Planck Early Results: Thermal dust in Nearby Molecular Clouds

Abstract

Planck allows unbiased mapping of Galactic sub-millimetre and millimetre
emission from the most diffuse regions to the densest parts of molecular
clouds. We present an early analysis of the Taurus molecular complex, on
line-of-sight-averaged data and without component separation. The emission
spectrum measured by Planck and IRAS can be fitted pixel by pixel using a
single modified blackbody. Some systematic residuals are detected at 353 GHz
and 143 GHz, with amplitudes around -7 % and +13 %, respectively, indicating
that the measured spectra are likely more complex than a simple modified
blackbody. Significant positive residuals are also detected in the molecular
regions and in the 217 GHz and 100 GHz bands, mainly caused by to the
contribution of the J=2-1 and J=1-0 12CO and 13CO emission lines. We derive
maps of the dust temperature T, the dust spectral emissivity index beta, and
the dust optical depth at 250 microns tau. The temperature map illustrates the
cooling of the dust particles in thermal equilibrium with the incident
radiation field, from 16-17 K in the diffuse regions to 13-14 K in the dense
parts. The distribution of spectral indices is centred at 1.78, with a standard
deviation of 0.08 and a systematic error of 0.07. We detect a significant
T-beta anti-correlation. The dust optical depth map reveals the spatial
distribution of the column density of the molecular complex from the densest
molecular regions to the faint diffuse regions. We use near-infrared extinction
and HI data at 21-cm to perform a quantitative analysis of the spatial
variations of the measured dust optical depth at 250 microns per hydrogen atom
tau/NH. We report an increase of tau/NH by a factor of about 2 between the
atomic phase and the molecular phase, which has a strong impact on the
equilibrium temperature of the dust particles.

Full text

Page 1

arXiv:1101.2037v3 [astro-ph.GA] 21 Jan 2011
Astronomy & Astrophysics manuscript no. Dust˙MC˙09jan2011˙AA
January 24, 2011
c ? ESO 2011
Planck Early Results: Thermal dust in Nearby Molecular Clouds
Planck Collaboration: A. Abergel43 ⋆, P. A. R. Ade66, N. Aghanim43, M. Arnaud53, M. Ashdown51,72, J. Aumont43, C. Baccigalupi64, A. Balbi26,
A. J. Banday70,6,58, R. B. Barreiro48, J. G. Bartlett3,49, E. Battaner74, K. Benabed44, A. Benoˆ ıt44, J.-P. Bernard70,6, M. Bersanelli24,38, R. Bhatia31,
J. J. Bock49,7, A. Bonaldi34, J. R. Bond5, J. Borrill57,67, F. R. Bouchet44, F. Boulanger43, M. Bucher3, C. Burigana37, P. Cabella26,
J.-F. Cardoso54,3,44, A. Catalano3,52, L. Cay´ on17, A. Challinor73,51,8, A. Chamballu41, L.-Y Chiang45, C. Chiang16, P. R. Christensen61,27,
D. L. Clements41, S. Colombi44, F. Couchot56, A. Coulais52, B. P. Crill49,62, F. Cuttaia37, L. Danese64, R. D. Davies50, R. J. Davis50, P. de
Bernardis23, G. de Gasperis26, A. de Rosa37, G. de Zotti34,64, J. Delabrouille3, J.-M. Delouis44, F.-X. D´ esert40, C. Dickinson50, K. Dobashi13,
S. Donzelli38,46, O. Dor´ e49,7, U. D¨ orl58, M. Douspis43, X. Dupac30, G. Efstathiou73, T. A. Enßlin58, H. K. Eriksen46, F. Finelli37, O. Forni70,6,
M. Frailis36, E. Franceschi37, S. Galeotta36, K. Ganga3,42, M. Giard70,6, G. Giardino31, Y. Giraud-H´ eraud3, J. Gonz´ alez-Nuevo64,
K. M. G´ orski49,76, S. Gratton51,73, A. Gregorio25, A. Gruppuso37, V. Guillet43, F. K. Hansen46, D. Harrison73,51, S. Henrot-Versill´ e56, D. Herranz48,
S. R. Hildebrandt7,55,47, E. Hivon44, M. Hobson72, W. A. Holmes49, W. Hovest58, R. J. Hoyland47, K. M. Huffenberger75, A. H. Jaffe41, A. Jones43,
W. C. Jones16, M. Juvela15, E. Keih¨ anen15, R. Keskitalo49,15, T. S. Kisner57, R. Kneissl29,4, L. Knox19, H. Kurki-Suonio15,32, G. Lagache43,
J.-M. Lamarre52, A. Lasenby72,51, R. J. Laureijs31, C. R. Lawrence49, S. Leach64, R. Leonardi30,31,20, C. Leroy43,70,6, M. Linden-Vørnle10,
M. L´ opez-Caniego48, P. M. Lubin20, J. F. Mac´ ıas-P´ erez55, C. J. MacTavish51, B. Maffei50, N. Mandolesi37, R. Mann65, M. Maris36,
D. J. Marshall70,6, P. Martin5, E. Mart´ ınez-Gonz´ alez48, S. Masi23, S. Matarrese22, F. Matthai58, P. Mazzotta26, P. McGehee42, P. R. Meinhold20,
A. Melchiorri23, L. Mendes30, A. Mennella24,36, S. Mitra49, M.-A. Miville-Deschˆ enes43,5, A. Moneti44, L. Montier70,6, G. Morgante37,
D. Mortlock41, D. Munshi66,73, A. Murphy60, P. Naselsky61,27, P. Natoli26,2,37, C. B. Netterfield12, H. U. Nørgaard-Nielsen10, F. Noviello43,
D. Novikov41, I. Novikov61, S. Osborne69, F. Pajot43, R. Paladini68,7, F. Pasian36, G. Patanchon3, O. Perdereau56, L. Perotto55, F. Perrotta64,
F. Piacentini23, M. Piat3, S. Plaszczynski56, E. Pointecouteau70,6, G. Polenta2,35, N. Ponthieu43, T. Poutanen32,15,1, G. Pr´ ezeau7,49, S. Prunet44,
J.-L. Puget43, W. T. Reach71, R. Rebolo47,28, M. Reinecke58, C. Renault55, S. Ricciardi37, T. Riller58, I. Ristorcelli70,6, G. Rocha49,7, C. Rosset3,
J. A. Rubi˜ no-Mart´ ın47,28, B. Rusholme42, M. Sandri37, D. Santos55, G. Savini63, D. Scott14, M. D. Seiffert49,7, P. Shellard8, G. F. Smoot18,57,3,
J.-L. Starck53,9, F. Stivoli39, V. Stolyarov72, R. Sudiwala66, J.-F. Sygnet44, J. A. Tauber31, L. Terenzi37, L. Toffolatti11, M. Tomasi24,38, J.-P. Torre43,
M. Tristram56, J. Tuovinen59, G. Umana33, L. Valenziano37, L. Verstraete43, P. Vielva48, F. Villa37, N. Vittorio26, L. A. Wade49, B. D. Wandelt44,21,
D. Yvon9, A. Zacchei36, and A. Zonca20
(Affiliations can be found after the references)
Preprint online version: January 24, 2011
ABSTRACT
Planck allows unbiased mapping of the sub-millimeter and millimeter emission from the most diffuse regions to the densest parts of molecular
clouds. We present an early analysis of the Taurus molecular complex, on line-of-sight-averaged data and without component separation. The
emission spectrum measured by Planck and IRAS can be fitted pixel by pixel using a single modified black-body. We derive maps of the temper-
ature, spectral index, and optical depth. The distribution of spectral indices is narrow, centered at 1.78, with a standard deviation of 0.08 and a
systematic error of 0.07. Some systematic residuals are detected at 353GHz and 143GHz, with amplitudes around -7% and +13%, respectively,
indicating that the measured spectra are likely more complex than a simple modified black-body. Significant positive residuals are also detected
in the molecular regions and in the 217GHz and 100GHz bands, mainly due to the contribution of the J = 2 → 1 and J = 1 → 012CO and
13CO emission lines. The temperature map illustrates the cooling of the dust particles in thermal equilibrium with the incident radiation field, from
16–17K in the diffuse regions to 13–14K in the dense parts. The optical depth map reveals the spatial distribution of the column density of the
molecular complex from the densest molecular regions to the faint diffuse regions. We use near-infrared extinction and Hi data at 21cm to perform
a quantitative analysis of the spatial variations of the measured optical depth per hydrogen atom τ/NH. The derived map of τ/NHshows where and
on what angular scale the transition occurs between the diffuse (∼ 1 × 10−25cm2) and dense regions (∼ 2 × 10−25cm2). We find a systematic and
sharp increase of τ/NHin the outer parts of the molecular phase where Av> 1, by at least a factor of 2. Such variations of τ/NHhave a strong
impact on the equilibrium temperature of the dust particles.
1. Introduction
Planck1(Tauber et al. 2010; Planck Collaboration 2011a) is the
third generation space mission to measure the anisotropy of the
cosmic microwave background (CMB). It observes the sky in
⋆Corresponding author; email: alain.abergel@ias.u-psud.fr.
1Planck (http://www.esa.int/Planck ) is a project of the European
Space Agency (ESA) with instruments provided by two scientific con-
sortia funded by ESA member states (in particular the lead countries
France and Italy), with contributions from NASA (USA) and telescope
reflectorsprovided by acollaboration between ESAand ascientificcon-
sortium led and funded by Denmark.
nine frequency bands covering 30–857GHz with high sensitiv-
ity and angular resolution from 31′to 5′. The Low Frequency
Instrument LFI; (Mandolesi et al. 2010; Bersanelli et al. 2010;
Mennella et al. 2011) covers the 30, 44, and 70GHz bands with
amplifierscooledto 20K. The HighFrequencyInstrument(HFI;
Lamarre et al. 2010; Planck HFI Core Team 2011a) covers the
100, 143, 217, 353, 545, and 857GHz bands with bolome-
ters cooled to 0.1K. Polarization is measured in all but the
highest two bands (Leahy et al. 2010; Rosset et al. 2010). A
combination of radiative cooling and three mechanical cool-
ers produces the temperatures needed for the detectors and op-
1

Page 2

Planck Collaboration: Thermal dust in nearby molecular clouds
tics (Planck Collaboration2011b). Two Data Processing Centers
(DPCs) check and calibrate the data and make maps of the sky
(Planck HFI Core Team 2011b; Zacchei et al. 2011). Planck’s
sensitivity, angular resolution, and frequencycoverage make it a
powerful instrument for galactic and extragalactic astrophysics
as well as cosmology. Early astrophysics results are given in
Planck Collaboration,2011h–u.This paperpresents the early re-
sults of the analysis of Planck/HFI observations of the Taurus
molecular cloud.
IRAS provided a complete view of the interstellar matter in
our Galaxy in four photometric bands from 12 to 100µm with
angular resolution of about 4′. The 12, 25, and 60µm bands
are mainly sensitive to the emission of the smallest interstel-
lar grains. They are aromatic hydrocarbons (large molecules)
and amorphous hydrocarbon grains, undergo stochastic heating
upon photon absorption, and tend to emit most of their energy
at wavelengths shortward of 100µm. The large particles have
dimensions of the order of 100nm and make up the bulk of
the dust mass. They are in equilibrium between thermal emis-
sion and absorption of UV and visible photons from incident
radiation. Only one IRAS band, at 100µm, is dominated by the
emission of this dust component. DIRBE and FIRAS on board
COBE producedall-sky maps at longer wavelengths, with angu-
lar resolution lower than IRAS (40′and 7◦, respectively), which
allowed the measurement of dust temperatures and spectral in-
dices. The dust temperature is found to be on average ∼17.5K
(with a spectral index β = 2) in the diffuse atomic medium
(Boulanger et al. 1996) and to be lower in molecular clouds
with no embedded bright stars (Lagache et al. 1998). Small
patches of molecular clouds have been observed in more de-
tail from the ground by the JCMT (Johnstone & Bally 1999), by
balloon borne experiments PRONAOS (Ristorcelli et al. 1998a)
and Archeops (D´ esert et al. 2008a), and from space by Spitzer
(e.g., Flagey et al. 2009)andHerschel (e.g.,Andr´ e et al. (2010);
Motte et al. (2010); Abergel et al. (2010)).
With Planck, the whole sky emission of thermal dust is
mapped from the submillimeter to the millimeter range, with
angular resolution comparable to IRAS. We have complete and
unbiased surveys of molecular clouds not only in terms of spa-
tial coverage, but also in terms of spatial content of the data.
Unlike ground or ballon observations, the maps contain all an-
gular scales without spatial filtering. This is extremely impor-
tant for galactic science, since the interstellar matter contains a
large range of intricate spatial scales. Moreover, the emission is
measured with unprecedented signal-to-noise ratio down to the
faintest parts surrounding the bright and dense regions. Up to
now, the rotational transitions of carbon monoxide (CO) were
the main tracer of the interstellar matter in molecular clouds.
With Planck thermal dust becomes a new tracer. The spectral
coverage and the sensitivity allow, for each line of sight, precise
measurements of the temperature, of the spectral index, and of
the optical depth independently of the excitation condition.
Molecular clouds present a wide range of physical condi-
tions (illumination, density, star forming activity), so are ideal
targets for studying the emission properties of the dust grains
and their evolution. The goal of this paper is to discuss the re-
sults of the early analysis of HFI maps of the Taurus complex,
which is one of the nearest giant molecular cloud (d = 140pc,
from Kenyon et al. 1994) with low mass star forming activity.
First we present the HFI data and the ancillary observations
usedforthispaper(Sect.2).Thenwedescribetheemissionspec-
trum of thermal dust measured by HFI and IRAS and discuss the
validity of the fitting of the measured spectra with one single
modified black-body (Sect.3). Maps of the temperature and of
the spectral index are analyzed in Sect.4. Then in Sect.5 we dis-
cuss the evolution of the optical depth/column density conver-
sion factor (τ/NH) from the atomic diffuse regions to the molec-
ular densest regions.
2. Observations
2.1. HFI data
We use the DR2 release of the HFI maps presented in Fig.1 and
beginning with Healpix form G´ orski et al. (2005) with Nside=
2048 (pixel size 1.′7). Their processing and calibration are de-
scribed in Planck HFI Core Team (2011b). An important step is
the removal of the CMB through a needlet internal linear com-
bination.
Thesystematic calibrationaccuracyof HFI is summarizedin
Table1 (from Planck HFI Core Team 2011a). For the two HFI
bands at 550 and 857GHz, the gain calibration is performed us-
ingFIRAS data.Thesystematicerrorsonthegaincalibrationare
7% for the 857 and 545GHz filters (estimated using the disper-
sion in different regions of the sky), and about 2% for the other
bands.
We estimate the statistical noise as follows (see also
AppendixB of Planck Collaboration (2011t) for details). Two
independent maps of the same sky have been computed by the
DPC from the first- and second-half ring of each pointing pe-
riod. As the coverage map is identical for these two maps, the
standard deviation of their half difference, σHR, is equal to the
standard deviation of the average map. For all bands, we com-
pare the computed value of σHRwith the standard deviation σref
of the DR2 map computed within a reference 48′× 48′window
centered at l = 165.◦43, b = −21.◦06, chosen in the lowest part
of the map (white square in the first image of Fig.1). Obviously,
the values of σrefgive only upper limits on the statistical noise
because of the contributions of CMB residuals, and of cosmic
infrared background(CIB) and thermal dust fluctuations that in-
crease with increasing frequencies. Table1 shows that for the
100, 143, and 217GHz bands, σHRis almost identical to σref.
Therefore we conclude that:
1. the standard deviation of CMB residuals is lower than the
statistical noise in all bands;
2. the standard deviation of the CIB anisotropies (CIBA) ap-
pears lower than the measured statistical noise in the 100,
143,and217GHzbands(whichiscompatiblewiththeCIBA
measurements in Planck Collaboration (2011n));
3. the computed values of σHRgive realistic estimates of the
statistical noise.
Forthisearlyanalysis,we takeaconstantstatistical noiseineach
band taken equal to the values of σHRin Table1.
2.2. Ancillary data
We combine the Planck maps with IRAS maps at 100µm
(3000GHz), using the IRIS (Improved Reprocessing of the
IRAS Survey) data computed by Miville-Deschˆ enes & Lagache
(2005). The statistical noise of the 100µm maps is about
0.06 MJysr−1per pixel (pixel size of 1.8′), while the system-
atic error in the gain calibration from DIRBE is estimated to
be 13.5% (from Miville-Deschˆ enes & Lagache 2005). For the
Taurus molecular cloud, the 100µm brightness is in the range
1–20MJysr−1, so the statistical noise translates into relative er-
rors in the range 0.03–6%, well below the systematic error on
the gain.
2

Page 3

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.1. IRAS and HFI maps of the Taurus molecular cloud, in MJysr−1. The 48′× 48′reference window is seen on the IRAS map at
100µm (3000GHz). For all maps the average brightness computed within the reference window is subtracted.
3

Page 4

Planck Collaboration: Thermal dust in nearby molecular clouds
Table 1. Calibration accuracy, statistical noise, standard deviation within the reference window (white square in the first panel of
Fig.1), median brightnesses, and average spectrum within the reference window.
Frequency (GHz)
Callibration accuracy
Statistical noise from σHR(MJy/sr)
σref(MJy/sr)
Median brightness (MJy/sr)
Reference spectrum (MJy/sr)
100
2%
0.014
0.013
0.042
0.010
143
2%
0.0086
0.0078
0.094
0.027
217
2%
0.018
0.019
0.41
0.11
353
2%
0.038
0.050
1.67
0.43
545
7%
0.049
0.13
6.37
1.48
857
7%
0.074
0.35
17.46
4.1
3000
13.5%
0.37
13.9
4.8
The atomic gas is traced on large scales using the Hi data
at 21cm taken with the Leiden/Dwingeloo 25-m telescope with
an angular resolution of 36′by Hartmann & Burton (1997). The
velocity spacing is 1.03km/s, and the LSR velocity range is
−450 < VLSR < 400km/s. The data have been corrected for
contaminationfrom stray light radiation to the 0.07K sensitivity
level (Hartmann et al. 1996).
Thelargescale surveyinthe12CO (J = 1 → 0)emissionline
taken by Dame et al. (2001) with the CfA telescope is used to
tracethemoleculargas.Thebeamwidthis 8.8′±0.2′.Fortheob-
servations of the Taurus molecular cloud, the sampling distance
is equal to 7.5′, the channel width is 0.65kms−1and the channel
rms noise is 0.25K. The data cubes have been transformed into
the velocity-integrated intensity of the line (WCO) by integrat-
ing the velocity range where the CO emission is significantly
detected using the moment method proposed by Dame et al.
(2001). The statistical noise level of the WCOmap is typically
1.2Kkms−1.
Inordertoanalysethecentralregionofthe TaurusMolecular
Cloud with the13CO J = 1 → 0 emission lines, we also use the
FCRAO survey of 98deg2conducted with an angular resolution
47′′(Narayanan et al. 2008; Goldsmith et al. 2008). We apply
the error beam scaling factor recently proposed by Pineda et al.
(2010), so that the intensities of the CfA and FCRAO surveys of
the12CO emission line are compatible. The statistical noise per
pixel(withpixelsizeof0.33′)ofthevelocity-integratedintensity
maps is about 0.4Kkms−1for the13CO line.
The column density can also be traced from the near-
infrared (NIR) extinction using the 2MASS point source cata-
log (e.g., Dobashi et al. (2005); Pineda et al. (2010)). For com-
parison with HFI data, we use the extinction map of the cen-
tral part of the Taurus molecular cloud recently created by
Pineda et al. (2010) and shown in Fig.2. It is Nyquist sampled
with an angular resolution of 200′′, and corrected for the con-
tribution of atomic gas to the total extinction. The infrared col-
ors are converted to visible extinction AV using the extinction
curve of Weingartner & Draine (2001), using the standard ra-
tio of selective to total extinction RV = 3.1 for the diffuse
ISM (Savage & Mathis 1979). As the number of background
stars used to compute the extinction decreases with increas-
ing extinction, the error in AVincreases from about 0.2mag at
low extinctions (AV = 0–1mag) to 0.5mag at large extinctions
(AV ∼ 10mag), with an average error of 0.29mag. For higher
extinctions (AV > 10mag) the extinction map only gives lower
limits.
3. Emission spectrum of thermal dust
3.1. Reference spectrum
The combination of IRAS and Planck data provides the spectral
energy distribution (SED) from 3000GHz (100µm) to 100GHz
Fig.3. Spectrum of one pixel in the non-molecular region.
Crosses: total brightness Itot, Triangles: average brightness Iref
within the reference 48′× 48′window (see on the first panel
of Fig.1), Square: Itot− Iref, Diamonds: CIB spectrum at the
central frequency of the HFI filters from 857 to 217GHz, from
Fixsen et al. (1998).
(3mm), for each pixel of the maps. The CMB has been removed
fromthemapsweuse.ThemapscouldcontainsomeCMBresid-
ual, but with an amplitude lower than the statistical noise even
in the low frequency channels (see Sect.2.1).
In all bands, the maps contain Galactic and non-Galactic
emission that is not associated with the Taurus complex.
Therefore for all maps we subtract the average brightness com-
putedwithinthereference48′×48′windowchoseninthefaintest
region (white square in the first image of Fig.1 and central co-
ordinates given above in Sect.2.1) of the map. This is illustrated
for one pixel in Fig.3. The average spectrum in the reference
window is also shown in Fig.3, together with the CIB spec-
trum (from FIRAS data by Fixsen et al.1998) at the central fre-
quencies of the HFI filters. We see that the reference spectrum
is mainly due to galactic atomic emission (there is no detected
emission within the12CO J = 1 → 0 line), since the CIB con-
tributes not more than 5-10%.
In order to derive the optical depth per column density in the
atomic phase (Sect.5.2) the emission measured within the same
reference window will be subtracted from the Hi data.
3.2. Choice of the spectral bands
TheIRASmapsat12,26,and60µmarenotusedforanyanalysis
of the emission of thermal dust particles (whichare by definition
inthermalequilibrium),becauseofthecontributionofsmalldust
particles transiently heated each time they absorb a UV/visible
photon.In all spectra presentedin this paper,we leave the 60µm
4

Page 5

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.2. Upper left panel: column density derived from the Hi data at 21cm (Hartmann & Burton 1997). Upper right panel:12CO
(J = 1 → 0) velocity integrated emission line (Dame et al. 2001). Lower left panel:13CO J = 1 → 0 velocity integrated emission
line (Narayanan et al. 2008; Goldsmith et al. 2008). Lower right panel: NIR extinction using 2MASS (Pineda et al. 2010).
data points in order to illustrate this contribution, but these data
points are not used to analyze the SED. In the 100µm band, the
contribution of these small particles is expected to be lower than
10% if the intensity of the interstellar radiation field is of the or-
der of the value in the local diffuse ISM (e.g., Compi` egne et al.
2011), as is the case in the Taurus molecular complex. This con-
tribution is in any case lower than the gain calibration error of
IRAS at 100µm (13.5%, see Sect.2.2).
For this early analysis, we do not use the data taken at 100
and 217GHz to analyze the thermal dust emission, since they
are expected to be contaminated in the molecular regions by ro-
tational J = 1 → 0 and J = 2 → 112CO emission lines and
by13CO emission lines with a lower amplitude. Higher J lines
in the other bands have a lower relative amplitude and are ne-
glected for this early analysis, as the emission of molecular lines
tracing the densest regions. Therefore, in a first step only the
bands at 3000, 857, 545, 353, and 143GHz (100, 350, 545, 850,
and 2098µm) are used to analyze the thermal dust emission.
In practice, we smoothed all maps to the angular
resolutionofthe143GHz
isotropic Gaussian beams and taking the FWHM from
Miville-Deschˆ enes & Lagache (2005) for IRAS and from
Planck HFI Core Team (2011a) for HFI. We do not take into
account the ellipticity of the PSF (Planck HFI Core Team
2011a). This may introduce some error for the detailed analysis
of individual structures, but our goal is not to to derive any
(FWHM:7.08′) assuming
quantitative results of individual structures, but to extract, from
a pixel per pixel analysis, some quantitative information on the
emission that emerges from the different phases. The 100GHz
map will be used to compute the residuals to the fits (see
Sect.3.5), and is left at its original resolution (9.′37). Figure 4
shows the spectra taken at positions in the non-molecular region
and in the molecular region.
3.3. Principle of fitting
In this early analysis, the fitting function is a single modified
black body:
Iν = τν0×
?ν
ν0
?β
× Bν(T),
(1)
whereτν0is the optical depthat frequencyν0, β is the spectralin-
dex, Bνis the Planck function, and T the temperature. All quan-
titative values of the optical depth will be given at the frequency
ν0= 1200GHz (250µm) to be comparableto previous analyses.
We define τν0= τ0.
The three computed parameters for each pixel are T, β, and
τ. We use the IDL MPFIT routine, which performs weighted
least squares curve fitting of the data (Markwardt 2009) tak-
ing into account the noise (statistical noise or calibration un-
certainty) for each spectral band. We apply color correction
5

Page 6

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.4. SED of two pixels (Left: non-molecular region, Right:
molecular region). Square= data, Solid line: fitted model,
Crosses= fitted model integrated within the bands. The fits
are performed using the 100µm, 857, 545, 353 and 143GHz
bands (red squares), and using the calibration error discussed
in Sects.2.1 and 2.2. The error bars are too small to be visi-
ble. Significant excess in the 217 and 100GHz bands due to
12CO and13CO emissions are detected in the molecular spec-
trum. On the other hand, a significant negative residual is ob-
served at 353GHz. The 60µm data points are not used to ana-
lyze the SED, because of the contribution of small dust particles
transiently heated each time they absorb a UV/visible photon.
factors computed using version 1 of the transmission curves
(Planck HFI Core Team 2011a).
The goal of such adjustment is to reduce the properties of
the SED measured for each line of sight in three parametersT,β,
and τ. The temperature, the spectral index and the optical depth
of the emitting dust particles along the line of sight can obvi-
ously vary, so the fitted values of the three parameters derived
for each line of sight, while representing some average proper-
ties, cannot get the complete picture of the dust particles located
along the line of sight. Moreover, we make the assumption that
the spectral index β of the measured spectra is constant from
far-infrared (FIR) to millimeter wavelengths. The spectral index
of dust emission may vary due to temperature-dependentmech-
anisms at low temperatures, including free charge carrier pro-
cesses, two-phonon difference processes, and absorption mech-
anisms in two-level systems (Agladze et al. 1996; Meny et al.
2007). Moreover the measured spectra can be broadened around
the peak of the modified black-body because of the contribu-
tion of dust at different temperatures, so the spectral index of
the measured spectra could decrease from the submmillimeter
(submm), around the peak to the millimeter, as illustrated by
Shetty et al. (2009b).
3.4. Example of spectra. Systematic errors on the
parameters derived from the fit
Figure4isanillustrationofthefittingfortwopixels,onetakenat
a position with detected CO emission (within the12CO J = 1 →
0 line), the other at a position with no detected CO emission.
We use for the fitting the statistical noise for HFI and IRAS data
discussed in Sect.2, taking into account the smoothing of the
map at the angular resolution of the 143GHz band.
Simulationshave been performedto understandand to quan-
tify the propagation of the calibration errors, the statistical
noise and the CIBA in the determination of T,β, and τ (see
AppendixA for details). The calibration errors propagate into
systematic errors in T,β, and τ of about 0.7K, 0.07, and 18%,
respectively. We have also shown that the statistical noise and
the CIBA propagates into statistical noises in T, β, and τ in the
range 0.1–1K, 0.025–0.25 and 2–20%, respectively, depending
on the 100µm brightness (10–1MJysr−1). Moreover, both for
systematic errors and statistical noises, the three parameters are
strongly anti-correlated or correlated (Fig.A.1).
The two spectra of Fig.4 show that, to first order, a single
modified black body gives a reasonable representation of the
SED measured by IRAS and HFI. It is obviousthat by increasing
the number of free parameters in our fit (e.g., by using two mod-
ified black bodies with different temperature and spectral index)
it is possible to improve the fits significantly, but this is not our
goal in this early paper. We use exactly the same method to fit
the spectra for all pixels of the map in order to derive the tem-
perature map and the spectral index maps shown in Fig.7.
3.5. Analysis of the residuals
The fit residuals allow us to assess the limitations of using a
single modified black body to fit the data. As seen in Sect.3.2,
fits are made to the 3000, 857, 545, 353, and 143GHz data all
smoothed to the angular resolution of 143GHz. The residual
map at 100GHz is computed from the difference between the
synthetic spectra smoothed at the 100GHz resolution and the
data at 100GHz. The residual map of the fitting in all bands is
shownin Figs.5. Figure6 shows the relativeresidualmap (resid-
ual map divided by measured map).
3.5.1. For the 5 fitted bands
We see in Fig.6 that the relative residuals are around 0 and be-
low 1–3% for the 3000, 857, and 545Hz bands. On the other
hand, the residuals at 353GHz are systematically negative, with
a median relative amplitude about −7%, while the residuals at
143GHz are systematically positive, with a median relative am-
plitude about +13%. As can be seen in Figs.5 and Fig.6, these
residuals are spatially correlated with the measured brightness,
so they are related to the emission spectrum of the dust particles
located in the complex.
We have seen in
Planck HFI Core Team 2011a) that the calibration errors
are estimated to 13.5% at 3000GHz (100µm), 7% at 857
and 545GHz, and 2% at 353 and 143GHz. These numbers
Sect.2.1(Table1, from
6

Page 7

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.5. Same as Fig1 for the fit residuals. The last image is the CO J = 1 → 0 integrated emission from Dame et al. (2001) (units:
Kkms−1).
7

Page 8

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.6. Same as Fig1 for the relative fit residuals (units: percentage).
8

Page 9

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.7. Temperature and spectral index maps.
Fig.8. Temperatureand spectral indexhistograms.Black: all pixels. Green:pixels without detected12CO emission. Red: pixels with
detected12CO emission but no detected13CO emission. Blue: pixels with detected13CO emission.
translate to a systematic error of about 5% and 4% on the 353
and 143GHz brightnesses computed from the fit of the five
bands, respectively. We conclude in this early analysis that
the negative residuals at 353GHz (with a median amplitude
about −7%) likely indicate a decrease of the value of β from
the 3000–545GHz spectral range (around the peak) to lower
frequencies due to a temperature distribution along the lines of
sight. On the other hand, the positive residuals at 143GHz (with
a median amplitude about +13%) suggest a flattening of the
emission spectra at low frequencies.
3.5.2. At 217 and 100GHz
As shown on Fig.5 there is a striking spatial correlationbetween
the residual maps at 100GHz and 217GHz, and the map of the
integrated emission of12CO J = 1 → 0 emission line, which
confirms that 100GHz and 217GHz residuals are from contam-
ination by CO molecular lines (mainly12CO, but also13CO and
other isotopes and molecules in the densest regions). However,
we have seen above that the measured dust spectra are more
complex than a single modified black body from 3000GHz to
100GHz, so the residuals computed at 100GHz and 217GHz in
this early analysis and shown on Fig.5 are only indicative.
4. Analysis of the temperature and spectral index
maps.
4.1. Temperature map
The temperature map is shown in Fig.7. The black regions are
artifacts: they correspond to low values of the temperature (be-
low 12K) due to statistical noise and CIBA in the faint regions
(with I100 µm< 1MJysr−1, as illustrated also in our simulations
presented in Fig.A.2). Excluding these regions, and also some
residual stripping in the faintest regions with amplitudes around
0.15 K, most of the variations seen on the temperature map are
realsince theiramplitudeis higherthanthe noisecomputedfrom
our simulations (about 0.1–1K for I100 µm = 10 − 1MJysr−1,
from FigA.2).
At least three regions with different temperature distribu-
tions can be identified in the temperature map (Fig.7) and its
histogram (Fig.8):
– theouterpartsofthemolecularcloud(withnodetected12CO
emission), with temperatures ∼ 16–17.5K;
– the molecular cloud with detected12CO emission but no de-
tected13CO emission, with temperatures ∼ 15–17.K;
– the densest parts of the molecular cloud with detected13CO
emission, coinciding with the well-known dense filaments,
with temperatures ∼ 13–16K.
9

Page 10

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.9. Correlation between the spectral index and the temper-
ature. Upper panel: for all pixels. Lower panel: for pixels with
I100 µm> 10MJysr−1.
Most of the differencesbetween the IRAS map at 100µm and the
HFI maps (Fig.1) are due to temperature variations. Except in
diffuse regions with uniformilluminationand constant dust tem-
perature,this demonstratesthat IRAS maps at 100µm used alone
cannot properly probe the gas column density. Comparable tem-
perature variations have also been found by Flagey et al. (2009)
in the central region of our field (average temperature about
14.5K with a dispersion of 1K) by combining Spitzer 160µm
andIRAS100µm mapsandassumingaconstantvalueofβ equal
to 2.
4.2. Spectral index map
The spectral index presents a symmetric distribution (Fig.8)
with average and median values both equal to 1.78 and a stan-
dard deviation σβ= 0.08. The standard deviation due to statisti-
cal noise and CIBA estimated from our simulations is in a range
0.025–0.25for I100 µm= 10−1MJysr−1(FigA.2). Moreoverwe
can see in Fig.7 and more explicitly in the first panel of Fig.9,
that there is a some anti-correlationbetween T andβ. The higher
values of β (> 1.8) are found in the coldest (about 14K) struc-
tures.
We have seen in AppendixA, and it has also been discussed
in detail by Shetty et al. (2009a,b), that the instrumental errors
always produce intrinsic anti-correlation between T and β. A
significant fraction of the anti-correlation seen in Fig.9 could
be due to noise. However, high values of β generally corre-
spond to bright regions, as illustrated in the second panel of
Fig.9 which shows the T −β correlation diagram for pixels with
I100 µm> 10MJysr−1: the T − β anti-correlation is still visible,
which shows that it cannot be due to statistical noise and CIBA.
Previous observations of thermal dust emission at FIR
to millimeter wavelengths, in a variety of galactic re-
gions, indicate an anti-correlation between the fitted val-
ues of the spectral index β and the temperature for T
30K, from Pronaos data (Ristorcelli et al. 1998b; Bernard et al.
1999; Stepnik et al. 2003; Dupac et al. 2001, 2002, 2003),
Archeops data (D´ esert et al. 2008b) and Herschel data (e.g.,
Anderson et al. 2010; Paradis et al. 2010). In the general case,
there is a combination of dust temperatures in the line of sight,
or differentgraintypes with differentoptical properties.We have
seen in Sect.3.5 that the real shape of the measured spectra from
3000 to 100GHz is more complex than a single modified black
body. Thereforewe do not conclude from Fig.9 and in this early
analysis that a T-β anti-correlation is an intrinsic emitting prop-
erty of the thermal dust particles, for T = 13 to19K.
<∼
4.3. Comparison with other Planck results and dust models
As shown in Planck Collaboration (2011t), both FIRAS and
HFI+IRAS spectra of the local diffuse ISM can be well-fit by a
modified blackbody with T = 17.9K and β = 1.8. Morever, me-
dian values of T = 17.7K and β = 1.8 are also found at b > 10◦
in the all sky analysis using the 3000, 857, and 545GHz bands
(Planck Collaboration 2011o). These two results are fully com-
patible with our distribution of spectral indexes (Fig.8) centered
on 1.78 with a standard deviation of 0.08. We have also seen in
Sect.3.4 that the systematic error in β is estimated to 0.07.
We compare here our results to the dust models of
Draine & Li (2007) and Compi` egne et al. (2011), computed
with the DustEM tool (http://www.ias.u-psud.fr/DUSTEM). As
far as the properties of thermal dust are concerned, silicates are
the same in both models whereas the carbon grains are taken
to be graphite (Draine & Li 2007) or hydrogenated amorphous
carbon (Compi` egne et al. 2011). We first compute dust emis-
sion models for all grain types in the diffuse ISM, i.e., heated
by the standard interstellar radiation field (ISRF) of Mathis et al.
(1983). Next, we generate simulated data points by taking the
flux densities of our model spectra in the bands at 100µm,
857, 545, 353 and 143GHz. We then apply our fitting proce-
dure to these simulated band flux densities. Fitting the model
of Draine & Li (2007) yields T ≃ 19.6 K and β ≃ 1.67. The
latter value is intermediate between that obtained from fits for
silicates (1.57) and graphite (1.93) alone. Fitting the model of
Compi` egne et al. (2011) yields T ≃ 20.5 K and β ≃ 1.52 (see
Fig.10). Individual fits for silicates and amorphous carbon give
similar values of β. We note that the largest residuals from a sin-
gle modified black-body are found between 150 and 250µm, in
the spectral gap between IRAS and HFI (Fig.10).
For both the Draine & Li (2007) and Compi` egne et al.
(2011) models, the fitted values of β are slightly below the cen-
tral value found in the Taurus molecular cloud (1.78, with a
systematical error of 0.07). However, it is worth noting that, in
order to account for the FIRAS spectrum of the diffuse ISM,
10

Page 11

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.11. Optical depth maps τλ0map, with λ0= 250µm. Left panel: total optical depth derived from the pixel by pixel fit of the HFI
and Planck data. Right panel : Optical depth map of the molecular phase alone (the optical depth associated to the atomic phase is
removed, see Sect.5.3).
Fig.10.Leftpanel:FitoftheDustEMmodelofCompi` egne et al.
(2011) for the diffuse ISM heated by the standard interstellar
radiation field (ISRF) of Mathis et al. (1983) (Black solid line :
model, Squares: model in the photometricbands at 100µm, 857,
545 and 143GHz, Red solid line: fitted spectrum). Right panel:
Relative residuals of the fit (solid line: for the continuousmodel,
Triangles: for the model in the photometric bands). The dashed
line shows the relative residuals of the fit for the Draine & Li
(2007) model.The increase of the residuals below 100µm is due
to the contribution of transiently heated small particles.
Li & Draine (2001) decreased β from 2.1 to 1.6 in the ab-
sorption efficiency of silicates at wavelengths above 250µm.
If we do not apply this correction and simply extrapolate the
absorption efficiency of silicates as a single power law with
β = 2.1 for λ ≥ 30 µm, our fit provides T ≃ 19.4K and
β ≃ 1.73 (18.2K and 1.97) for the model of Compi` egne et al.
(2011) (Draine & Li 2007) respectively. The value of β ob-
tained with the Compi` egne et al. (2011) model is then com-
patible with the observations. Finally, the dust temperature de-
rived from the Compi` egne et al. (2011) model is significantly
higher than the value of 17.9K found by Planck Collaboration
(2011t) in diffuse clouds: this is because the amorphous carbon
of Compi` egne et al. (2011) efficiently absorbs the ISRF in the
near-IR, between 1 and 10µm, conversely to graphite or sili-
cates.
Thisfirst comparisonofthePlanckdataandrecentdustmod-
els shows that the emission of thermal dust can be representedat
a first by a single modified black body with a constant spectral
index β.
5. Optical depth per unit column density
We have seen in the previous section that the spectral cover-
age of Planck/HFI allows the measurement of the temperature
and of the spectral index β for each line of sight. The third ad-
justable parameteris the opticaldepthτ. To allow directcompar-
ison of optical depth results with the other Planck Early Results
papers, we fitted the data using only the bands at 3000, 857,
and 545GHz, holding β fixed at 1.8. Compared to fits with five
bands (including 353 and 143GHz), the fitted optical depths do
not change by more than about 10%.
For the first time we have an unbiased map of the optical
depth of thermal dust in a molecular complex from the most dif-
fuseregionstothedensestparts.TheopticaldepthmapinFig.11
has a dynamic range better than 100. The statistical error and
the systematic noise in τ are estimated to be about 1–10% and
12%, respectively, using the method described in AppendixA
(but with a fixed value of β = 1.8 and considering fitting of only
the three bands at 3000, 857, 545GHz).
11

Page 12

Planck Collaboration: Thermal dust in nearby molecular clouds
5.1. Independent tracers of the column density
5.1.1. Atomic phase
The column density of the atomic gas is traced using the Hi
data at 21cm taken with the Leiden/Dwingeloo 25-m telescope
with an angular resolution of 36′(Hartmann & Burton 1997). In
the optically thin hypothesis, the velocity-integrated emission
can be converted to column density using the classical factor
1K−1km−1s = 1.81 × 1018cm−2. However, the Hi emission is
subject to self absorption in the cold neutral medium (CNM),
and NHcan be underestimated. An exact calculation requires to
know the density profiles of the CNM components along each
line of sight. This has been done by Heiles & Troland (2003)
by measuring the emission/absorption of the 21cm line against
a number of continuum sources. Correction factors around 1.25
are found in the Taurus/Perseus region. In our case, the precise
correction, pixel by pixel for each line of sight is not possi-
ble. We have tested the simple correction method discussed in
Planck Collaboration(2011t) and whichassumes a constantspin
temperatureTS, whichis notreallyjustified since TSvaries from
warm neutral media (WNM) to CNM. Factors of about 1.1-1.5
are obtained for TS = 100K. In this early analysis we decide to
apply a constant multiplicative factor of 1.25, with a conserva-
tive uncertainty of 20%, to derive from the Hi data the column
density map for the atomic phase (Fig.2). In any case, we have
checked that a different choice for the correction method does
not affect the quantitative analysis of the optical depth per col-
umn density in the molecular phase (see below).
The Taurus molecular cloud is 15◦from the galactic plane,
and contains large scale emission associated with background
atomic gas with LSR velocities from −50kms−1to 0kms−1.
This explains the North-South galactic gradient in the HFI and
IRAS maps (Fig.1), and also in the optical depth map (Fig.11).
An East-West gradient due to a filamentary structure which ex-
tends away from the Galactic plane and which crosses the east-
ern part of Taurus is also detected, with velocity in the same
range as the velocity in the12CO J = 1 → 0 emission line, i.e.
from ∼ 0kms−1to ∼ 15kms−1(Narayanan et al. 2008).
5.1.2. Molecular phase
The column density associated with the molecular regions
can be traced with the NIR extinction map of Pineda et al.
(2010) (Fig.2), which gives the extinction due to dust associ-
ated with the non-atomic component. Special care is taken by
Pineda et al. (2010) to remove the overall extinction associated
withHi locatedbetweenthebackgroundstars usedandthe Earth
(0.3mag),andalsotheextinctionassociatedwiththewidespread
Hi emission (0.12mag).
The J = 1 → 0 line of12CO is a common tracer of the
molecular phase. However this line is sensitive to variations
in abundance (depletion in densest regions, formation, destruc-
tion), excitation conditions, and radiative transfer effects (the
line is generally not optically thin), which explains the differ-
ence between maps of integrated12CO(J = 1 → 0) emission
(Dame et al. 2001; Fig.2) and our optical depth map (Fig.11).
A detailed comparison between the NIR extinction and the inte-
grated emission of the12CO(J = 1 → 0) and13CO(J = 1 → 0)
lines has been presented by Pineda et al. (2010). In this paper,
our strategy is to use the NIR extinction map of Pineda et al.
(2010) as a quantitative tracer of the column density of the
molecular phase, and to use the12CO(J = 1 → 0) integrated
emission map of Dame et al. (2001), which covers the whole
Fig.12.Opticaldepthasafunctionoftheatomiccolumndensity,
for pixels with no detected CO emission. The red line shows the
result of the linear regression: τ250= 1.05 × 10−25× NH+ 4.3 ×
10−5.
complex, to define regions containing (or not) molecular mate-
rial.
5.2. Optical depth per unit column density in the atomic
medium
To measure τ/NHin the atomic phase, we use the column den-
sity map derived from Hi data presented on Fig.2. We subtract
from this map the averaged column density computed within
the reference window (see Sect.3.1). Then we smooth our op-
tical depth map (Fig.11) at the angular resolution of the Hi data
(FWHM 36′) assuming Gaussian beams, and select all pixels
with no detected CO emission smoothed to the Hi resolution
(WCO< 0.5Kkms−1). With this criterion we exclude the pixels
containing molecular emission traced with the12CO J = 1 → 0
line.
The optical depth τ as a function of the atomic column den-
sity for the selected pixels is shown in Fig.12. The relationship
presentssomedispersionwhichmaybedueto theuncertaintyon
the Hi opacity correction (estimated to 20%, see Sect.5.1.1), to
the statistical noise on the computed values of τ (about 1-10%,
see above),and also to the contributionof some molecularmate-
rial not detected on the12CO survey. However, the relationship
appearslinearoverthefullrangeofcolumndensityfrom1×1020
cm−2to 4 × 1021cm−2with a slope of τ/NH= 1.1 ± 0.2 × 10−25
cm2. The uncertainty of τ/NHtakes into account the uncertainty
in the opacity correction of Hi data, the statistical noise and the
systematic error in the optical depth map.
We conclude that the value of τ/NHcomputed in the atomic
medium in the Taurus region appears identical to the standard
value for the diffuse ISM, 1×10−25cm2(Boulanger et al. 1996).
Actually, we have no Hi data at the same angular resolution
as HFI in order to analyze the spatial variation of τ/NHin the
atomic medium. Finally, the τ-NHlinear relationship (Fig.12)
presents a faint non-zeropositiveresidual τ(NH= 0) ≃ 4×10−5,
whichmaybeduetoaminorcontributionofdustassociatedwith
the warm ionized medium or to the zodiacal emission from in-
terplanetary dust particles.
12

Page 13

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.13. Map of the optical depth per unit column density, τ/NH,
in the molecular phase (for W (CO) > 3Kkms−1).
5.3. Optical depth per unit column density in the molecular
phase
Inordertomeasureτ/NHinthemolecularphase,weneedtosub-
tractfromtheopticaldepthmaptheopticaldepthassociatedwith
the atomic phase. We have no Hi data taken with the same an-
gular resolution as Planck/HFI. However, the local densities are
higher in the molecular phase than in the atomic one, so we can
consider that, in lines of sight containing detected CO emission,
the small scale spatial fluctuations in the optical depth maps are
dominated by density fluctuations in the molecular phase. Thus
first we compute the optical depth map of the atomic medium
alone τHIby multiplying the Hi column density by the value of
τ/NHfound in the previous section. Then we subtract from the
optical depth map the τHImap in order to obtain the “molecular
phase” optical depth map (Fig.11). We see that the north-south
and east-west gradients detectable in the total optical depth map
have disappeared, as expected. Finally, we obtain the map of
τ/NHin the molecular phase shown on Fig.13 by dividing the
molecular phase optical depth map (Fig. 11) by the column den-
sity map computed from the NIR extinction map of Pineda et al.
(2010) (Fig.2).
5.4. Discussion
5.4.1. Previous observations
The possibility for a higher value τ/NH in dense clouds
than in the diffuse ISM has been a long-standing issue
(Ossenkopf & Henning1994;Henning et al.1995).Thiswasnot
unexpected, as dust grains must go through coagulation pro-
cesses in dense environments, which tends to increase τ/NH
(e.g., Ossenkopf & Henning 1994; Stognienko et al. 1995). Low
grain temperatures (∼ 13K) have been observed also with the
PRONAOS balloon in relatively diffuse clouds, the translucent
Polaris Flare (Bernard et al. 1999) and one molecular filament
(for A>∼2) in the Taurus molecular cloud (Stepnik et al. 2003).
As demonstrated by the authors, such a low temperature can-
not be explained by the effect of extinction alone: one need to
increase the value of τ/NH(with NHderived from the NIR ex-
tinction), by a factor of about 3 compared to the standard value
for the diffuse ISM of 1 × 10−25cm2.
An increase of τ/NH in the FIR by a factor ≥ 1.5–4 (al-
ways with NH derived from the NIR extinction) has been de-
tected from ISOPHOT observations of several high latitude
translucent clouds (Cambr´ esy et al. 2001; Burgo et al. 2003;
Ridderstad et al. 2006; Kiss et al. 2006; Lehtinen et al. 2007)
and TMC-2 (Burgo & Laureijs 2005), and by Spitzer observa-
tions of the Perseus molecular cloud (Schnee et al. 2008) and of
the Taurus molecular cloud (Flagey et al. 2009). As the decrease
in temperature is generally observed to be associated with a de-
crease of the 60µm over 100µm intensity ratio, which traces the
abundance of small grains relative to that of big grains, coagu-
lation has often been invoked to explain this emissivity increase
(Bernard et al. 1999; Stepnik et al. 2003; Cambr´ esy et al. 2005).
However, the increase of τ/NHwith increasing column den-
sity is not systematically observed. No excess is detected in
the Corona Australis molecular cloud from Spitzer/MIPS or
APEX/Laboca data using also the NIR extinction as a tracer
of the column density (Juvela et al. 2009). Finally, contradic-
tory results have also been obtained using the12CO(J = 1 →
0) emission line to trace the column density. For instance,
Roman-Duval et al. (2010) found that the deviations between
FIR emission, measured by Herschel/SPIRE and Spitzer/MIPS,
and gas surface density are more probably due to H2envelopes
not traced by CO and therefore not accounted in the column
density, than by gas-to-dust ratio or τ/NHvariations. On large
scales, Paradis et al. (2009) conclude from DIRBE, Archeops,
and WMAP data that the dust that gives an excess of τ/NHin
the submm may recover its diffuse ISM value in the millimeter.
This contradicts current scenarios of dust coagulation,for which
a constant emissivity increase over the whole FIR-submm wave-
length range is predicted for aggregates of astronomical silicate
grains. Dust optical constants in the FIR-submillimeter range,
however, are not well constrained by laboratory studies.
In any case, instruments before Planck never had the angular
resolution, spectral coverage, sensitivity, and mapping capabil-
ity to perform full and unbiased mapping of the thermal dust
emission within individual complexes, from the most diffuse re-
gions to the densest parts. The key observational questions are:
where, and on which angular scale do the dust properties evolve
in the ISM. This is the first step in understanding the physical
processes that regulate the optical properties of thermal dust.
5.4.2. Planck results
We see on Fig.13, and on the first panel of Fig.14, that in the
molecular phase τ/NH systematically increases from 1 to 2 ×
10−25cm2for increasing NHfrom 1 to 3 × 1021cm−2(derived
from the NIR extinction), or Avfrom 0.5 to 1.5. For Av> 1.5,
τ/NHis about 2 × 10−25cm2. It is interesting to note that the
same value of τ/NH was found by Flagey et al. (2009) in the
central region of the Taurus molecular cloud from IRAS 100µm
and Spitzer 160µm maps.
The low values of τ/NH(0.5 − 1 × 10−25cm2) corresponds
to regions with relatively low column densities (AV< 1) and are
affected by large errors mainly due to the noise in the extinction
map (about 0.2mag at low extinctions, as seen in Sect.2.2).
The increase of τ/NHfrom 1 × 10−25cm2to 2 × 10−25cm2
obviously tends to decrease the equilibrium temperature of the
dust particles. Comparing the map of τ/NH in the molecular
phase (Fig.13) with the temperature map (Fig.7), we see an
13

Page 14

Planck Collaboration: Thermal dust in nearby molecular clouds
Fig.14. Optical depth per unit column density τ/NHin the molecular phase (for W (CO) > 3Kkms−1), as a function of the column
density NHderived from the 2MASS extinction, and as a function of the velocity integrated emission within the13CO (J = 1 → 0)
and12CO (J = 1 → 0) lines.
obvious anti-correlation. Fig.15 shows that the temperature de-
creases from ∼ 16K to ∼ 14K when τ/NHincreases from ∼ 1
to ∼ 2 × 10−25cm2. For constant intensity of the incident radia-
tion field the temperatureof the dust particles should follows the
relationship Tdust α (τ/NH)−1/(4+β), which is is over-plotted on
Fig.15. We see that the variations of τ/NHstrongly impact the
dust temperature.
The observed saturation for τ/NH ∼ 2 × 10−25cm2may be
due to different effects :
1. The intensity of the incident radiative obviously decreases
in dense regions, so that the equilibrium temperature of the
dust particles decreases for a given value of τ/NH. This can
explain the points located on Fig.15 below the line corre-
spondingtoaconstantintensityoftheincidentradiationfield
and with τ/NH∼ 2×10−25cm2andT = 14−15K . Radiative
transfereffects must be consideredfora completeanalysis of
the spatial variationsof thedust temperaturewithin the dens-
est regions, which is beyond the scope of this paper.
2. As there is no embeddedheating star, the distribution of dust
temperatures along a “cold” line of sight, with a low value
of the measured temperature, should be generally broader
than along lines of sight with higher measured temperatures.
Moreover the measured temperatures for cold lines of sight
are always warmer than the average temperature, so the val-
ues of τ/NH for cold line of sight may underestimate the
average values for dust particles (see also Cambr´ esy et al.
2001; Lehtinen et al. 2007; Schnee et al. 2008).2
3. As seen in Sect.2.2, the NIR extinction map is converted
into column density using the standard ratio of selective to
total extinction RV = 3.1 corresponding to the diffuse ISM.
However, RVis expected to increase at large densities (with
typical extinction Av > 3), up to about 4.5 due to grain
growth by accretion and coagulation (Whittet et al. 2001).
This increase lowers the column densities derived from the
extinction. Therefore the computed values of τ/NHcould be
systematically underestimated in dense regions.
Finally, the increase of τ/NH is also seen on the τ/NH–
W(13CO) correlation diagram (second panel of Fig.13), with
2We can also conclude that the inverse correlation of τ/NHwith T is
robust against the unavoidable combination of dust temperature on the
line of sight, and reveals a real anti-correlation of τ/NHand T for the
dust particles.
Fig.15. Temperature as a function of the optical depth per unit
column density τ/NH in the molecular phase (for W (CO) >
3Kkms−1). Solid line: Tdust
which corresponds to a constant intensity of the incident radi-
ation field. The low values of τ/NH(0.5 − 1 × 10−25cm2) corre-
sponds to regions with relatively low column densities (AV< 1)
and are affected by large errors mainly due to the noise in the
extinction map.
α (τ/NH)−1/(4+β)relationship,
a comparable pattern as the τ/NH–NH since the13CO inten-
sity is very sensitive to the density. On the other hand, the
τ/NH− W(12CO) correlation diagram (third panel of Fig.13)
shows that τ/NHlinearly increases with W(12CO). This very dif-
ferent behavior is due to the fact that the measured intensity of
the12CO J = 1 → 0 line strongly depends on the competition
between formation and destruction, on excitation conditions, on
the depletion and on radiative transfer effects (e.g., Pineda et al.
(2010), Liszt et al. (2010)).
6. Conclusions
Combined with IRAS maps at 100µm (3000GHz), HFI maps
at 857, 545, 353, and 143GHz allow the precise measurement
of the emission spectrum of thermal dust with unprecedented
sensitivity, from the faintest atomic regions to the densest parts
of the molecular cloud.
While the dust particles located along the lines of sight have
no reason to be at the same temperature and may have different
14

Page 15

Planck Collaboration: Thermal dust in nearby molecular clouds
optical properties, we find that, for each pixel of the map, the
measured spectra are reasonably fitted with one single modified
black-body, which gives one temperature, one spectral index,
and one optical depth per pixel. However, the modified black-
body can be slightly broadened around the peak of the spectrum
because of the range of dust temperature along the line of sight,
which explains the negative residuals found at 353GHz (around
−7%). On the other hand, the positive residuals at 143GHz
(around +13%) could be attributed to a slight decrease of the
spectral index at low frequency.
The temperature map we derive from the pixel per pixel fits
provides a spectacular description of the cooling of the thermal
dust across the whole complex from about 17.5K to about 13K.
These variations can be due to variations of both the excitation
conditions and the optical properties of the dust particles.
The spectral index β presents limited spatial variations. The
distribution is centered on 1.78, with systematic error estimated
to be 0.07 and standard deviation 0.08. Slightly higher values
(> 1.8) are found in the coldest (about 14K) structures, but in
this early analysis they cannot be attributed to intrinsic prop-
erties in the emission spectrum of thermal dust particles. We
have checked that the synthetic spectra computed with the post-
Spitzer dust models of Draine & Li (2007) and Compi` egne et al.
(2011) have almost identical values of their spectral indexes.
We also derivea optical depthmap with a veryhighdynamic
range. Using the NIR extinction as an independant tracer of the
column density, we report a systematic and sharp increase of the
measured optical depth per unit column density in the molecu-
lar phase for Av > 1, by a factor of about 2 compared to the
value found in the diffuse atomic ISM. The increase of the op-
tical depth per unit column density for the dust particles could
be even higher in dense regions, due to radiative transfer effects,
the presence of a temperaturedistribution along the line of sight,
and the increase of RVin dense regions.
Finally, the optical depth map reveals the spatial distribution
ofthecolumndensityofthe molecularcomplexfromthedensest
molecular regions to the faint diffuse regions.
Appendix A: Error propagation - Simulation of the
fitting
A.1. Principle of the simulations
We have performed Monte-Carlo simulations in order to un-
derstand the propagation of the calibration errors, the statistical
noise and the CIBA in the determination of the temperature T,
thespectralindexβ,andtheopticaldepthτfromthefitofthefive
bandsat 3000GHz (100µm),857,545,353,and143GHz with a
single modified black body (Sect.3.3). In practice, we computed
1000 synthetic spectra with the same values of the temperature
and β (T = 17K and β =1.8) at the central frequency of the
five bands. We take a fixed value of the optical depth (τ = 1) to
study the calibration errors, and fixed values of the brightness at
100µm to study statistical noise and CIBA. Then for each band
we add some error randomnly computed using a Gaussian dis-
tribution with standard deviationsσ (and mean of 0) equal to the
assumed noise. Finally, we apply our fitting procedure, and ob-
tain for each simulation a set of 1000 values of T,β, and τ. For
the different simulations we have conducted, the standard devia-
tions obtained for each parameters are given on TableA.1, while
Fig.A.1 shows the correlations between the three parameters.
A.2. Calibration errors
In order to study the propagation of calibration errors, we take
standard deviations of the simulated noise equal to the calibra-
tion errors presented in Sect.2.1. For the two HFI bands at 545
and 857GHz, we consider that the calibration errors are fully
correlated between the two bands, so in the simulation we take
the same realizationof the simulatedGaussian noise.At the con-
trary, the calibration error at 143GHz is not correlated with the
calibration error of the two high frequency bands.
The fitted values of T and β computed for the 1000 synthetic
spectra are presented in Fig.A.1 (black symbols). We observe
the classical anti-correlation intrinsic to the noise identified by
several authors (e.g., Shetty et al. 2009b). The optical depth τ is
also anti-correlatedwith T dueto the temperaturedependanceof
the Planck function. Finally τ is correlated with β, as expected
since both T–β and T–τ are anti-correlated. To first order, we
can consider that for each band the calibration error is constant
on the maps, so the errors on T,β, and τ (Fig.A.1 and TableA.1)
aresystematic,affectingsystematically(inthesamedirectionfor
all pixels) the three parameters derived from the fits. Obviously
these calculations are preliminary, since other systematic effects
are neglected, but they give for this early analysis an estimate on
the systematic errors on the three parameters T,β, and τ which
are derived from the data.
A.3. Statistical errors and CIB anisotropies
The statistical noise on the data is considered to be non-
correlated both spatially and spectrally. We take standard devi-
ations of the simulated noise equal to the statistical noise used
for the pixel per pixel fitting of the data at 100µm, 857, 545,
and 143GHz presented in Sect.2. We also take into account
the noise due to the CIBA, using the standard deviations mea-
sured by Planck/HFI (Planck Collaboration 2011n) and IRAS at
100µm (Penin et al. 2011).
The correlation diagrams of Fig.A.1 and the standard devia-
tions given in TableA.1 show that the effects of the statistical
noise and CIBA have a smaller amplitude than the effects of
the systematic errors, but they depend on the absolute bright-
ness, as illustrated in Fig.A.2. It is interesting to note that above
I100 µm= 1MJysr−1, the fitted values of T, β, and τ are not bi-
ased, since ?T? ≃ 17K, ?β? ≃ 1.8, and ?τ? = 1 (relative value).
On the contrary, below I100 µm= 1MJysr−1, we see that ?T? de-
creases, while ?β? and ?τ? increase. Therefore we consider that
pixels with I100 µm< 1MJysr−1cannot be used for any quanti-
tive analysis of the fitted parameters.
Acknowledgements. A description of the Planck Collaboration and a list of
its members, indicating which technical or scientific activities they have been
involved in, can be found at http://www.rssd.esa.int/Planck. We thank Gopal
Narayanan and Jorge Pineda for providing FCRAO and NIR extinction data.
References
Abergel, A., Arab, H., Compi` egne, M., et al. 2010, A&A, 518, L96+
Agladze, N. I., Sievers, A. J., Jones, S. A., Burlitch, J. M., & Beckwith, S. V. W.
1996, ApJ, 462, 1026
Anderson, L. D., Zavagno, A., Rod´ on, J. A., et al. 2010, A&A, 518, L99+
Andr´ e, P., Men’shchikov, A., Bontemps, S., et al. 2010, A&A, 518, L102+
Bernard, J. P., Abergel, A., Ristorcelli, I., et al. 1999, A&A, 347, 640
Bernard, J.-P., Abergel, A., Ristorcelli, I., et al. 1999, A&A, 347, 640
Bersanelli, M., Mandolesi, N., Butler, R. C., et al. 2010, A&A, 520, A4+
Boulanger, F., Abergel, A., Bernard, J., et al. 1996, A&A, 312, 256
Burgo, C. D. & Laureijs, R. J. 2005, MNRAS, 360, 901
Burgo, C. D., Laureijs, R. J.,´Abrah´ am, P., & Kiss, C. 2003, MNRAS, 346, 403
Cambr´ esy, L., Boulanger, F., Lagache, G., & Stepnik, B. 2001, A&A, 375, 999
15