

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Figure 5.154:GAUSSCLUMPS, clump mass function - uniform crowded cube, changing Thresh

5.3. Results 165

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Figure 5.155:GAUSSCLUMPS, clump mass function - sparse cube, changing MaxNF

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Figure 5.156:GAUSSCLUMPS, clump mass function - uniform sparse cube, changing MaxNF

5.3. Results 166

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Figure 5.157:GAUSSCLUMPS, clump mass function - crowded cube, changing MaxNF

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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-


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.


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


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


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


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


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


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


Figure 6.5: Radius vs. LTE mass for clumps

identified in the original12CO maps and12CO


Figure 6.6: LTE mass vs. Virial mass for clumps

identified in the original12CO maps and12CO


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)


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.


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


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


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


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


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.


Figure 6.19: Radius vs LTE mass for CO clumps

in NGC 2024


in NGC 2071


in Ophiuchus


in Serpens


in Taurus


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-

--


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


clumps in Ophiuchus

Figure 6.27: LTE mass vs virial mass for CO

clumps in Serpens



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


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


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).


-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


-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 -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


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.


Figure 6.34:12CO matches with SCUBA cores

in NGC 2024.


in NGC 2024.


in NGC 2071.


in NGC 2071.


in Ophiuchus.


in Ophiuchus.



in Serpens.


in Serpens.


in NGC 2024.


in NGC 2024.


in NGC 2071.


in NGC 2071.



in Ophiuchus.


in Ophiuchus.


in Serpens.


in Serpens.


in Taurus.


in Taurus.


Figure 6.52: C18O matches with SCUBA cores

in NGC 2024.


in NGC 2024.


in NGC 2071.


in NGC 2071.


in Ophiuchus.


in Ophiuchus.



in Serpens.


in Serpens.


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 6.64: SCUBA cores in Ophiuchus,




Figure 6.66: SCUBA cores in Serpens, coloured

to illustrate a match with a CO clump.

Figure 6.67: SCUBA cores in Serpens, coloured



Figure 6.68: SCUBA cores in Taurus, coloured


Figure 6.69: SCUBA cores in Taurus, coloured




Here we set the noise parameter to 10*rms when

running the FELLWALKER algorithm to locate

CO clumps.



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


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


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


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.


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).


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


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


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


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


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).


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


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


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-

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sere

fers

toth

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uth-

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sof

10.

Cor

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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.

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16h

26m

27s

6-2

423

”57’

0.05

42.

7(6)

8.93

(23)

29K

1328

K0

267.

88

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p10

16h

27m

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5-2

426

”38’

0.01

71.

7(5)

1.76

(22)

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128

K1

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438

”08’

0.02

32.

3(5)

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(22)

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114

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16h

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417

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0.02

66.

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5.6(

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m33

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28

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008

2.5(

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25

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s18∗

04h

18m

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728

21”3

0’0.

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5.6(

6)3.

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K38

8K

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02

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s21∗

04h

18m

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028

22”0

0’0.

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9.1(

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35(2

3)11

K16

8K

90.

80

Taur

s22∗

04h

18m

42s

428

21”3

0’0.

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1.8(

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8K

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21

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s24↑∗

04h

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728

23”2

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4.5(

6)3.

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38

Ser

pp2

18h

29m

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16”3

9’0.

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3.0(

6)1.

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pp3

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pp1

118

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15”0

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2.7(

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ps2

18h

30m

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601

09”0

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50.

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30m

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5.4(

5)7.

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18h

30m

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401

16”1

5’0.

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3.7(

5)7.

25(2

2)15

K12

31K

150.

03

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C20

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05h

41m

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0-0

154

”20’

0.16

86.

9(4)

7.15

(22)

59K

1264

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d.

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)


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)


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).


Figure B.2: NGC 202412CO integrated intensity map from HARP (in units of Kkms−1).


Figure B.4: NGC 202413CO integrated intensity map from HARP (units of Kkms−1).


Figure B.5: NGC 2024 C18O channel map from HARP showing mean intensity (in Kelvin) in




Figure B.6: NGC 2024 C18O integrated intensity map from HARP (units of Kkms−1).


B.2 NGC 2071 CO maps


channels centred at -15 kms−1 (bottom left), -5 kms−1 (bottom right), 5 kms−1 (top left) and 15



Figure B.11: NGC 2071 C18O channel map from HARP showing mean intensity (in Kelvin) in




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.


Figure B.14: Ophiuchus12CO integrated intensity map from HARP (units of Kkms−1).


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).


Figure B.16: Ophiuchus13CO integrated intensity map from HARP (units of Kkms−1).


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).


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).


Figure B.20: Serpens12CO integrated intensity map from HARP (units of Kkms−1).


Figure B.21: Serpens13CO channel map from HARP showing mean intensity (in Kelvin) in chan-


(top right).


Figure B.22: Serpens13CO integrated intensity map from HARP (units of Kkms−1).


Figure B.23: Serpens C18O channel map from HARP showing mean intensity (in Kelvin) in chan-


(top right).


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-


(top right).


Figure B.26: Taurus12CO integrated intensity map from HARP (units of Kkms−1).


Figure B.27: Taurus13CO channel map from HARP showing mean intensity (in Kelvin) in chan-


(top right).


Figure B.28: Taurus13CO integrated intensity map from HARP (units of Kkms−1).


Figure B.29: Taurus C18O channel map from HARP showing mean intensity (in Kelvin) in chan-


(top right).


Figure B.30: Taurus C18O integrated intensity map from HARP (units of Kkms−1).

APPENDIX C

CHAPTER 3 FIGURES

282

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



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




287

Figure C.5: NH3 column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field




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



289

Figure C.7: SO column density maps at 10 years with 100 G0 field (top left), with 1000 G0 field




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



291

Figure C.9: HCO+ column density maps at 10 years with 1000 G0 static field (top left), with 1000




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




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




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




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




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




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




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


moving field at 1000 years (top right) . Maps at 5000 years for a 100 G0 static field (bottom left)


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




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




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




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




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




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





cm−2.

306

Figure C.24: CS column density maps at 10 years with 1000 G0 static field and 200 cores (top





cm−2.

307

Figure C.25: N2H+ column density maps at 10 years with 1000 G0 static field and 200 cores (top





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





cm−2.

310

Figure C.28: H2CO column density maps at 10 years with 1000 G0 static field and 200 cores (top





cm−2.

311

Figure C.29: SO column density maps at 10 years with 1000 G0 static field and 200 cores (top





cm−2.

312

Figure C.30: HCN column density maps at 10 years with 1000 G0 static field and 200 cores (top





cm−2.

Structure and Depletion in Star Forming Clouds - UCL Discovery

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