Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations

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4Astronomy & Astrophysicsmanuscript no. DL07˙Planck˙v20 c© ESO 2014September 10, 2014

Planck intermediate results. XXIX. All-sky dust modelling withPlanck, IRAS, and WISE observations

Planck Collaboration: P. A. R. Ade78, N. Aghanim54, M. I. R. Alves54, G. Aniano54 ∗, M. Arnaud66, M. Ashdown63,5, J. Aumont54,C. Baccigalupi77, A. J. Banday84,9, R. B. Barreiro60, N. Bartolo27, E. Battaner86,87, K. Benabed55,83, A. Benoit-Levy21,55,83, J.-P. Bernard84,9,

M. Bersanelli30,46, P. Bielewicz84,9,77, A. Bonaldi62, L. Bonavera60, J. R. Bond8, J. Borrill12,80, F. R. Bouchet55,83, F. Boulanger54,C. Burigana45,28,47, R. C. Butler45, E. Calabrese82, J.-F. Cardoso67,1,55, A. Catalano68,65, A. Chamballu66,14,54, H. C. Chiang24,6,

P. R. Christensen74,33, D. L. Clements51, S. Colombi55,83, L. P. L. Colombo20,61, F. Couchot64, B. P. Crill61,75, A. Curto5,60, F. Cuttaia45,L. Danese77, R. D. Davies62, R. J. Davis62, P. de Bernardis29, A. de Rosa45, G. de Zotti42,77, J. Delabrouille1, C. Dickinson62, J. M. Diego60,

H. Dole54,53, S. Donzelli46, O. Dore61,10, M. Douspis54, B. T. Draine76, A. Ducout55,51, X. Dupac36, G. Efstathiou57, F. Elsner55,83, T. A. Enßlin71,H. K. Eriksen58, E. Falgarone65, F. Finelli45,47, O. Forni84,9, M. Frailis44, A. A. Fraisse24, E. Franceschi45, A. Frejsel74, S. Galeotta44, S. Galli55,K. Ganga1, T. Ghosh54, M. Giard84,9, E. Gjerløw58, J. Gonzalez-Nuevo60,77, K. M. Gorski61,88, A. Gregorio31,44,49, A. Gruppuso45, V. Guillet54,F. K. Hansen58, D. Hanson72,61,8, D. L. Harrison57,63, S. Henrot-Versille64, C. Hernandez-Monteagudo11,71, D. Herranz60, S. R. Hildebrandt10,E. Hivon55,83, W. A. Holmes61, W. Hovest71, K. M. Huffenberger22, G. Hurier54, A. H. Jaffe51, T. R. Jaffe84,9, W. C. Jones24, E. Keihanen23,

R. Keskitalo12, T. S. Kisner70, R. Kneissl35,7, J. Knoche71, M. Kunz16,54,2, H. Kurki-Suonio23,40, G. Lagache54, J.-M. Lamarre65, A. Lasenby5,63,M. Lattanzi28, C. R. Lawrence61, R. Leonardi36, F. Levrier65, M. Liguori27, P. B. Lilje58, M. Linden-Vørnle15, M. Lopez-Caniego60, P. M. Lubin25,

J. F. Macıas-Perez68, B. Maffei62, D. Maino30,46, N. Mandolesi45,4,28, M. Maris44, D. J. Marshall66, P. G. Martin8, E. Martınez-Gonzalez60,S. Masi29, S. Matarrese27, P. Mazzotta32, A. Melchiorri29,48, L. Mendes36, A. Mennella30,46, M. Migliaccio57,63, M.-A. Miville-Deschenes54,8,

A. Moneti55, L. Montier84,9, G. Morgante45, D. Mortlock51, D. Munshi78, J. A. Murphy73, P. Naselsky74,33, P. Natoli28,3,45,H. U. Nørgaard-Nielsen15, D. Novikov51, I. Novikov74, C. A. Oxborrow15, L. Pagano29,48, F. Pajot54, R. Paladini52, D. Paoletti45,47, F. Pasian44,

O. Perdereau64, L. Perotto68, F. Perrotta77, V. Pettorino39, F. Piacentini29, M. Piat1, S. Plaszczynski64, E. Pointecouteau84,9, G. Polenta3,43,N. Ponthieu54,50, L. Popa56, G. W. Pratt66, S. Prunet55,83, J.-L. Puget54, J. P. Rachen18,71, W. T. Reach85, R. Rebolo59,13,34, M. Reinecke71,

M. Remazeilles62,54,1, C. Renault68, I. Ristorcelli84,9, G. Rocha61,10, G. Roudier1,65,61, J. A. Rubino-Martın59,34, B. Rusholme52, M. Sandri45,D. Santos68, D. Scott19, L. D. Spencer78, V. Stolyarov5,63,81, R. Sudiwala78, R. Sunyaev71,79, D. Sutton57,63, A.-S. Suur-Uski23,40, J.-F. Sygnet55,J. A. Tauber37, L. Terenzi38,45, L. Toffolatti17,60,45, M. Tomasi30,46, M. Tristram64, M. Tucci16,64, G. Umana41, L. Valenziano45, J. Valiviita23,40,B. Van Tent69, P. Vielva60, F. Villa45, L. A. Wade61, B. D. Wandelt55,83,26, I. K. Wehus61, N. Ysard23, D. Yvon14, A. Zacchei44, and A. Zonca25

(Affiliations can be found after the references)

Preprint online version: September 10, 2014

ABSTRACT

We present all-sky dust modelling of the high resolutionPlanck, IRASandWISEinfrared (IR) observations using the physical dust model presentedby Draine & Li in 2007 (DL). We study the performance of this model and present implications for future dust modelling. Thepresent work extendsto the full sky the dust modelling carried out on nearby galaxies usingHerschelandSpitzerdata. We employ the DL dust model to generate mapsof the dust mass surface densityΣMd , the dust optical extinctionAV, and the starlight intensity heating the bulk of the dust, parametrized byUmin.We test the model by comparing these maps with independent estimates of the dust optical extinctionAV. The DL model reproduces the observedspectral energy distribution (SED) satisfactorily over most of the sky, with small deviations in the inner Galactic disk, and in low ecliptic latitudeareas, presumably due to zodiacal light contamination. In the Andromeda galaxy (M31), the present dust mass estimates agree remarkably well(within 10 %) with DL estimates based on independentSpitzerandHerscheldata. In molecular clouds, we compare the DLAV estimates withmaps generated from stellar optical observations from the 2MASS survey. The DLAV estimates are a factor of about 3 larger than values estimatedfrom 2MASS observations. In the diffuse interstellar medium (ISM) we compare the DL optical extinction AV estimates with optical estimatesfrom approximately 2× 105 quasi-stellar objects (QSOs) observed in the Sloan digitalsky survey. The DL AV estimates are larger than thosedetermined from the QSOs, and this discrepancy depends onUmin. We propose an empirical renormalization of the DLAV estimate, dependentof Umin, which compensates for the systematic differences found here. This renormalization, bringing into agreement theAV estimates on QSOs,also brings into agreement theAV estimates on molecular clouds. In the diffuse ISM, the DL fitting parameterUmin, effectively determined by thewavelength where the SED peaks, appears to trace variationsin the far-IR opacity of the dust grains. Therefore, some of the physical assumptionsof the DL model need to be revised. We provide a family of SEDs normalized by optical reddening, parameterized byUmin; these will be theconstraints for a next generation of dust models.

Key words. ISM: general – Galaxy: general – submillimeter: ISM

1. Introduction

Studying the interstellar medium (ISM) is important in a widerange of astronomical disciplines, from star and planet formationto galaxy evolution. Dust changes the appearance of galaxies by

∗ Corresponding author: G. Aniano, [email protected]

absorbing ultraviolet (UV), optical, and infrared (IR) starlight,and emitting mid-IR and far-IR (FIR) radiation. Dust is an im-portant agent in the chemical and thermodynamical evolutionof the ISM. Physical models of interstellar dust that have beendeveloped are constrained by such observations. In the presentwork, we study the ability of a physical dust model to reproduce

http://de.arxiv.org/abs/1409.2495v1

PlanckCollaboration: All-sky dust modelling

IR emission and optical extinction observations, using thenewlyavailablePlanck1 data.

The Planck data provide a full-sky view of the MilkyWay (MW) at submillimetre (submm) wavelengths, with muchhigher angular resolution than earlier maps made by the DiffuseInfrared Background Experiment (DIRBE) (Silverberg et al.1993) on theCosmic background explorer(COBE) space-craft (Boggess et al. 1992). These new constraints on thespectral energy distribution (SED) emission of large dustgrains were modelled by Planck Collaboration XI (2014, here-after Pl-MBB) using a modified blackbody (MBB) spec-tral model, parameterized by optical depth and dust tem-perature. That study, along with previousPlanck results,confirmed spatial changes in the dust submm opacity evenin the high latitude sky (Planck Collaboration XXIV 2011;Planck Collaboration Int. XVII 2014). The dust temperature,which reflects the thermal equilibrium, is anti-correlatedwiththe FIR opacity. The dust temperature is also affected by thestrength of the interstellar radiation field (ISRF) heatingthe dust.The bolometric emission per H atom is rather constant at highlatitude, consistent with a uniform ISRF, but over the full sky,covering lines of sight through the Galaxy, the ISRF certainlychanges. The all-sky submm dust optical depth was also cali-brated in terms of optical extinction. However, no attempt wasmade to connect these data with a self-consistent dust model.That is the goal of this complementary paper.

Several authors have modelled the dust absorption and emis-sion in the diffuse ISM, e.g. Draine & Lee (1984); Desert et al.(1990); Dwek (1998); Zubko et al. (2004); Compiegne et al.(2011); Jones et al. (2013); Siebenmorgen et al. (2014). We fo-cus on one of the most widely used dust models presented byDraine & Li (2007, hereafter DL). Earlier, Draine & Lee (1984)studied the optical properties of graphite and silicate dust grains,while Weingartner & Draine (2001) and Li & Draine (2001) de-veloped a carbonaceous-silicate grain model that has been quitesuccessful in reproducing observed interstellar extinction, scat-tering, and IR emission. DL presented an updated physical dustmodel, extensively used to model starlight absorption and IRemission. The DL dust model employs a mixture of amorphoussilicate grains and carbonaceous grains. The grains are assumedto be heated by a distribution of starlight intensities. Themodelassumes optical properties of the dust grains and the model SEDsare computed from first principles.

The DL model has been successfully employed to study theISM in a variety of galaxies. Draine et al. (2007) employed DLto estimate the dust masses, abundances of polycyclic aromatichydrocarbon (PAH) molecules, and starlight intensities intheSpitzerInfrared Nearby Galaxies Survey – Physics of the Star-Forming ISM and Galaxy Evolution (SINGS, Kennicutt et al.2003) galaxy sample. This survey observed a sample of 75nearby (within 30 Mpc of the Galaxy) galaxies, covering thefull range in a 3-dimensional parameter space of physical prop-erties, with theSpitzer Space Telescope(Werner et al. 2004).Wiebe et al. (2009) used the DL model with Balloon-borneLarge Aperture Submillimeter Telescope (BLAST, Pascale etal.2008) andSpitzerdata to fit SEDs for seven nearby galaxies,finding a normalization discrepancy with the dust emission from

1 Planck (http://www.esa.int/Planck) is a project of theEuropean Space Agency (ESA) with instruments provided by two sci-entific consortia funded by ESA member states (in particularthe leadcountries France and Italy), with contributions from NASA (USA) andtelescope reflectors provided by a collaboration between ESA and a sci-entific consortium led and funded by Denmark.

MBB fits. The Key Insights on Nearby Galaxies: a FIR Surveywith Herschel (KINGFISH) project, additionally observed asubsample of 61 of the SINGS galaxies with theHerschelSpace Observatory(Pilbratt et al. 2010). Aniano et al. (2012)presented a detailed resolved study of two KINGFISH galaxies,NGC 628 and NGC 6946, using the DL model constrained bySpitzerandHerschelphotometry. Aniano et al. (2014) extendedthe preceding study to the full KINGFISH sample of galaxies.Draine et al. (2014, hereafter DA14), presented a resolved studyof the nearby Andromeda galaxy (M31), where high spatial res-olution can be achieved. The DL model proved able to repro-duce the observed emission from dust in the KINGFISH galaxiesand M31. Ciesla et al. (2014) used the DL model to fit the vol-ume limited, K-band selected sample of galaxies of theHerschelReference Survey (Boselli et al. 2010), finding it systematicallyunderestimated the 500µm photometry.

The new Planck all-sky maps, combined with ancillaryInfrared Astronomical Satellite(IRAS, Neugebauer et al. 1984)and Wide-field Infrared Survey Explorer(WISE, Wright et al.2010) maps allow us to explore the dust thermal emission fromthe MW ISM with greater spatial resolution and frequency cov-erage than ever before. Here we test the compatibility of theDLdust model with these new observations.

We employ WISE 122 (12µm), IRAS 60 (60µm), IRAS100 (100µm), Planck857 (350µm), Planck545 (550µm), andPlanck353 (850µm) maps to constrain the dust emission SED inthe range 10µm < λ < 970µm. These data allow us to generatereliable maps of the dust emission using a Gaussian point spreadfunction (PSF) with 5′ full width at half maximum (FWHM).Working at lower resolution (1◦ FWHM), we can add the DIRBE140 and DIRBE 240 photometric constraints.

We employ the DL dust model to characterize:

– the dust mass surface densityΣMd;– the dust optical extinctionAV;– the dust mass fraction in small PAH grainsqPAH;– the fraction of the total luminosity radiated by dust that arises

from dust heated by intense radiation fields,fPDR;– the starlight intensityUmin heating the bulk of the dust.

The estimated dust parameters for M31 are compared with thosederived using the independent maps in DA14.

We compare the DL optical extinction estimates with thoseof Pl-MBB. We further compare the DL model reddening esti-mates with near IR reddening estimates from quasi-stellar ob-jects (QSOs) and from stellar reddening maps in dark cloudsobtained from 2MASS (Skrutskie et al. 2006). These reveal sig-nificant systematic discrepancies that will require a revision ofthe DL model. We find an empirical parameterization that renor-malizes the current DL model and provides insight into what isbeing compensated for through the renormalization.

We determine the observed FIR intensity per unit of opti-cal extinction that should be reproduced by the next generationof self-consistent dust models. We also provide thePlanck217(1.38 mm) andPlanck143 (2.10 mm) photometric constraints,which are not used in the current dust modelling.

This paper is organized as follows. In Section 2 we describethe data sets used. In Section 3 we present the DL dust model:

2 From now on we will refer to theWISE, IRAS, and DIRBE bandsasWISE12, IRAS60, IRAS100, DIRBE 100, DIRBE 140, and DIRBE240, by attaching the band reference wavelength (inµm) to the space-craft or instrument name, and to thePlanckbands asPlanck857,Planck545,Planck353,Planck217,Planck143, andPlanck100, by attachingthe band reference frequency (in GHz) to the spacecraft name.

2

http://www.esa.int/Planck


in Section 3.1 the model parametrization; and in Section 3.2themodel-fitting strategy. In Section 4 we describe the modellingresults, robustness, and validation: we present the model param-eter maps (Section 4.1); we analyze the model ability to fit thedata (Sect. 4.2); the importance ofIRAS60 as a constraint (Sect.4.3.1); and the dependence of the mass estimate on the data sets(Sect. 4.3.2). In Section 4.4 we compare the dustΣMd estimatesfor M31 with independent estimates based on different data sets.In Section 5 we compare the dustAV estimates with the MBBall-sky modelling results fromPl-MBB. In Section 6 we com-pare the dustAV estimates on diffuse regions with estimatesfrom QSO colours. In Section 6.3 we propose a dust model em-pirical correction (called “renormalization”) to compensate forthe discrepancies found. In Section 6.4 we present the observedFIR intensity per unit of optical extinction, i.e., the new photo-metric constraints that should be fitted by the next generationof dust models. In Section 7 we compare the dustAV predic-tions with estimates from stellar observations toward molecularclouds and the performance of the renormalized model in theseenvironments. In Section 8 we discuss the discrepancy of theFIR emission per unit of optical extinction of the DL model. Weconclude in Section 9. In Appendix A we show the details of thecomparison on M31 presented in Section 4.4. In Appendix B wepresent the details of the QSOAV estimation. In Appendix Cwe analyze the impact of cosmic infrared background (CIB)anisotropies in our dust modelling.

2. Data sets

We use the publicly available, nominal missionPlanck maps(Planck Collaboration I 2014). The zodiacal light has been es-timated and removed (Planck Collaboration XIV 2014) fromthese maps. The cosmic microwave background, provided bytheSMICA algorithm (Planck Collaboration XII 2014), was alsoremoved from eachPlanckmap. We use the zero level estima-tion and unit conversion factors given inPl-MBB. A residualdipole oriented towardl = 263.◦99, b = 48.◦26, and a constantoffset were removed from the maps to adjust them to a coherentGalactic zero level (Pl-MBB). We have checked that the resultsof this manuscript are not significantly changed when we usethe most recent version of thePlanckdata available within thePlanckconsortium.

We additionally useIRAS60 andIRAS100 maps. We em-ploy the IRAS 100 map presented inPl-MBB. It combinesthe small scale (< 30′) features of the map presented bythe improved reprocessing of theIRASsurvey (IRIS) team byMiville-Deschenes & Lagache (2005), and the large scale (>30′) features of the map presented by Schlegel et al. (1998, here-after SFD). The zodiacal light emission has been estimated andremoved from the SFD map, and therefore it is removed from themap we are employing3. We employ theIRAS60 map presentedby the IRIS team, with a custom estimation and removal of thezodiacal light4.

WISE mapped the sky at 3.4, 4.6, 12, and 22µm.Meisner & Finkbeiner (2014) presented a reprocessing of theentireWISE12 imaging data set, generating a high resolution,full-sky map that is free of compact sources and was cleaned

3 The zodiacal light emission contributes mainly at scales larger than30′, therefore, its contribution is subtracted when we retain the largescales of the SDF map.

4 The new IRIS data reduction and a description are availableat http://www.cita.utoronto.ca/˜mamd/IRIS/IrisOverview.html

from several contaminating artefacts. The zodiacal light contri-bution was estimated and subtracted using the model presentedby Kelsall et al. (1998). About 18 % of the sky is still contam-inated by the Moon or other solar system objects. Aniano et.al, ( A14, in preparation) presents an improved data reductionand artefact removal for theWISE12 data, which we use in thepresent modelling. The zodiacal light contamination has been re-moved more effectively fromWISE12 than from itsIRAScoun-terpart, and therefore we do not includeIRAS12 or IRAS25.Currently, there is no artefact-freeWISE22 full-sky map avail-able.

For typical lines of sight in the diffuse ISM, the dust SEDpeaks in theλ = 100− 160µm range. Unfortunately, no highresolution, all-sky maps are available in this wavelength range5.DIRBE produced low resolution (FWHM= 42′) all-sky mapsat 140 and 240µm, which can be used to test the robustnessof our modelling. Additionally, we perform a lower resolution(1◦ FWHM) modelling, including the DIRBE 140 and DIRBE240 photometric constraints. We use the DIRBE zodiacal light-subtracted mission average (ZSMA) maps. This modelling al-lows us to evaluate the importance of adding photometric con-straints near the dust SED peak, which are absent in thePlanckandIRASdata.

The most relevant information on the data sets that are usedis presented in Table 1. The amplitudes of the CIB anisoropies(CIBA), which depend on the angular scale used, are listedin Table 1 correspond to those at the modelling resolution.Following Pl-MBB we do not remove the CO contributions tothePlanckbands6.

All maps were convolved to yield a Gaussian PSF, withFWHM = 5.′0, slightly broader than all the maps’ native reso-lution. Small residual zodiacal light is still present in the maps,potentially affecting the dust mass estimates in low ecliptic lat-itude areas. We use the Hierarchical Equal Area isoLatitudePixelization (HEALPix) of a sphere coordinates (Gorski et al.2005)7. We work at resolutionNside = 2048, so the maps havea total of 12× 2048× 2048= 50331648 pixels. Each pixel is aquadrilateral of area 2.94 arcmin2 (i.e., about 1.′7 on a side). Allmaps and results presented in the current paper are performedusing this resolution, except those of Sects.4.3.2 and 6.4.

3. The DL model

The DL dust model is a physical approach to modelling dust. Itassumes that the dust consists of a mixture of amorphous sil-icate grains and carbonaceous grains heated by a distributionof starlight intensities. We employ the “Milky Way” grain sizedistributions (Weingartner & Draine 2001), chosen to reproducethe wavelength dependence of the average interstellar extinctionwithin a few kiloparsec of the Sun. The silicate and carbona-ceous content of the dust grains has been constrained by obser-vations of the gas phase depletions in the ISM. The carbonaceousgrains are assumed to have the properties of PAH molecules orclusters when the number of carbon atoms per grainNC . 105,but to have the properties of graphite whenNC ≫ 105. DL de-

5 The FIS instrument (Kawada et al. 2007) on board theAkari space-craft (Murakami et al. 2007) observed the sky at four FIR bands in the50− 180 µm range, but the data are not yet public.

6 The current CO maps are noisy in the low surface brightness areas,and therefore subtracting these small contributions increases the noiselevel significantly.

7 A full description ofHEALPix and its software library can be foundathttp://healpix.jpl.nasa.gov.

3

http://www.cita.utoronto.ca/~mamd/IRIS/IrisOverview.html

http://www.cita.utoronto.ca/~mamd/IRIS/IrisOverview.html

http://healpix.jpl.nasa.gov


Table 1.Description of the data used.

Band λa FWHMb Calibration Offsetd Dipolee CIBUncertaintyc anisotropiesf

[ µm] [arcmin] [%] [MJy sr−1] [MJy sr−1] [MJy sr−1]Planck100 GHzg 3000 9.66 0.5 0.00403± 0.00078 −0.0023821± 0.0000075Planck143 GHzg 2098 7.27 0.5 0.01324± 0.00092 −0.0034858± 0.0000081Planck217 GHzg 1283 5.01 0.5 0.0384± 0.0029 −0.006067± 0.000017Planck353 GHz 850 4.86 1.2 0.085± 0.011 −0.008939± 0.000043 0.019Planck545 GHz 550 4.84 10.0 0.095± 0.036 0.014806± 0.000091 0.059Planck857 GHz 350 4.63 10.0 0.09± 0.10 0± 0 0.010DIRBE 240 µm 248 42.0 11.6 0.8499± 0.0085DIRBE 140 µm 148 42.0 10.6 0.9088± 0.0147DIRBE 100 µm 100 42.0 13.6 0.5841± 0.0050IRAS100 µm 100 4.3 13.5 −0.1743± 0.0050 0.090IRAS60 µm 60 4.0 10.4 0.3442± 0.0014 0.048WISE12 µm 12 0.25 10.0a Mean band wavelength.b FWHM of the PSF of the original map.c Assumed calibration uncertainty as a percentage of the image intensity.d Zero level subtracted from the map.e Residual dipole oriented towardsl = 263.◦99, b = 48.◦26, subtracted from the map.f Root mean square (rms) of the CIB anisotropies in the band at5′ resolution.g Planck217,Planck143, andPlanck100 bands are not used to constraint the current dust model.

scribes the detailed computation of the model SED, and AD12describes its use in modelling resolved dust emission regims.

3.1. Parameterization

The IR emission of the DL dust model is parametrized by sixparameters,ΣMd , qPAH, Umin, Umax, α, andγ. The definition ofthese parameters is now reviewed.

The model IR emission is proportional to the dust mass sur-face densityΣMd.

The PAH abundance is measured by the parameterqPAH, de-fined to be the fraction of the total grain mass contributed byPAHs containingNC < 103 C atoms8. As a result of single-photon heating, the tiny PAHs contributing toqPAH radiate pri-marily at λ < 30µm , and this fraction is heavily constrainedby theWISE12 band. Weingartner & Draine (2001) computedseven different grain size distributions for dust grains in the dif-fuse ISM of the MW, which are used in DL. The models inthis “MW3.1” series are all consistent with the average inter-stellar extinction law9, but have different PAH abundances in therange 0.0047 ≤ qPAH ≤ 0.047. Draine et al. (2007) found thatthe SINGS galaxies span the full range ofqPAH models com-puted, with a median value ofqPAH = 0.034. Models are fur-ther extrapolated into a (uniformly sampled)qPAH grid, usingδqPAH = 0.001 intervals in the range 0≤ qPAH ≤ 0.10, as de-scribed by AD12.

Each dust grain is assumed to be heated by radiation with anenergy density per unit frequency

uν = U × uMMP83ν , (1)

whereU is a dimensionless scaling factor anduMMP83ν is the

ISRF estimated by Mathis et al. (1983) for the solar neighbour-hood. A fraction (1− γ) of the dust mass is assumed to be

8 For the size distribution in the DL models, the mass fractioncon-tributed by PAH particles containingNC < 106 C atoms is 1.478qPAH.

9 In the details of their size distributions and dust composition (e.g.,the lack of ices), these models will not be as appropriate fordust in darkmolecular clouds.

heated by starlight with a single intensityU = Umin, and theremaining fractionγ of the dust mass is exposed to a power-law distribution of starlight intensities betweenUmin andUmax,with dM/dU ∝ U−α. From now on, we call these the “diffusecloud” and the “PDR” (for photodissociation regions) compo-nents respectively. AD12 found that the observed SEDs in theNGC 628 and NGC 6946 galaxies are consistent with DL mod-els with Umax = 107. Given the limited number of photometricconstraints, we will use only models withUmax = 107 and alsofix α = 2, a typical value found in AD12. The DL models pre-sented in DL07 are further interpolated into a (finely sampled)Umin grid usingδUmin = 0.01 intervals, as described by A14.

Therefore, in the present work the DL parameter grid hasonly four dimensions,ΣMd, qPAH, Umin, andγ. We explore theranges 0.00≤ qPAH ≤ 0.10, 0.01≤ Umin ≤ 30, and 0≤ γ ≤ 1.0.For each model, the DL model library contains the model SEDin a finely-spaced wavelength grid with for 1µm < λ < 1cm.

As a derived parameter, we define the ratio

fPDR ≡LPDR

Ldust, (2)

whereLPDR is the luminosity radiated by dust in regions whereU > 102 andLdust is the total power radiated by the dust. Clearly,fPDR depends on the fitting parameterγ in the numerator and,through the denominator, also depends onUmin. Dust heatedwith U > 102 will emit predominantly in theλ < 100µm range;therefore, theIRAS60 to IRAS100 intensity ratio can be in-creased to very high values by takingfPDR → 1. Conversely,for a givenUmin, the minimumIRAS60/IRAS100 intensity ratiowill correspond to models withfPDR = 0.

Another derived quantity, the mass-weighted mean starlightheating intensity〈U〉, for α = 2, is given by

〈U〉 = (1− γ) Umin + γUminln (Umax/Umin)1− Umin/Umax

. (3)

Adopting the updated carbonaceous and astrosilicate densi-ties recommended by DA14, the DL model used here is consis-

4


tent with the MW ratio of visual extinction to H column den-sity, AV/NH = 5.34 × 10−22 mag cm2 (i.e., NH/E(B − V) =5.8× 1021 cm−2 mag−1, Bohlin et al. 1978), for a dust to H massratioΣMd/NHmH = 0.0091. The dust surface density correspondsto

AV = 0.74

(

ΣMd

105M⊙ kpc−2

)

mag. (4)

3.2. Fitting strategy and implementation

For each individual pixel, we find the DL parameters{ΣMd , qPAH, Umin, γ} that minimize

χ2 ≡∑

k

[Sobs(λk) − SDL(λk)]2

σ2λk

, (5)

whereSobs(λk) is the observed flux density per pixel,SDL(λk)is the DL emission SED convolved with the filterk responsefunction, andσλk is the 1σ uncertainty in the measured intensitydensity at wavelengthλk. We use a strategy similar to that ofAD12 and defineσλk as a sum in quadrature of five uncertaintysources:

– the calibration uncertainty (proportional to the observedin-tensity);

– the zero-level “offset” uncertainty;– the residual dipole uncertainty;– CIB anisotropies;– the instrumental noise.

Values for these uncertainties (except the noise) are giveninTable 1. To produce the best-fit parameter estimates, we fit theDL model to each pixel independently of the others.

We observe that for a given set of parameters{qPAH, Umin},the model emission is bi-linear in{ΣMd , γ}. This allows us toeasily calculate the best-fit values of{ΣMd , γ} for a given pa-rameter set{qPAH, Umin}. Therefore, when looking for the best-fit model in the full four-dimensional model parameter space{ΣMd , qPAH, Umin, γ}, we only need to perform a search overthe two-dimensional subspace spanned by{qPAH, Umin}. The DLmodel emission convolved with the instrumental bandpasses,SDL(λk), were pre-computed for a{qPAH, Umin} parameter grid,allowing the multi-dimensional search for optimal parameters tobe performed quickly by brute force, without relying on nonlin-ear minimization algorithms.

In order to determine the uncertainties on the estimated pa-rameters in each pixel, we proceed as follows: we simulate 100observations by adding noise to the observed data; we fit eachsimulated SED using the same fitting technique as for the ob-served SED; and we study the statistics of the fitted parame-ters for the various realizations. The noise added in each pixelis a sum of the five contributions listed in the previous para-graph, each one assumed to be Gaussian distributed. We follow astrategy similar to that of AD12, taking a pixel-to-pixel indepen-dent contribution for the data noise and correlated contributionsacross the different pixels for the other four sources of uncer-tainty. For simplicity, we assume that none of the uncertaintiesare correlated across the bands. The parameter error estimate at agiven pixel is the standard deviation of the parameter values ob-tained for the simulated SEDs. For typical pixels, the uncertaintyon the estimated parameters is a few percent of their values (e.g.,Figure 2 shows the signal-to-noise (S/N) ratio ofΣMd).

4. Dust modelling results, robustness, andvalidation

4.1. Parameter maps

The maps of the model best-fit parameters trace Galactic struc-tures. Galactic molecular cloud complexes are resolved and, inaddition, several extended extragalactic sources are present (e.g.,M31, discussed in Appendix A). Figure 1 shows the all-sky mapsof the fitted dust parameters. The left column corresponds toaMollweide projection of the sky in Galactic coordinates, and thecentre and right columns correspond to orthographic projectionsof the southern and northern hemispheres, centred on the corre-sponding Galactic poles.

A14 presents the correctedWISEdata andqPAH maps. Themass fraction in the PAH grains is relatively small, and therefore,variations inqPAH do not have a major impact on theΣMd andoptical extinction AV estimates. If instead of using theWISEdata to constrainqPAH, we simply fixqPAH = 0.04, theΣMd andAV estimates will only change by a few percent.

The fPDR map shows artefact structures aligned with theecliptic plane especially at high Galactic and low eclipticlati-tudes. These artefacts are likely to be caused by residual zodi-acal light in theIRAS60 maps. As shown in Section 4.3.1, thedust mass estimates are not strongly biased in these regions.

Figure 2 shows a map of the dust emitted luminosity surfacedensity,ΣLd, the mean intensity heating the dust,〈U〉, theχ2 perdegree of freedom (dof) of the fit,χ2/Ndof, and a map of theS/N ratio of the dust mass surface densityΣMd.

Theχ2/Ndof map scatter around unity in the high Galacticlatitude areas, where the data uncertainties are noise-dominated.Theχ2/Ndof is slightly larger than 1 in the inner Galactic diskand several other localized areas. In the outer Galactic disk theχ2/Ndof is smaller than 1, presumably due to overestimation ofthe uncertainties. Over much of the sky the fit to the FIR SEDis not as good as inPl-MBB; there the MBB fit has three fittingparameters in contrast with the DL model which has only two,ΣMd andUmin

10.

4.2. Dust model photometric performance: residual maps

As shown in theχ2/Ndof map in Figure 2, the DL model fitsthe observed SED satisfactorily (within 1σ) over most of thesky areas. However, the model SEDs have systematic departuresfrom the observed SED in the inner Galactic disk, at low eclipticlatitude, and in localized regions. The departures of the model inthe low ecliptic latitude regions could be caused by defectsin thezodiacal light estimation (and removal) in the photometricmapsthat the model cannot accommodate. In the Magellanic Clouds(MC) the DL model fails to fit the data11. The MC exhibit sur-prisingly strong emission at submm and millimetre wavelengths.Planck Collaboration XVII (2011) conclude that conventionaldust models cannot account for the observed 600− 3 000µmemission without invoking unphysically large amounts of verycold dust. (Draine & Hensley 2012) suggest that magnetic dipoleemission from magnetic grain materials could account for theunusually strong submm emission from the Small MC.

10 The qPAH parameter does not affect significantly the FIR SED; itonly affects significantly theWISE12 photometry. ThefPDR parameteraffect mostly IRAC 60 photometry, without contributing significantly tothe remaining FIR bands.

11 The MC appear as two red spots in the southern hemisphere in thetop row of Figure 4

5


3.8 6.5 Log (ΣMd /(M

O • kpc-2))

-180

-150

-120

-90

-60

-300

306090120

150

-60

-30

0

30

60

3.8 6.5 Log (ΣMd /(M

O • kpc-2))

-180

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-90 -90

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0

30 30

60 60

90 90

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150

150

-60

-30

0

30

60

0.0 2.0 Umin 0.0 2.0 Umin

0.0 0.30 fPDR 0.0 0.30 fPDR

Fig. 1. DL fitted parameter maps. The top row corresponds to the dust mass surface density,ΣMd , the middle row to the mass-weighted meanstarlight intensity heating the dust,Umin, and the bottom row to the fraction of dust luminosity emitted by dust heated with high stellar intensities,fPDR. The left column corresponds to a Mollweide projection of the sky in Galactic coordinates, and the centre and right columns correspondto orthographic projections of the southern and northern hemispheres centred on the corresponding Galactic poles. A Galactic coordinate grid isplotted in the maps of the first row. Lines of ecliptic latitude at±10◦ are plotted in the maps of the bottom row.

Figures 3 and 4 show the model departures from the photo-metric constraints used in the fits. Each panel shows the differ-ence between the model predicted intensity and the observedin-tensity, divided by the observed uncertainty. The systematic de-partures show that the physical model being used does not havesufficient parameters or flexibility to fit the data perfectly.

By increasingγ (i.e., the PDR component), the DL modelcan increase theIRAS 60 to IRAS 100 ratio to high values,without contributing much to thePlanck intensities. Thus, inprinciple, the model should never underpredict theIRAS 60emission. Figure 3 shows the model performance for fitting theIRASbands; several high latitude areas (mostly withfPDR = 0)haveIRAS60 overpredicted andIRAS100 underpredicted. Bothmodel components (the diffuse cloud and PDR components)have anIRAS60 / IRAS100 intensity ratio slightly larger thanthe ratio observed in these regions. There are several areaswherethe IRAS60 / IRAS100 ratio is below the value for the best-fitUmin, hence in these areas the model (withfPDR = 0) overpre-

dicts IRAS60. This systematic effect is at the 1− 2σ level (i.e.,10− 20 %).

In the inner Galactic disk the DL model tends to underpredictthe 350µm and overpredict the 850µm emission (see Figure 4).The observed SED is systematically steeper than the DL SEDin the 350− 850µm range (i.e., betweenPlanck857 andPlanck353). Similar results were found in the central kiloparsec of M31in the 250−500µm range (DA14). The MBB fit of these regions,presented inPl-MBB, finds larger values of the opacity spectralindex β (β ≈ 2.2) than the typical value found in the low-andmid-range dust surface density areas (β ≈ 1.65). The DL SEDpeak can be broadened by increasing the PDR component (i.e.,by raisingγ or fPDR), but it cannot be made steeper than theγ = 0 ( fPDR = 0) models, and the model therefore fails to fit the350− 850µm SED in these regions.

Following DA14, we define

ΥDL =log(κDL ∗ F857/κDL ∗ F353)

log(857GHz/353GHz), (6)

6


5.5 9.8 Log (ΣLd /(L

O • kpc-2)) 5.5 9.8 Log (ΣLd

/(LO • kpc-2))

0.0 2.0 <U> 0.0 2.0 <U>

0.0 2.0 χ2/DOF 0.0 2.0 χ2/DOF

0.00 20.00 ΣMd S/N 0.00 20.00 ΣMd

S/N

Fig. 2. DL derived parameters. The top row corresponds to the dust luminosity surface density,ΣLd , the second row shows the mean intensityheating the dust,〈U〉, the third row shows theχ2 per degree of freedom of the fit,χ2/Ndof, and the bottom row the S/N map of the dust masssurface densityΣMd .

as the effective power-law index of the DL dust opacity between350µm and 850µm, whereκDL ∗ F is the assumed absorptioncross-section per unit dust mass convolved with the respectivePlanckfilter. For the DL model12 this ratio isΥDL ≈ 1.8. We

12 If the Planckfilters were monochromatic at the nominal frequen-cies, thenΥDL = 1.82 (see Table 2 in DA14). For the realPlanckfilterstheΥDL value is a constant close to 1.8.

define

ΥPlanck=log[Iν(Planck857)/Iν(Planck353)]

log(857GHz/353GHz). (7)

If the dust temperatures in the fitted DL model were left un-changed, then the predictedPlanck857/Planck353 intensity ra-tio could be brought into agreement with observations ifΥDLwere changed byδΥ = ΥPlanck− ΥDL . Figure 5 shows theδΥ

7


-1.0 1.0 Dep. IRAS 60 -1.0 1.0 Dep. IRAS 60

-1.0 1.0 Dep. IRAS 100 -1.0 1.0 Dep. IRAS 100

Fig. 3. Comparison between the model and theIRASdata used to constrain the fit. Each panel shows the model departure from the data definedas Dep.= (Model − Map)/Uncertainty. The top row corresponds toIRAS60, and the bottom row toIRAS100. The polar projection maps aresmoothed to 1◦ resolution to highlight the systematic departures, and lines of Ecliptic latitude at±10◦ are added for reference.

map, i.e., the opacity corrections that would bring the DL SEDinto agreement with the observed SEDif the dust temperaturedistribution is left unchanged. The observed SED is steeperthanthe DL model in the inner Galactic disk (δΥDL ≈ 0.3) and shal-lower in the MC (δΥDL ≈ −0.3). Clearly, modifying the dustopacity would change the dust emission, and therefore the dusttemperature distribution. Therefore, theδΥ map should be re-garded as a guide on how to modify the dust opacity in futuredust models, rather than as the exact correction to be applied tothe opacity law per se. In the low-and mid-range surface densityareasδΥ ≈ 0.1, while δΥ ≈ 0.3 in the inner Galactic disk. Thelarge dispersion of the pixels in the low surface brightnessareasis mainly due to instrumental noise. The dispersion in the largesurface brightness areas may be an indicator of dust evolution,i.e., variations in the optical or FIR properties of the dustgrainsin the diffuse ISM.

4.3. Robustness of the mass estimate

4.3.1. Importance of IRAS 60

To study the potential bias introduced byIRAS60, due to a pos-sible non ideal zodiacal light estimation (whose relative contri-bution is the largest in theIRAS60 band) or the inability of theDL model to reproduce the correct SED in this range, one canperform modelling without theIRAS60 constraint. In this casewe setγ = 0, i.e., we allow only the diffuse cloud component( fPDR = 0), and so we have a two-parameter model.

Figure 6 shows the ratio of the dust mass estimated withoutusing theIRAS60 constraint and withγ = 0 to that estimatedusingIRAS60 and allowingγ to be fitted (i.e., our original mod-elling). The left panel shows all the sky pixels and the rightpanelonly the pixels withfPDR > 0. In the mid-and-high-rangesurfacemass density areas (ΣMd > 105M⊙ kpc−2), where the photometry

has good S/N, both models agree well, with a rms scatter be-low 5 %. The inclusion or exclusion of theIRAS60 constraintdoes not significantly affect our dust mass estimates in these re-gions. In the low surface density areas, inclusion of theIRAS60does not change theΣMd estimate in thefPDR > 0 areas, but itleads to an increase of theΣMd estimate in thefPDR = 0 pix-els. In the fPDR = 0 areas, the model can overpredictIRAS60in some pixels, and therefore, when this constraint is removed,the dust can be fitted with a largerUmin value reducing theΣMd

needed to reproduce the remaining photometric constraints. Inthe fPDR > 0 areas, the PDR component has a small contributionto the longer wavelengths constraints, and therefore removingthe IRAS60 constraint and PDR component has little effect intheΣMd estimates.

4.3.2. Dependence of the mass estimate on the photometricconstraints

The Planck and IRAS data do not provide photometric con-straints in the 120µm < λ < 300µm range. This is a potentiallyproblematic situation, since the dust SED typically peaks in thiswavelength range. We can add the DIRBE 140 and DIRBE 240constraints in a low resolution (FWHM> 42′) modelling totest this possibility.

We compare two analyses performed using a 1◦ FWHMGaussian PSF. The first uses the same photometric constraints asthe high resolution modelling (WISE, IRAS, andPlanck), and thesecond additionally uses the DIRBE 140 and DIRBE 240 con-straints. The results are shown in Figure 7. Both model fits agreevery well, with differences between the dust mass estimates ofonly a few percent. Therefore, our dust mass estimates are notsubstantially affected by the lack of photometric constraints nearthe SED peak. This is in agreement with similar tests carriedoutin Pl-MBB.

8


-1.0 1.0 Dep. Planck 857 -1.0 1.0 Dep. Planck 857



Fig. 4.Comparison between the model and thePlanckdata used to constrain the fit. Each panel shows the model departure from the data definedas Dep.= (Model - Map)/Uncertainty. The top row correspond toPlanck857, the central row toPlanck545, and the bottom row toPlanck353.The polar projection maps are smoothed to 1◦ resolution to highlight the systematic departures, and lines of Ecliptic latitude at±10◦ are added forreference.

4.4. Validation on M31

In Appendix A we compare our dust mass estimates in theAndromeda galaxy (M31) with estimates based on an indepen-dent data set and processing pipelines. Both analyses use the DLmodel. This comparison allows us to analyse the impact of thephotometric data used in the dust modelling. We conclude thatthe model results are not sensitive to the specific data sets usedto constrain the FIR dust emission, validating the present mod-elling pipeline and methodology.

9


-0.30 0.30 δϒ -0.30 0.30 δϒ

0.00

0.31

0.62

0.93

1.24

1.55

1.86

2.17

2.48

2.79

3.10

103 104 105 106 107

-0.4

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0.2

0.4

103 104 105 106 107

ΣMd [M

O • kpc-2]

-0.4

-0.2

0.0

0.2

0.4δϒ

Fig. 5. Correction to the FIR opacity power law-index (δΥ) needed to bring the DL SED into agreement with thePlanckobservations. The polarprojection maps are smoothed to 1◦ resolution to highlight the systematic departures. The bottom row shows the scatter of theδΥmap as a functionof ΣMd . Colour corresponds to the logarithm of the density of points, i.e., the logarithm of number of sky pixels that have a given (ΣMd , δΥ) valuein the plot. The curves correspond to the mean value and the±1σ dispersion.

0.00

0.36

0.71

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103 104 105 106 1070.7

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All sky pixels

103 104 105 106 107

ΣMd with IRAS 60 [M

O • kpc-2]

0.7

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Σ Md w

ithou

t IR

AS

60 /

Σ Md w

ith I

RA

S 60

0.00

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103 104 105 106 1070.85

0.90

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103 104 105 106 107

ΣMd with IRAS 60 [M

O • kpc-2]

0.85

0.90

0.95

1.00

1.05

1.10

Σ Md w

ithou

t IR

AS

60 /

Σ Md w

ith I

RA

S 60

Fig. 6. Comparison between the dust mass estimates when theIRAS60 constraint is excluded or included in the fit. The left panel show all thesky pixels, and the right panel only thefPDR > 0 pixels. The vertical axis corresponds to the ratio of the inferred mass density of a fitwithoutusingthe IRAS60 constraint to that obtained when this constraint is present (see text). Colour corresponds to the logarithm of the density of points (seeFigure 5). The horizontal curve correspond to the mean value.

10


0.60 1.4 ΣMd with DIRBE / ΣMd

without DIRBE 0.60 1.4 ΣMd with DIRBE / ΣMd

without DIRBE

Comparison of DL07 M, with v.s. without DIRBE

0.8 0.9 1.0 1.1 1.2ΣMd

with DIRBE / ΣMd without DIRBE

Nu

mber

of

pix

els

Mean = 1.00

Fig. 7.Comparison between the dust mass estimates obtained with and without the DIRBE 140 and DIRBE 240 photometric constraints. The toprow shows maps of the ratio between the two dust mass estimates, and the bottom row shows the corresponding histogram. Both model fits areperformed using a 1◦ FWHM Gaussian PSF. The difference between the dust mass estimates is relatively small (within a few percent) and so it issafe to perform a modelling of the sky without the DIRBE constraints. In the bottom row, the points below 0.8 and over 1.2 were added to the 0.8and 1.2 bars, respectively.

11


5. Comparison between the DL and MBB results

We now compare the DL optical extinction estimates with theestimates from the MBB dust modelling presented inPl-MBB,noted AV,DL and AV,MBB respectively. Both estimates are basedon the samePlanckand IRAS100 data, but our DL modellingalso includesIRAS60 andWISE12 constraints. The DL modelhas two extra parameters (γ andqPAH) that can adjust theIRAS60 andWISE12 intensity fairly independently of the remainingbands. Therefore, the relevant data that both models are usingin determining the FIR emission are essentially the same. TheMBB extinction map has been calibrated with external (optical)observational data, and so this comparison allows us to testtheDL modelling against those independent data.

Pl-MBB estimated the optical extinction13 AV,QSO for asample of QSOs from the Sloan Digital Sky Survey (SDSS)(York et al. 2000). A single normalization factorΠwas chosen toconvert their optical depthτ353 map (the parameter of the MBBthat scales linearly with the total dust emission, similar to the DLΣMd) into an optical extinction map:AV,MBB ≡ Π τ353.

DL is a physical dust model and therefore fitting the ob-served FIR emission directly provides an optical extinction esti-mate, without the need for an extra calibration. However, iftheDL dust model employs incorrect physical assumptions (e.g., thevalue of the FIR opacity), it may systematically over or underestimate the optical extinction corresponding to observedFIRemission.

Figure 8 shows the ratio of the DL and MBBAV estimates.The top row shows the ratio map. The bottom row shows itsscatter and histogram. Over most of the sky (0.1 mag< AV,DL <20 mag), theAV,DL values are larger than theAV,MBB by a factorof 2.40±0.40. This discrepancy is roughly independent ofAV,DL.The situation changes in the very dense areas (inner Galacticdisk). In these areas (AV,DL ≈ 100 mag), the AV,DL are largerthan theAV,MBB estimates by 1.95± 0.10.

In the diffuse areas (AV,DL . 1), where theAV,MBB has beencalibrated using the QSOs,AV,DL overestimates theAV,MBB val-ues, and thereforeAV,DL should overestimate theAV,QSO by asimilar factor. The optical extinction overestimation arises fromtwo factors.

– The DL dust physical parameters were chosen so that themodel reproduces the SED proposed by Finkbeiner et al.(1999), based on FIRAS observations. It was tailoredto fit the high latitude Iν/N(HI) with Umin ≈ 1. Thehigh latitude SED fromPlanck observations differs fromthat derived from FIRAS observations. The difference de-pends on the frequency and can be as high as 20 %(Planck Collaboration VIII 2014). The best fit to the meanPlanck+ IRASSED on the QSO lines of sight is obtainedfor Umin ≈ 0.66. The dust total emission (luminosity) ofPlanck observations and the Finkbeiner et al. (1999) SEDare similar. The dust total emission per unit of optical red-dening (or mass) scales linearly withUmin. Therefore, weneed 1/0.66 ≈ 1.5 more dust mass to reproduce the ob-served luminosity. This is in agreement with the results ofPlanck Collaboration Int. XVII (2014) who have used thedust - HI correlation at high Galactic latitudes to measurethe dust SED per unit of HI column density. They find thattheir SED is well fit by the DL model forUmin = 0.7 afterscaling by a factor 1.45.

13 Pl-MBB actually determine optical reddeningE(B−V) for the QSOsample. Since a fixed extinction curve withRV = 3.1 (see App. B.2) wasused, this is equivalent to determining the optical extinction AV.

– The optical extinction per gas column density used to con-struct the DL model is that of Bohlin et al. (1978). Recentobservations show that this ratio needs to be decreased by afactor of approximately 1/1.4 (Liszt 2014a,b).

Therefore, we expect theAV,DL to overestimation theAV,QSO by≈ 2.1. In Section 6.2 we proceed to make a more direct estima-tion.

We observe that the standard deviation ofAV,DL/ AV,MBB inthe QSO lines of sight is 10 %, and therefore the relatively largesystematic variations in the ratio of theAV,DL/ AV,QSO versusUmin (that will be discussed in Section 8) should also be presentin the MBB fit. Other existing dust models also have similar sys-tematic variations in the ratio of their predictedAV to the AV,QSOversusUmin.

In the inner Galactic disk the DL emissivity is shallower thanthe observed SED (δΥ ≈ 0.3, see Section 4.2). The DL emissiv-ity is fixed and its SED cannot be adjusted to match the observedSED closely, while the MBB model (with one extra effective de-gree of freedom) fits the observed SED better in these regions.Neither theAV,MBB values nor theAV,DL values were externallycalibrated in these regions.

6. Variation in optical extinction to FIR emission indiffuse areas: QSO analysis

We seek to understand whether the overestimation of the opti-cal extinction per unit of FIR emission for the DL model (by afactor of 2.4) is constant across the sky, or if it depends on themodel parameters. We describe the motivations of the analysisand QSO sample to be used in Sect. 6.1. We compare the DLand QSO AV estimates (AV,DL, AV,QSO) in Sect. 6.2. We usethe results of this analysis to propose a renormalization oftheDL model that compensates for the systematic departures foundacross the sky in Section 6.3. We provide the observed FIR SEDsper unit of optical extinction set in Section 6.4. Finally, we dis-cuss the ability of the DL model to fit the proposed SEDs inSection 6.5.

6.1. The QSO sample

We estimate AV,QSO and proceed to compare theAV,DL andAV,QSO estimates directly, and study the discrepancies as a func-tion of the DL parameterUmin.

SDSS provides a sample of 272 366 QSOs that allows us tostudy the optical properties of Galactic dust. A subsample of105 783 (an earlier data release) was used inPl-MBB to nor-malize the opacity maps derived from the MBB fits in order toproduce an extinction map.

The use of QSOs as calibrators has several advantages overother cross-calibrations:

– QSOs are extragalactic, and at high redshift, so all the de-tected dust in a given pixel is between the QSO and us, amajor advantage with respect to maps generated from stellarreddening studies;

– the QSO sample is large and well distributed across diffuse(AV . 1) regions at high Galactic latitude, providing goodstatistics;

– SDSS photometry is very accurate and well understood.

In Appendix B we describe the SDSS QSO catalogue in de-tail, and how for each QSO we measure the extinctionAV,QSO

12


1.8 3.0 AV,DL / AV,MBB 1.8 3.0 AV,DL / AV,MBB

0.00

0.35

0.70

1.05

1.40

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,DL

/ AV

,MB

B

AV,DL v.s. AV,MBB, all sky

1.8 2.0 2.2 2.4 2.6 2.8 3.0AV,DL / AV,MBB

Nu

mb

er

of

pix

els

Mean = 2.39

Fig. 8. Comparison between DL and MBBAV estimates, notedAV,DL and AV,MBB respectively. The top row shows the ratio of theAV,MBB andAV,DL maps. The polar projection maps are smoothed to 1◦ resolution to highlight the systematic departures. The bottom row shows the ratio of theAV,MBB and AV,DL estimates as a function of theAV,DL estimate (left) and its histogram (right). In the bottom left panel the colour corresponds tothe logarithm of the density of points (see Figure 5). The curves correspond to the mean value and the±1σ dispersion. The DL and MBB analysesare based on the same data sets.

from the optical SDSS observations. For clarity, in the nextsec-tion we will denote the DL extinction based on modelling theFIR emission, asAV,DL.

6.2. AV,QSO – AV,DL comparison

In this section, we present a comparison of the DL and QSOextinction, as a function of the fitted parameterUmin. This studyprovides information on variations in the dust optical properties,and will allow us to gain valuable checks of the validity of theassumptions of the DL model.

Figure 9 compares the DL and QSOAV estimates. It showsthe slopeǫ(Umin) when fitting theAV,QSOversusAV,DL data witha line through the origin for a group of QSOs. To compute theǫ(Umin), we sort the QSO lines of sight with respect of theUminvalue of the Galactic dust, and divide them in 10 groups having(approximately) equal number of QSOs each. We observe thatǫ(Umin), a weighted mean ofAV,QSO/AV,DL in eachUmin bin, is astrong function ofUmin. The slope of fitting theAV,QSO versusAV,DL for the combined sample of QSOs is〈ǫ〉 ≈ 0.52. Therefore,on average the DL model overpredicts the observedAV,QSO bya factor of 1/0.52 = 1.9, with the discrepancy being larger forsightlines with smallerUmin values. There is a 24 % differencebetween the 2.4 factor that arises from the comparison betweenAV,DL and AV,QSO indirectly via the MBB AV fit, and the factor of1.9 found here. This is due to the use of a different QSO sample

(Pl-MBB used a smaller QSO sample), which accounts for 10 %of the difference, and the way that the QSOAV is computed fromthe SDSS photometry (see Appendix B for details), responsibleof the remaining 14 %.

For a given FIR SED, the DL model predicts the optical red-dening unambiguously, with no freedom for any extra calibra-tion. However, if one had the option to adjust the DL extinctionestimates by multiplying them by a single factor (i.e., ignoringthe dependence ofǫ on Umin), one would reduce the optical ex-tinction estimates by a factor of 0.52.

6.3. Dependence of the AV,DL overestimation on Umin in thediffuse ISM

The ratio of the DL predicted extinction, based on FIR obser-vations, to that estimated with optical photometry of QSOs is afunction ofUmin. Therefore, to have a better estimate of the op-tical extinction AV, one can parametrize the model predictiondepartures, and adjust theAV maps to compensate for this bias.

The optical extinction discrepancy can be approximated as alinear function ofUmin:

AV,QSO≈ (0.31Umin + 0.35)AV,DL, (8)

13


0.2 0.4 0.6 0.8 1 1.20.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Umin

ε =

QS

O A

V v

ers

us

DL

07

AV s

lop

e

ε = 0.31 Umin

+ 0.35

<ε> = 0.52

V V

Fig. 9. Ratio between the QSO extinction estimatesAV,QSO and the DLextinction estimatesAV,DL , as a function of the fitted parameterUmin.Empirically, the slope ofAV,QSO versus AV,DL (ǫ) can be approximatedby a linear function ofUmin.

We define a renormalized DL optical reddening as14:

AV,RQ = (0.31Umin + 0.35)× AV,DL. (9)

Empirically, AV,RQ is our best estimator of the QSO extinctionAV,QSO.

Pl-MBB proposed the dust radiance (the total luminosityemitted by the dust) as a tracer of dust column density in thediffuse ISM. This would be expectedif the radiation field heat-ing the dust were uniform, and the variations of the dust tem-perature were only driven by variation of the dust FIR-submmopacity in the diffuse ISM. The dust radiance is proportional toUmin×AV,DL. Our best fit of the renormalization factor as a func-tion of Umin is an intermediate solution between the radiance andthe non-renormalized model column density (AV,DL). TheAV,RQincreases withUmin but with a slope smaller than 1. Figure 9shows that our renormalization is a better fit of the data thantheradiance.

6.4. Observed FIR SED per unit of optical extinction

The parameterUmin is largely determined by the wavelengthwhere the SED peaks; as a corollary, SEDs for different values ofUmin differ significantly. TheAV values obtained from the QSOanalysis,AV,QSO, allow us to normalize the observed SEDs (perunit of optical extinction) and generate a one-parameter familyof Iν/AV. This family is indexed by theUmin parameter; the QSOlines of sight are grouped according to the fitted GalacticUminvalue. We divide the sample of “good” QSOs in 10 bins, con-taining 22 424 QSOs each15.

To obtain theIν/AV values we proceed as follows. For eachband andUmin, we would like to perform a linear regression ofthe Iν values as a function ofAV,QSO. The large scatter and non-Gaussian distribution ofAV,QSO and the scatter onIν make itchallenging to determine such a slope robustly. Therefore,wesmooth the maps to a Gaussian PSF with 30′ FWHM to reducethe scatter onIν, redo the dust modelling (to obtain a coherentUmin estimate), and perform the regression on the smoothed (less

14 We add the letter “Q” to indicate the renormalization using theAV,QSO.

15 A few of the bins contain 22 425 QSOs

noisy) maps. The non-Gaussian distribution ofAV,QSO do notintroduce any bias in the slope found16.

Unfortunately, the complex statistics of theAV,QSOestimates(that derive from variations in the QSO physical properties),makes it hard to obtain a reliable estimate of the uncertaintiesin the (normalizing) AV estimates. The statistical uncertaintiesin the AV estimates are rather small due to the large size of theQSOs sample: our determination of the FIR intensities per unitof optical extinction is mostly uncertain due to systematicbiases.HI column densities obtained from the Leiden/Argentina/Bonn21cm (LAB) survey (Kalberla et al. 2005) for our QSO sight-lines result in a mean valueNH = 7.7× 1021cm−2 E(B− V), 8%smaller than theNH = 8.3× 1021cm−2 E(B− V) found by Liszt(2014b). Therefore, we infer ourAV,QSO normalization may beuncertain to about 5− 10 %. The instrumental calibration uncer-tainties translate directly to the FIR intensities per unitof opticalextinction. Therefore, the normalization of each SED may beuncertain to about≈ 15 %.

Table 2 provides a set of empirical FIR intensities per unit ofoptical extinction,indexed by the DL Umin value. The set formsone SED for eachUmin value. The map values forPlanck217andPlanck143, which were not used to constrain the DL model,are also included in Table 2.

Table 2 additionally includes theΣLd/AV values from the DLfit. The fact that the DL fits the observed SED relatively well,makesΣLd a good estimate of the integral of the observed SEDs,i.e., the DL SEDs are used as a tool to interpolate the inten-sity between the bands, and the integrated SEDs are relativelymodel independent. Table 2 shows that the luminosity perAVis a monotonic function ofUmin, and therefore luminosity is notthe best tracer ofAV in the diffuse ISM; our AV,RQ is the besttracer of AV in the diffuse ISM.

Within eachUmin bin, the SEDs differ due to variations inthe dust properties. We normalize each SED by its DLΣLd, andstudy the SEDs mean scatter around the mean SED. The last rowof Table 2 presents such rms scatters. For each band, the scattersare similar for the differentUmin bins, and therefore we quote themean scatter for all the bins. The large scatter inPlanck217 andPlanck143 is partially due to stochastic noise in the data. Thelarge scatter inIRAS100 is due to variations infPDR betweenthe SEDs. The scatter in the remaining bands is mainly due tovariations in the dust SEDs.

Figure 10 present the set of SEDs. The left panel shows theSEDs for the differentUmin values. The right panel shows eachSED divided by the mean to highlight the differences betweenthe individual SEDs.

6.5. DL fit to the observed FIR SED per unit of opticalextinction

How does the DL model and its renormalized version comparewith the new FIR constraints proposed in Sect.6.4?

The DL SED reproduces correctly the observed SED overmost of the sky (see Section 4.2). Systematic departures in thelow surface areas can be due to poor zodiacal light estimationin the data. Even in these areas, the departures are within thephotometric uncertainties.

Figure 11 shows the measured intensity per unit of opticalextinction (red crosses) for the DL prediction. The different pan-els correspond to the different bands:IRAS100; Planck 857;Planck545; andPlanck353. In each panel, the black curve cor-responds to the DL predicted intensity, and the red curves tothe

16 See discussion in Appendix B.2, and Figure B.2.

14


Table 2.FIR observed emission per unit of optical extinction

SED DL fit DL fit Intensity per AV

# Umin ΣLd/107 Planck143 Planck217 Planck353 Planck545 Planck857 IRAS100 IRAS60[L⊙ kpc−2mag−1] [MJy sr−1 mag−1]

1 0.4178 2.28 0.0506 0.221 0.937 3.22 9.33 10.2 2.202 0.4674 2.33 0.0509 0.211 0.908 3.17 9.36 10.8 2.273 0.4984 2.39 0.0488 0.208 0.901 3.15 9.36 11.4 2.394 0.5207 2.54 0.0510 0.215 0.933 3.27 9.73 12.4 2.675 0.5407 2.46 0.0490 0.205 0.894 3.14 9.35 12.2 2.466 0.5602 2.62 0.0505 0.215 0.935 3.28 9.77 13.2 2.937 0.5793 2.73 0.0512 0.219 0.954 3.36 10.1 14.0 2.828 0.5984 2.65 0.0529 0.211 0.912 3.22 9.64 13.7 2.999 0.6182 2.67 0.0498 0.207 0.899 3.18 9.54 14.0 2.7610 0.6383 2.80 0.0496 0.211 0.928 3.28 9.90 14.9 2.9211 0.6590 2.98 0.0549 0.220 0.963 3.41 10.3 15.9 3.1612 0.6810 2.89 0.0486 0.207 0.914 3.25 9.86 15.7 3.1113 0.7056 3.01 0.0507 0.210 0.926 3.29 10.0 16.4 3.2914 0.7333 3.14 0.0494 0.213 0.945 3.36 10.3 17.3 3.5115 0.7644 3.35 0.0509 0.214 0.944 3.36 10.3 18.2 4.4016 0.7960 3.23 0.0492 0.208 0.921 3.29 10.1 18.3 3.7517 0.8289 3.21 0.0467 0.202 0.898 3.21 9.93 18.5 3.7718 0.8673 3.13 0.0465 0.191 0.848 3.04 9.50 18.2 3.7719 0.9123 3.31 0.0445 0.194 0.868 3.13 9.82 19.5 4.1120 0.9776 3.27 0.0415 0.180 0.802 2.91 9.19 19.2 4.32rms fluctuations in each bin [%] 41.30a 12.97a 4.72 3.08 4.43 7.71 29.43b

a The main source of fluctuations is statistical noise in the band photometry.b The main source of fluctuations is variation offPDR in the lines of sight.

100 300 1000 3000

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10

0.4180.4670.4980.5210.5410.5600.5790.5980.6180.6380.6590.6810.7060.7330.7640.7960.8290.8670.9120.978

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Fig. 10.FIR measured intensity per unit of optical extinction as a function of the fitted parameterUmin. In the right panel, the SEDs are dividedby the mean SED, i.e., normalized with the SED per unit of optical extinction obtained without binning onUmin.

renormalized QDL intensity prediction. The DL model under-predicts the FIR per unit of optical extinctionAV by signifi-cant amounts, especially for sightlines with low fitted values ofUmin. The DL model emission is less sensitive toUmin at longerwavelengths (i.e., the black curves are more horizontal at longerwavelengths). We observe that the renormalization of the DLAV

values brings into agreement the observed and predicted bandintensities per unit of extinction (red curves).Note that the redand black curves are not the product of a fit to these data, theycorrespond to the original and renormalized models respectively.

Figure 12 shows the fit of the DL model to the mean SEDover the QSO lines of sight. The observed SED was computedsimilarly as the ones in Table 2 (performing a linear regression oftheIν values as a function ofAV,QSO), but using all the QSOs, i.e.,without binning inUmin. It is quite close to the mean of the SEDspresented in Table 2. The DL model fit was done using the same

bands as in the main fit. DL fits the observed FIR SED within1.7% in theIRAS60, 100,Planck857,Planck545, andPlanck353 bands. Moreover the models also predictsPlanck217 andPlanck 143 fluxes (not used to constrain the fit) within 1.7%.DL differs from DIRBE bands by about 6%17. It is remarkablethat the DL spectral shape fit thePlanck857 –Planck143 SEDwithin 1.7%.

We conclude that the DL model has approximately the cor-rect SED shape to fit the diffuse ISM, and aUmin-dependentrenormalization brings the model optical extinction into agree-ment with theIRASandPlanckdata.

17 The DIRBE photometry employed is not reliable: The DIRBE mapsare quite noisy in the 30′ beams used to extract the observed SED.

15


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Fig. 11.FIR measured intensity per unit of optical extinction as a function of the fitted parameterUmin. The top row corresponds toIRAS100(left) andPlanck857 (right) and the bottom row toPlanck545 (left) andPlanck353 (right). The red crosses correspond to the the values providedin Table 2. The DL predictions are plotted in black and the renormalized model (RQ) predictions in red. The renormalized QDL model predictsthe FIR intensity remarkably well.

100 1000λ [µm]

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/ A

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rg c

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fPDR = 0.0537

Umin = 0.560

AV = 1.86 mag

-1.9%

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+1.5%-0.2%

-1.5%

+6.0%+1.0%+0.3%

+0.1%

Fig. 12. DL fit to the mean SED over the QSO lines of sight. Thecrosses are the model predicted fluxes in the bands, the red horizon-tal lines are the measured flux, and red rectangles around them is a 10%uncertainties. The red symbols correspond toIRAS60, 100,Planck857,545, and 353, while the blue symbols to DIRBE 140, 240,Planck217,and 143, not used to constrain the fit. The solid black line to the totalDL SED, while the green solid line correspond to its PDR componentand the blue solid line to the diffuse cloud component. In each band weshow the percentual deviation of the model from the observedflux.

7. Variation in optical extinction to FIR emission indense areas: molecular clouds

In Sect. 6 we presented an analysis of the DL optical perfor-mance in the diffuse sky, comparing itsAV estimates with thosederived from a QSO sample. We now extend the analysis tomolecular clouds. We further study the dependence of the op-timal renormalization as a function of the remaining relevant fit-ted parameter:ΣMd. We present the extinction maps based onstellar observations on Sect. 7.1. We compare the DL and stellarextinction maps on Sect. 7.2. We finally discuss a model renor-malization for molecular clouds in Sect. 7.3.

7.1. Extinction maps of molecular clouds

Schneider et al. (2011) presented optical extinction maps,notedAV,2M, of several clouds computed using stellar observationsfrom the 2MASS catalogue in theJ, H, andK bands. We nowcompare theseAV,2M maps with the DL estimates generated bymodelling the dust FIR emission,AV,DL. The Schneider et al.(2011) AV maps were computed using a 2′ Gaussian PSF, andwe degrade them to a 5′ Gaussian PSF to perform our analy-sis. We use the maps of the Cepheus, Chamaeleon, Ophiuchus,Orion, and Taurus cloud complexes.

The 2MASS maps were corrected for a zero level off-set (adding an inclined plane) using an algorithm similar to

16


that adopted to estimate the background in the analysis of theKINGFISH sample of galaxies, described in AD12. The algo-rithm iteratively and simultaneously matches the zero level andinclination of the AV,RQ and AV,2M maps, as well as estimatingthe areas that are considered background.

Figure 13 shows the 2MASSAV,2M map, the DLUmin map,the DL AV,DL map (divided by 2.95, see Sect. 7.2 ) and the renor-malized AV,RQ map for the Chamaeleon region. The inner (highAV) areas correspond to lowerUmin values, as the heating radi-ation field gets extincted when penetrating into the dense cloud.The remaining cloud complexes show similarAV − Umin be-haviour.

7.2. 2MASS – DL optical extinction comparison in molecularclouds

For each cloud we find an approximate linear relation betweenthe AV,2M map and theAV,DL map. However, as in the case of thediffuse ISM, the (FIR based)AV,DL estimates are significantlylarger than the (optical)AV,2M estimates. For the selected clouds,the DL model overestimates the 2MASS stellarAV by factors of2−3. Table 3 provides the multiplicative factors needed to makethe DL AV maps agree with the 2MASSAV maps.

Table 3.Mean ratio between the DL and 2MASS extinction es-timates in molecular clouds.

Cloud name AV,DL versus AV,2M slopea

Cepheus 2.67Chamaeleon 2.95Ophiuchus 2.19Orion 2.73Taurus 2.86a Note that theAV,RQ versus AV,2M slope is very close to 1.0,

the renormalized DL estimate predicts the 2MASSAV

accurately in most pixels.

Figure 14 shows the comparison of the DL maps and the2MASS maps in the Chamaeleon cloud. The left panel shows theAV,DL versus AV,2M values, and the right panel the renormalizedAV,RQ versus AV,2M values. After multiplicative adjustment, theAV,DL and AV,2M estimates agree reasonably well over the entirecloud complex. The low surface brightness areas are sensitiveto background level mismatch. The renormalization presentedin Section 6.3, computed in diffuse (AV < 1, although most ofthe QSO haveAV ≈ 0.1) regions, actually brings theAV,DL andAV,2M estimates into better agreement in the molecular cloudsthan the re-scaledAV,DL.

Figure 15 shows the comparison of the renormalizedAV,RQmaps and theAV,2M maps in all the clouds. The model renormal-ization was originally computed to bring into agreement theDLand QSOAV estimates in the diffuse ISM. The renormalizationalso accounts quite well (within 10 %) for the discrepanciesbe-tween 2MASS and DLAV estimates in molecular clouds in the0 < AV < 3 range, and even does passably well (within 30 %) upto AV ≈ 8.

7.3. Dependence of the DL AV overestimation on Umin inmolecular clouds.

In the diffuse ISM analysis, we concluded thatUmin is actuallysimultaneously tracing variations in the radiation field heatingthe dust, and in the dust opacity. One could expect that both phe-nomena are also present in other environments, e.g., molecularclouds, but their relative contribution in determining theSEDpeak (and thereforeUmin) need not be the same as in the dif-fuse ISM. Therefore, a renormalization of the DLAV based on2MASS data should, in principle, be different from that deter-mined using the QSOs.

Figure 16 compares the DL and 2MASSAV estimates. It isanalogous to Figure 9, but using the 2MASSAV estimatesAV,2Minstead of those from QSOs. It shows the ratioAV,DL / AV,2M,as a function of the fittedUmin. This includes the pixels from thefive cloud complexes with 1< 2MASSAV < 5. For eachUminvalue, the solid curve correspond to the best fit slope of theAV,DLversusAV,2M values (i.e., it is an estimate of a weighted mean ofthe AV,DL / AV,2M ratio). The straight solid line correspond to afit to the solid curve in the 0.2 < Umin < 1.0 range. In this fit,eachUmin is given a weight proportional to the number pixelsthat have this value in the clouds (i.e., most of the weight isforthe pixels within the 0.2 < Umin < 0.8 range. The dashed linecorrespond to the renormalization proposed in Sect. 6.3 (Eq. 9)that brings into agreement theAV,DL estimates with the QSOsAV,QSO.

The straight line in Figure 16 correspond to a renormal-ization tailored to bring into agreement theAV,DL and AV,2Mestimates, i.e., a “2MASS” renormalization for molecular theclouds, notedAV,RC. The 2MASS renormalization is given by

AV,RC = (0.33Umin + 0.27)× AV,DL. (10)

Empirically, AV,RC is our best estimator of the 2MASS extinctionAV,2M. Surprisingly, the 2MASS normalizationAV,RC for molec-ular clouds is quite close to the QSO normalizationAV,QSO.

8. Discusion

The DL AV estimates, based on the dust FIR emission, differsignificantly from estimates based on optical observations. Wedescribe this discrepancy and discuss possible origins in Sect.8.1. With the aim of obtaining a more accurateAV map, weempirically correct the DLAV estimate in Sect. 8.2.

8.1. DL FIR emission and optical extinction disagreement

In the diffuse ISM, the DL, at first sight, provide good fits tothe Galactic SED as observed byWISE, IRAS, andPlanck, as ithas been the case in the past for external galaxies observed withSpitzerandHerschel. However, the fit is not fully satisfactory,because the optical extinction from the model does not agreewith the observed extinction toward QSOs and molecular clouds.The optical extinction disagreement can be decomposed in twolevels:

– a basic disagreement, which corresponds to the mean factorof 1.9 between the DL and QSOsAV values;

– a secondary disagreement, which is expressed in the depen-dence of the ratios between the DL and QSOAV values onUmin.

The result of the SED fit depends on the spectral shape ofthe dust opacity. The DL model spectral shape departs slightly

17


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Fig. 13.2MASS and DL estimates in the Chamaeleon cloud region. The top row shows the (background corrected) 2MASSAV,2M map (left) andthe DLUmin map (right). The bottom row shows the DLAV,DL estimate divided by 2.95 (left), and the renormalized modelAV,RQ estimates (right).(See Sect. 7.2 for a derivation of the 2.95 factor)

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Fig. 14.2MASS and DL AV comparison in the Chamaeleon cloud. The left panel shows theAV,DL versus AV,2M values, and the right panel therenormalized AV,RQ versus AV,2M values. The diagonal lines correspond toy = 2.95x, andy = x respectively, and the curves correspond to themean value.

18


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Fig. 15.Comparison of the renormalizedAV,RQ and 2MASSAV,2M es-timates. The individual pixels of the Cepheus, Chamaeleon,Ophiuchus,Orion, and Taurus clouds are combined. Colour corresponds to the log-arithm of the density of points (see Figure 5). The diagonal line corre-spond toy = x, and the curve correspond to the mean value.

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Fig. 16. Renormalization of the DLAV values in molecular clouds.Pixels from the five molecular complexes with 1< AV < 5 are includedhere. Colour corresponds to the logarithm of the density of points (seeFigure 5). For eachUmin value, the solid curve correspond to the bestfit slope of the AV,DL versus AV,2M values. The straight solid line cor-respond to a fit to the solid curve in the 0.2 < Umin < 1.0 range, whereeachUmin is given a weight proportional to the number pixels that havethis value in the clouds. The straight solid line provides the AV,RC renor-malization (Eq. 10) . The dashed line correspond to the renormalizationfound in the QSO analysis (Eq. 9), i.e., the line that provides the AV,RQ

renormalization (represented as a solid line in Figure 9).

from that of thePlanck 857, 545, and 353 data in the diffuseISM (shown by Figure 12). This makes the DL model fit witha lowerUmin value than the true radiation field intensity, whichturns into an increase of theAV estimates18. This global dis-agreement could also be indicating that the DL dust materialhas

18 For example, if an MBB with T= 19K, β = 1.9 is fitted with anMBB with β = 1.8, using theIRAS100,Planck857,Planck545, andPlanck353 bands, then the fitted amplitude will be 30 % larger than the

a FIR–submm opacity per unit of optical extinction that is toolow. Other dust models with different (but fixed) optical proper-ties may show a different global factor, possibly closer to 1.

The second issue shows that variations in the FIR–submmopacity, in its normalization per unit of optical extinction, or thespectral shape, are needed across the sky; we take this to be evi-dence of dust evolution. This discrepancy will be present for alldust models based on fixed dust optical properties, possiblywitha different magnitude depending of the details of the specificmodel.

8.2. Optical exctinction AV estimates of dust models

With the aim of obtaining an accurateAV map of the sky, weproposed the renormalized DLAV estimates (AV,RQ in Eqs. 9and AV,RC in 10) that compensates for the discrepancy betweenthe observed FIR emission and the optical extinction in the di-rections of QSOs and molecular clouds. Essentially, it rescalesone of the model outputs (the dust optical extinctionAV) by afunction of Umin, to match data. Planck Collaboration Int. XIV(2013) presented an independent comparison of the renormal-ized AV,RQ estimates withγ−ray observations in the Chamaeleoncloud. They concluded that the “renormalized”AV,RQ estimatesare in closer agreement withγ− ray AV estimates than the (non-renormalized)AV,DL estimates. We now discuss the model renor-malization in a more general context.

The renormalized DL estimates (AV,RQ and AV,RC) provide agood AV determination in the areas where they were calibrated,but they do not provide any insight into the physical dust proper-ties per se; the renormalized dust model becomes simply a fam-ily of SEDs used to fit the data, from which we construct and cal-ibrate an observable quantity (AV,RQ and AV,RC). Unfortunately,the fitted parameters of the renormalized model (Umin) lack aphysical interpretation:Umin is not solely tracing the heating in-tensity of the radiation field, as was assumed in DL.

The AV estimate of the DL dust model is a function of itsfitted parameters, i.e.,AV = f (ΣMd , qPAH, γ, Umin). In general, ifwe fit a dust model with several parameters,AV will be a func-tion of the “most relevant” parameters19. The DL model assumesAV = f (ΣMd) = k × ΣMd, with k = 0.74× 10−5 mag M−1

⊙ kpc2.Our proposed renormalizations are a first step toward a “func-tional renormalization” by extendingAV = k × ΣMd into AV =

g(Umin)× k× ΣMd, where we takeg(Umin) to be a linear functionof Umin. Due to the larger scatter in the QSOAV estimates, onlya simple linear functiong(Umin) can be robustly estimated in thediffuse ISM. In molecular clouds, where the data are less noisy,one could find a smooth functiong′(Umin) which better matchesthe AV,DL / AV,2M fit for eachUmin (i.e., in Figure 16, the solidcurve “flattens” forUmin > 0.8, departing from its linear fit).

Unfortunately any renormalization procedure, while leadingto a more accurateAV estimate, does not provide any further in-sight into the dust physical properties. Real physical knowledgewill arise from a new generation of dust models that should beable to predict the correct optical extinctionAV from first prin-ciples. The next generation of dust models should be able to fitthe empirical SEDs presented in Sect. 6.4 directly. While sucha new generation of dust models is not yet available, we can fornow correct for the systematic departures via Eqs. 9 and 10 inthe diffuse and dense regions, respectively.

original one. Therefore, a discrepancy ofδΥ = 0.1 is likely to producea bias in theAV estimates of the order of 30 %.

19 In the MBB approach, one should consider a function of the formAV = f (τ353, T, β).

19


9. Conclusions

We present a full-sky dust modelling of the newPlanck data,combined with ancillaryIRASandWISEdata, using the DL dustmodel. We test the model by comparing these maps with inde-pendent estimates of the dust optical extinctionAV using SDSSQSO photometry and 2MASS stellar data. Our analysis providesnew insight on interstellar dust and a newAV map over the fullsky.

The DL model fits the observedPlanck, IRAS, and WISESEDs well over most of the sky. Moreover, in the diffuse ISMthe DL model fits the observed SED in thePlanck857 –Planck143 range satisfactorily. The modelling is robust against changesin the angular resolution, as well as adding DIRBE 140 andDIRBE 240 photometric constraints. The high resolution param-eter maps that we generated trace the Galactic dusty structureswell, using a state-of-the-art dust model. We produced the bestpossible optical extinctionAV maps using the DL model.

In the diffuse ISM, the DL AV estimates are larger than es-timates from QSO optical photometry by approximately a fac-tor of 2, and this discrepancy depends systematically onUmin.In molecular clouds, the DLAV estimates are larger than esti-mates based on 2MASS stellar photometry by a factor of about3. Again, the discrepancy depends in a similar way onUmin.

We conclude that the current parameterUmin, associated withthe peak wavelength of the SED, does not only trace variationsin the intensity of the radiation field heating the dust.Umin alsotraces dust evolution: i.e., variations in the optical and FIR prop-erties of the dust grains in the diffuse ISM. DL is a physical dustmodel. Physical dust models have the advantage that, if success-ful, they give some support to the physical assumptions madeabout the interstellar dust and ISM properties that they arebasedon. Unfortunately, the discrepancies found in this study indicatethat some of the physical assumptions of the model need to berevised.

We provide a one-parameter family of SEDs per unit of dustoptical extinction in the diffuse ISM. These SEDs, which relatethe dust emission and absorption properties, are independent ofthe dust/gas ratio or problems inferring total H column densityfrom observations. The next generation of dust models will needto reproduce these new SED estimates.

We propose an empirical renormalization of the DLAVvalues as a function of the DLUmin parameter. The renormal-ized DL AV estimates trace the QSOAV estimates. The pro-posed renormalization (AV,RQ), derived in the diffuse ISM, alsobrings into agreement the DLAV estimates with those derivedfrom 2MASS optical photometry toward molecular clouds in the0 < AV < 5 range. We propose a second renormalized DLAVestimate (AV,RC) tailored to trace theAV estimates in molec-ular clouds more precisely, (and see also the comparison withFermi γ − rays data in Planck Collaboration Int. XIV (2013)).The renormalized mapAV,RQ is the most accurate estimate of theoptical extinction in the diffuse ISM based on our QSOs analysis.Comparison of theAV,RQ map against other tracers of interstel-lar extinction, probing different environment, would further testits accuracy and check for any potential systematics in the QSOanalysis.

Acknowledgements.The development ofPlanck has been supported by:ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF(Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MICINN,JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG(Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland);RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE (EU).A description of the Planck Collaboration and a list of its members, includ-ing the technical or scientific activities in which they havebeen involved, can

be found athttp://www.sciops.esa.int/index.php?project=planck&page=Planck_Collaboration.

The research leading to these results has received funding from theEuropean Research Council under the European Union’s Seventh FrameworkProgramme (FP7/2007-2013)/ ERC grant agreement n 267934.

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http://www.sciops.esa.int/index.php?project=planck&page=Planck_Collaboration


Appendix A: Comparison with Spitzer + Herschelmodelling of the Andromeda galaxy

The Andromeda galaxy is the nearest large spiral galaxy. Itprovides a useful benchmark to validate the current dust mod-elling. Its isophotal radius isR25 = 95′ (de Vaucouleurs et al.1991), corresponding toR25 = 20.6 kpc at the assumed distanced = 744 kpc (Vilardell et al. 2010).

Several authors have modelled the dust properties of M31.Planck Collaboration Int. XXV (2014) presented an indepen-dent study to M31 usingPlanck maps and MBB dust model.In particular DA14 presented a DL based modelling of M31 us-ing the IRAC (Fazio et al. 2004) and MIPS (Rieke et al. 2004)instruments onSpitzer, and the PACS (Poglitsch et al. 2010)and SPIRE (Griffin et al. 2010) instruments onHerschel. Thisdata set has 13 photometric constraints (IRAC 3.6µm, 4.5µm,5.8µm, and 8.0µm, MIPS 24µm, 70µm, and 160µm, PACS70µm, 100µm, and 160µm, and SPIRE 250µm, 350µm, and500µm) from a different set of instruments than those used inour analysis. The high resolution modelling traces the structuresof M31 in great detail, providing maps ofUmin and dust sur-face density, and enables a comparison to be made with gasand metallicity observations. The modelling techniques are de-scribed and validated on NGC628 and NGC6946 in AD12, andlater expanded to the full KINGFISH galaxy sample in AD13.

We compare the dust mass surface density maps20 of themodelling presented by DA14 (from now on called “Herschel”)degraded to a 5′ Gaussian PSF, with the current modelling,called “Planck”. In theHerschelmodelling, a tilted plane is fittedto the background areas, and subtracted from the original imagesto remove the Milky Way cirrus emission. Therefore, we need toadd the cirrus emission back to theHerschelmass estimates be-fore comparing to thePlanckmodelling. The zero level of theHerschelmodelling was restored with an algorithm similar tothat used to estimate the background planes in the KINGFISHdust modelling (see AD12). This algorithm iteratively fits an in-clined plane to the difference in mass surface densities over thebackground points.

M31 does not have considerable quantities of cold dust,which would be detected in thePlanckmodelling but not in theHerschelmodelling. Therefore, we expect both modellings toagree well.

Figure A.1 presents the comparison of the two dust mod-els. The “Herschel” and “Planck” approaches agree very well:the resolved mass differences between the two analyses is small,only 10 % across most of the galaxy. The remaining parameterestimates also agree well. In conclusion, the model resultsap-pear not to be sensitive to the specific data sets used to constrainthe FIR dust emission. This comparison validates the presentmodelling pipeline and methodology.

PIP52 (the reference is still not in the Planck.bib file, I willupdate this as soon as it becomes available) presented an inde-pendent MBB modelling of M31 using the samplePlanckdataas the current analysis, and found compatible results with ourDL modelling.

Appendix B: QSO AV estimation

The intrinsic colours of an unobscured QSO depend strongly onits redshift21 (ζ). We first estimate the (redshift dependent) un-

20 Both dust mass surface density maps correspond to the line ofsightprojected densities, not corrected for the M31 inclination.

21 We will denote the QSO redshift asζ, instead of the usualz to avoidconfusion with the longest wavelength SDSS filterz.

obscured QSO colour for each band pair. By comparing eachQSO colours with the expected unobscured colours, we can es-timate its reddening. Assuming a typical dust extinction curve,we can combine the reddening estimates of the band pairs intoasingle extinction estimate for each QSO. This analysis relies onthe fact that the mean colour excess of a group of QSO scaleslinearly with the DL AV estimates (see Figure B.2).

B.1. SDSS QSO catalogue

The SDSS is a photometric and spectroscopic survey, usinga dedicated 2.5-m telescope at Apache Point Observatory inNew Mexico. It has produced high quality observations of ap-proximately 104 deg2 of the northern sky in five optical andnear IR bands:u, g, r, i, andz, centred at 354.3 nm, 477.0 nm,623.1 nm, 762.5 nm, and 913.4 nm respectively (York et al.2000). The SDSS seventh data release (DR7) (Abazajian et al.2009) contains a sample of 105 783 spectroscopically confirmedQSOs,and the SDSS tenth data release (DR10) (Paris et al. 2013)contains an additional sample of 166 583 QSOs.

In order to avoid absorption from the intergalactic medium,each SDSS band is only usable up to the redshift at which theLyα line (121.57 nm vacuum wavelength) enters (from the blueside) into the filter. Therefore, we can use theu-band, for QSOswith ζ < 1.64,g-band forζ < 2.31, r-band forζ < 3.55, i-bandfor ζ < 4.62, andz-band forζ < 5.69. We also limit the studyto 0.35< ζ < 3.35, to have enough QSOs per unit of redshift toestimate reliably the redshift-dependent unobscured QSO intrin-sic colour (see Sect. B.2). We also remove the few QSOs that liein very luminous (Ldust> 108L⊙ kpc−2), very massive (AV > 1),very hot (Umin > 1.2) or very cold (Umin < 0.3) lines of sight.This leaves 261 841 useful QSOs.

B.2. Unobscured QSO intrinsic colours and extinctionestimation

A typical QSO spectrum has several emission and absorptionlines superimposed on a power-law-like continuum. Dependingon the QSO redshift, the lines fall in different filters. Therefore,for each optical band pair (X, Y), the unobscured QSO intrinsiccolourCX,Y(ζ) depends on the QSO redshift. Given two photo-metric bandsX andY, in order to estimate the unobscured QSOintrinsic colourCX,Y(ζ), we proceed as follows.

We will see that the intrinsic dust properties appear to de-pend on the parameterUmin. Therefore, to avoid introducing apotential bias when computingCX,Y(ζ), we group the lines ofsight according toUmin, and analyze each group independently.The functionsCX,Y(ζ) should, in principle, not depend onUmin,and therefore, all the estimatesCX,Y(ζ,Umin) should be simi-lar for the differentUmin sets. Working independently on eachUmin, for each redshiftζ we choose all the QSOs in the interval[ζ − 0.05, ζ + 0.05], or the 2000 closest QSOs if there are morethan 2000 QSOs in the interval, and fit the QSOs colour (X− Y)as a function of the dust column density:

(X − Y) = CX,Y(ζ,Umin) + ηX,Y(ζ,Umin) × AV,DL, (B.1)

where AV,DL is the DL estimated dust extinction in each QSOline of sight. The functionCX,Y(ζ,Umin) is the best estimate ofthe colour difference (X−Y) of an unobscured QSO (AV,DL = 0)at redshiftζ, estimated from the lines of sight of dust fitted withUmin. The functionηX,Y(ζ,Umin) should be essentially indepen-

21


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nck"

Fig. A.1. Comparison of M31 maps as seen byHerschelandPlanck. The top row shows maps of the dust mass generated usingSpitzerandHerscheldata at high resolution (left) and the current estimates using IRASandPlanckdata (right). The bottom row shows the ratio map of the twomass estimates (convolved to a common resolution and with the zero level matched) on the left, and their scatter on the right. The diagonal linesin the bottom right panel, correspond to a one-to-one relationship, and a±20 % difference about that. The colour in the last panel corresponds tothe density of points. Even though the two analyses are basedon completely independent data, they agree remarkably well, differing by less than10 % across most of the galaxy.

dent ofζ22. Variations in the functionηX,Y(ζ,Umin) with respectto Umin give us information about the dust properties.

Once we computeCX,Y(ζ,Umin) for the different values ofUmin, we average them for each redshiftζ to obtainCX,Y(ζ). ForeachUmin andζ, the weight given to eachCX,Y(ζ,Umin) value isproportional to the number of QSO in the [ζ − 0.05, ζ + 0.05]interval. Figure B.1 shows the results of this unobscured QSOintrinsic colour estimation algorithm for the bandsi andz. ThefunctionsCi,z(ζ,Umin) are shown for the different values ofUmin,using redder lines for largerUmin, and greener for smallerUmin.Their weighted meanCi,z(ζ) is shown in black.

For each QSO, we define its reddeningEX,Y as:

EX,Y = (X − Y) −CX,Y(ζ). (B.2)

TheEX,Y values should not depend on the redshift, and thereforewe can group all the QSOs of a givenUmin into a sub samplewith the same intrinsic colour. Note that no additional hypothe-ses on the QSO spectral shape or dust extinction curve need to

22 See the discussion following Eq. B.6.

be made to compute the QSO intrinsic colours. Working with allthe QSOs with a givenUmin, we fit

EX,Y = ηX,Y(Umin) × AV,DL, (B.3)

and identify the outlier QSOs that depart by more than 3σfrom the expected linear relationship. Figure B.2 shows thetyp-ical QSOEg,r versus AV,DL fit for Umin = 0.6. In this case,ηg,r (Umin = 0.6) = 0.19. Although the QSOEX,Y versus AV,DLrelationship has large scatter due to variations in the QSOsspec-tra (continuum and lines) and intrinsic obscuration in the QSOs,as long as there is no selection bias with respect toAV,DL ourstudy should be robust. The fact that the mean QSOEX,Y foreachAV,DL (curve) and the best fit of the QSOEX,Y versusAV,DL(straight line) in Figure B.2 agree remarkably well, supports thevalidity of the preceding analysis.

Once we have computedEX,Y for all the band pairs andUmin,we remove the QSOs that are considered as outliers in any of thecomputations to obtain a cleaner sample of “good” QSOs. Wereiterate the full procedure twice using the “good” QSO sample

22


0.5 1 1.5 2 2.5 3 3.5−0.1

0

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Redshift (ζ)

Ci,z

(ζ,

Um

in)

Fig. B.1.Unobscured QSO intrinsic colours, as a function of Redshift(ζ), for the bandsi andz. The functionsCi,z(ζ,Umin), are shown for thedifferent values ofUmin, using redder traces for largerUmin, and greenerfor smallerUmin. Their weighted meanCi,z(ζ) is shown in black. TheLyα line affects thei band photometry forζ > 4.62, but we restrict ouranalysis toζ < 3.35 to have enough QSOs per Redshift interval. Forζ > 3.35 the estimatedCi,z(ζ) becomes noisy.

0

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r [m

ag]

Fig. B.2. Colour excessEg,r versus AV,DL for the QSOs withUmin =

0.6. Colour corresponds to the density of points (see Figure 5). Thestraight line corresponds to the best fit for all the QSOs. ForeachAV,DL ,the black curve correspond to the meanEg,r for the QSOs in an intervalwith radiusδAV,DL = 0.01. Even though the QSOs show significant scat-ter, theEg,r versus AV,DL relationship is very linear; the meanEg,r foreach AV,DL curve does not show significant departures from the straightline.

form the previous iteration, resulting in a final “cleanest”samplecontaining 224 245 QSOs withζ < 3.35 (for which we have Lyαfree photometry in ther-, i-, andz-bands), 135,953 withζ < 2.31(where we can use ther-band), and 77 633 QSO withζ < 1.64,where we can use all the SDSS bands. We have an estimate ofthe intrinsic coloursCX,Y, and an estimate of the reddeningEX,Yfor each QSO that is retained by the redshift constraints.

Even though the unobscured QSO intrinsic colours are com-puted independently for each band pair, we do obtain consistentresults across the band pairs, i.e.,

CX,Y(ζ) −CY,Z(ζ) ≈ CX,Z(ζ), (B.4)

holds for all the bandsX, Y, andZ, over all the redshiftsζ consid-ered. Working with the HI column density maps as an estimate ofthe extinction instead of theAV,DL gives very similar estimatesof CX−Y(ζ), and is independent of any dust modelling, so thismeans we did not translate potential dust modelling systematicsinto our QSO estimates.

In order to compare theAV,DL estimate with a QSO estimate,we need to derive a QSO extinctionAV from the different colourexcessEX,Y. We proceed as follows.

For a given QSO spectrum and extinction curve shape, wecan compute the SDSS magnitude increase per dust extinctionAX/AV for X = u, g, r, i, andz. These ratios depend on the as-sumed extinction curve and QSO spectral shape, and thereforeon the QSO redshift. Using the QSO composite spectrum ofVanden Berk et al. (2001) and the extinction curve presentedbyFitzpatrick (1999) parametrized viaRV, we compute the ratiosAX/AV:

δX(ζ,RV) ≡ AX/AV. (B.5)

Figure B.3 showsδX(ζ,RV = 3.1) as a function of the QSO red-shift ζ, for the different bandsX = u, g, r, i, andz. Even thoughthe QSO intrinsic colours are strong functions of its redshift, theextinction curves are smooth enough thatδX(ζ,RV = 3.1) ismostly redshift independent.

0.5 1 1.5 2 2.5 3

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δ X

(ζ,R

V=

3.1

)= A

X /

AV

V V

Fig. B.3.QSO magnitude increase per unit of dust extinctionAV as afunction of the QSO redshift. We use an extinction curve withRV = 3.1.Theu andg band curves are shown in a thinner trace forζ > 1.64 andζ > 2.31, the redshifts at which the intergalactic Lyα line can affect thephotometry in these bands.

Using the extinction curves withRV = 3.1 (which was alsoused to constrain the optical properties of the grains used in theDL model), for each redshiftζ, we define:

δ[X,Y](ζ) =1

δX(ζ,RV = 3.1) − δY(ζ,RV = 3.1), (B.6)

andAV,QSO,[X,Y] = δ[X,Y] × EX,Y. (B.7)

Finally, for each QSO, we define itsAV,QSOas the average ofthe AV,QSO,[X,Y] values for all the band pairs that are allowed byits redshiftζ.

Appendix C: Impact of the CIB anisotropies andinstrumental noise on the parameter estimation.

We study the impact of CIB anisotropies (CIBA) and instrumen-tal (stochastic) noise in our mass estimates in the diffuse ISM

23


(where their effect should be the largest). We simulate data byadding CIBA and instrumental noise to DL SEDs, and fit themwith the same technique as we use to fit the observed data. Theresults quantify the deviations of the recovered parameters fromthe original ones.

We start by a family of four DL SEDs withUmin =

0.4, 0.6, 0.8, and 1.0, a typical fPDR = 0.05, andqPAH = 0.03.We normalize each SED to the meanAV found for the QSO linesof sight in eachUmin. We replicate each SED 100 000 times, addCIB anisotropies and instrumental noise. The noise added has 2components. We add (band-to-band) independent noise to simu-late stochastic instrumental noise with amplitudes given by Pl-MBB, Table B.1, 30′ resolution. We further add a typical CIBSED (also fromPl-MBB, Table B.1, 30′ row), that is completelycorrelated across thePlanckbands, and partially correlated withthe IRASbands, as recommended inPl-MBB, Appendix B. Wefinally fit each simulated SED with DL model, as we did in themain data fit.

Figure C.1 shows the recoveredΣMd divided by the originalΣMd, and recoveredUmin for the SEDs. Each set of points corre-spond to the different originalUmin. The inclined solid line cor-respond to the renormalization curve given by Eq. 9, (rescaledto match the meanAV of the simulated SEDs). There is not aglobal bias in the recoveredΣMd, nor Umin; the distribution ofthe recoveredΣMd andUmin are centered in the original values.Although CIBA and instrumental noise do generate a trend inthe same direction as the renormalization, their impact is signif-icantly smaller than the observed renormalization: they donotspan the full range found over the QSOs lines of sight. Moreover,the renormalization found in Section 6.3 is independent of themodelling resolution; one obtain similar renormalizationcoef-ficients working at 5′, 30′, and 60′ FWHM. For those resolu-tions, the instrumental noise and CIBA have a very differentmagnitude, and therefore, their impact would be quite differ-ent. Therefore, CIBA and instrumental noise are not a signifi-cant source of theAV systematic departures with respect toUminfound in Section 6.3.

0

4

8

12

16

20

24

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.7

0.8

0.9

1.0

1.1

1.2

1.3

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Recovered Umin

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Σ Md O

rigin

al/R

ecov

ered

Fig. C.1. Comparison of the original and recovered dust mass underCIBA and instrumental noise simulation in the diffuse ISM. Colour cor-responds to the density of points (see Figure 5).

1 APC, AstroParticule et Cosmologie, Universite Paris Diderot,CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne ParisCite, 10, rue Alice Domon et Leonie Duquet, 75205 Paris Cedex

13, France

2 African Institute for Mathematical Sciences, 6-8 Melrose Road,Muizenberg, Cape Town, South Africa

3 Agenzia Spaziale Italiana Science Data Center, Via del Politecnicosnc, 00133, Roma, Italy

4 Agenzia Spaziale Italiana, Viale Liegi 26, Roma, Italy

5 Astrophysics Group, Cavendish Laboratory, University ofCambridge, J J Thomson Avenue, Cambridge CB3 0HE, U.K.

6 Astrophysics & Cosmology Research Unit, School of Mathematics,Statistics & Computer Science, University of KwaZulu-Natal,Westville Campus, Private Bag X54001, Durban 4000, South Africa

7 Atacama Large Millimeter/submillimeter Array, ALMA SantiagoCentral Offices, Alonso de Cordova 3107, Vitacura, Casilla 7630355, Santiago, Chile

8 CITA, University of Toronto, 60 St. George St., Toronto, ON M5S3H8, Canada

9 CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulousecedex 4, France

10 California Institute of Technology, Pasadena, California, U.S.A.

11 Centro de Estudios de Fısica del Cosmos de Aragon (CEFCA),Plaza San Juan, 1, planta 2, E-44001, Teruel, Spain

12 Computational Cosmology Center, Lawrence Berkeley NationalLaboratory, Berkeley, California, U.S.A.

13 Consejo Superior de Investigaciones Cientıficas (CSIC), Madrid,Spain

14 DSM/Irfu/SPP, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France

15 DTU Space, National Space Institute, Technical UniversityofDenmark, Elektrovej 327, DK-2800 Kgs. Lyngby, Denmark

16 Departement de Physique Theorique, Universite de Geneve, 24,Quai E. Ansermet,1211 Geneve 4, Switzerland

17 Departamento de Fısica, Universidad de Oviedo, Avda. CalvoSotelo s/n, Oviedo, Spain

18 Department of Astrophysics/IMAPP, Radboud UniversityNijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

19 Department of Physics & Astronomy, University of BritishColumbia, 6224 Agricultural Road, Vancouver, British Columbia,Canada

20 Department of Physics and Astronomy, Dana and David DornsifeCollege of Letter, Arts and Sciences, University of Southern

24


California, Los Angeles, CA 90089, U.S.A.

21 Department of Physics and Astronomy, University College London,London WC1E 6BT, U.K.

22 Department of Physics, Florida State University, Keen PhysicsBuilding, 77 Chieftan Way, Tallahassee, Florida, U.S.A.

23 Department of Physics, Gustaf Hallstromin katu 2a, University ofHelsinki, Helsinki, Finland

24 Department of Physics, Princeton University, Princeton, NewJersey, U.S.A.

25 Department of Physics, University of California, Santa Barbara,California, U.S.A.

26 Department of Physics, University of Illinois at Urbana-Champaign,1110 West Green Street, Urbana, Illinois, U.S.A.

27 Dipartimento di Fisica e Astronomia G. Galilei, Universit`a degliStudi di Padova, via Marzolo 8, 35131 Padova, Italy

28 Dipartimento di Fisica e Scienze della Terra, Universita di Ferrara,Via Saragat 1, 44122 Ferrara, Italy

29 Dipartimento di Fisica, Universita La Sapienza, P. le A. Moro 2,Roma, Italy

30 Dipartimento di Fisica, Universita degli Studi di Milano,ViaCeloria, 16, Milano, Italy

31 Dipartimento di Fisica, Universita degli Studi di Trieste, via A.Valerio 2, Trieste, Italy

32 Dipartimento di Fisica, Universita di Roma Tor Vergata, Via dellaRicerca Scientifica, 1, Roma, Italy

33 Discovery Center, Niels Bohr Institute, Blegdamsvej 17,Copenhagen, Denmark

34 Dpto. Astrofısica, Universidad de La Laguna (ULL), E-38206 LaLaguna, Tenerife, Spain

35 European Southern Observatory, ESO Vitacura, Alonso de Cordova3107, Vitacura, Casilla 19001, Santiago, Chile

36 European Space Agency, ESAC, Planck Science Office, Caminobajo del Castillo, s/n, Urbanizacion Villafranca del Castillo,

Villanueva de la Canada, Madrid, Spain

37 European Space Agency, ESTEC, Keplerlaan 1, 2201 AZNoordwijk, The Netherlands

38 Facolta di Ingegneria, Universita degli Studi e-Campus,ViaIsimbardi 10, Novedrate (CO), 22060, Italy

39 HGSFP and University of Heidelberg, Theoretical PhysicsDepartment, Philosophenweg 16, 69120, Heidelberg, Germany

40 Helsinki Institute of Physics, Gustaf Hallstromin katu 2, Universityof Helsinki, Helsinki, Finland

41 INAF - Osservatorio Astrofisico di Catania, Via S. Sofia 78,Catania, Italy

42 INAF - Osservatorio Astronomico di Padova, Vicolodell’Osservatorio 5, Padova, Italy

43 INAF - Osservatorio Astronomico di Roma, via di Frascati 33,Monte Porzio Catone, Italy

44 INAF - Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11,Trieste, Italy

45 INAF/IASF Bologna, Via Gobetti 101, Bologna, Italy

46 INAF/IASF Milano, Via E. Bassini 15, Milano, Italy

47 INFN, Sezione di Bologna, Via Irnerio 46, I-40126, Bologna,Italy

48 INFN, Sezione di Roma 1, Universita di Roma Sapienza, PiazzaleAldo Moro 2, 00185, Roma, Italy

49 INFN/National Institute for Nuclear Physics, Via Valerio 2, I-34127Trieste, Italy

50 IPAG: Institut de Planetologie et d’Astrophysique de Grenoble,Universite Grenoble Alpes, IPAG, F-38000 Grenoble, France,

25


CNRS, IPAG, F-38000 Grenoble, France

51 Imperial College London, Astrophysics group, Blackett Laboratory,Prince Consort Road, London, SW7 2AZ, U.K.

52 Infrared Processing and Analysis Center, California Institute ofTechnology, Pasadena, CA 91125, U.S.A.

53 Institut Universitaire de France, 103, bd Saint-Michel, 75005, Paris,France

54 Institut d’Astrophysique Spatiale, CNRS (UMR8617) UniversiteParis-Sud 11, Batiment 121, Orsay, France

55 Institut d’Astrophysique de Paris, CNRS (UMR7095), 98 bisBoulevard Arago, F-75014, Paris, France

56 Institute for Space Sciences, Bucharest-Magurale, Romania

57 Institute of Astronomy, University of Cambridge, Madingley Road,Cambridge CB3 0HA, U.K.

58 Institute of Theoretical Astrophysics, University of Oslo, Blindern,Oslo, Norway

59 Instituto de Astrofısica de Canarias, C/Vıa Lactea s/n, La Laguna,Tenerife, Spain

60 Instituto de Fısica de Cantabria (CSIC-Universidad de Cantabria),Avda. de los Castros s/n, Santander, Spain

61 Jet Propulsion Laboratory, California Institute of Technology, 4800Oak Grove Drive, Pasadena, California, U.S.A.

62 Jodrell Bank Centre for Astrophysics, Alan Turing Building, Schoolof Physics and Astronomy, The University of Manchester, OxfordRoad, Manchester, M13 9PL, U.K.

63 Kavli Institute for Cosmology Cambridge, Madingley Road,Cambridge, CB3 0HA, U.K.

64 LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay, France

65 LERMA, CNRS, Observatoire de Paris, 61 Avenue del’Observatoire, Paris, France

66 Laboratoire AIM, IRFU/Service d’Astrophysique - CEA/DSM -CNRS - Universite Paris Diderot, Bat. 709, CEA-Saclay, F-91191Gif-sur-Yvette Cedex, France

67 Laboratoire Traitement et Communication de l’Information, CNRS(UMR 5141) and Telecom ParisTech, 46 rue Barrault F-75634ParisCedex 13, France

68 Laboratoire de Physique Subatomique et de Cosmologie, UniversiteJoseph Fourier Grenoble I, CNRS/IN2P3, Institut NationalPolytechnique de Grenoble, 53 rue des Martyrs, 38026 Grenoble

cedex, France

69 Laboratoire de Physique Theorique, Universite Paris-Sud 11 &CNRS, Batiment 210, 91405 Orsay, France

70 Lawrence Berkeley National Laboratory, Berkeley, California,U.S.A.

71 Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str. 1,85741 Garching, Germany

72 McGill Physics, Ernest Rutherford Physics Building, McGillUniversity, 3600 rue University, Montreal, QC, H3A 2T8, Canada

73 National University of Ireland, Department of ExperimentalPhysics, Maynooth, Co. Kildare, Ireland

74 Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark

75 Observational Cosmology, Mail Stop 367-17, California Institute ofTechnology, Pasadena, CA, 91125, U.S.A.

76 Princeton University Observatory, Peyton Hall, Princeton, NJ08544-1001, U.S.A.

77 SISSA, Astrophysics Sector, via Bonomea 265, 34136, Trieste, Italy

78 School of Physics and Astronomy, Cardiff University, QueensBuildings, The Parade, Cardiff, CF24 3AA, U.K.

79 Space Research Institute (IKI), Russian Academy of Sciences,Profsoyuznaya Str, 84/32, Moscow, 117997, Russia

80 Space Sciences Laboratory, University of California, Berkeley,California, U.S.A.

81 Special Astrophysical Observatory, Russian Academy of Sciences,Nizhnij Arkhyz, Zelenchukskiy region, Karachai-CherkessianRepublic, 369167, Russia

82 Sub-Department of Astrophysics, University of Oxford, KebleRoad, Oxford OX1 3RH, U.K.

83 UPMC Univ Paris 06, UMR7095, 98 bis Boulevard Arago,F-75014, Paris, France

84 Universite de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex4, France

85 Universities Space Research Association, Stratospheric Observatoryfor Infrared Astronomy, MS 232-11, Moffett Field, CA 94035,U.S.A.

86 University of Granada, Departamento de Fısica Teorica y delCosmos, Facultad de Ciencias, Granada, Spain

87 University of Granada, Instituto Carlos I de Fısica Teorica yComputacional, Granada, Spain

88 Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478Warszawa, Poland

26

Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations

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Transcript of Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations