J/MNRAS/508/2964 Study of clumps, cores and hubs with ALMA (Anderson+, 2021)
An ALMA study of hub-filament systems - I. On the clump mass concentration
within the most massive cores.
Anderson M., Peretto N., Ragan S.E., Rigby A.J., Avison A.,
Duarte-Cabral A., Fuller G.A., Shirley Y.L., Traficante A., Williams G.M.
<Mon. Not. R. Astron. Soc. 508, 2964-2978 (2021)>
=2021MNRAS.508.2964A 2021MNRAS.508.2964A (SIMBAD/NED BibCode)
ADC_Keywords: Star forming region ; Molecular clouds ; Positional data ;
Infrared ; Radio sources ; Millimetric/submm sources ;
Photometry ; Photometry, classification
Keywords: methods: observational - techniques: interferometric -
stars: formation - stars: massive - ISM: clouds - submillimetre: ISM
Abstract:
The physical processes behind the transfer of mass from parsec-scale
clumps to massive star-forming cores remain elusive. We investigate
the relation between the clump morphology and the mass fraction that
ends up in its most massive core (MMC) as a function of infrared
brightness, i.e. a clump evolutionary tracer. Using Atacama Large
Millimeter/submillimeter Array (ALMA) 12 m and Atacama Compact Array,
we surveyed six infrared dark hubs in 2.9 mm continuum at ∼3 arcsec
resolution. To put our sample into context, we also re-analysed
published ALMA data from a sample of 29 high-mass surface density
ATLASGAL sources. We characterize the size, mass, morphology, and
infrared brightness of the clumps using Herschel and Spitzer data.
Within the six newly observed hubs, we identify 67 cores, and find
that the MMCs have masses between 15 and 911 M☉ within a radius
of 0.018-0.156 pc. The MMC of each hub contains 3-24 per cent of the
clump mass (fMMC), becoming 5-36 per cent once core masses are
normalized to the median core radius. Across the 35 clumps, we find no
significant difference in the median fMMC values of hub and non-hub
systems, likely the consequence of a sample bias. However, we find
that fMMC is ∼7.9 times larger for infrared dark clumps compared to
infrared bright ones. This factor increases up to ∼14.5 when comparing
our sample of six infrared dark hubs to infrared bright clumps. We
speculate that hub-filament systems efficiently concentrate mass
within their MMC early on during its evolution. As clumps evolve, they
grow in mass, but such growth does not lead to the formation of more
massive MMCs.
Description:
Here, we focus on a specific morphological category of clumps:
hub-filamentary systems (HFS; Myers P.C. 2009ApJ...700.1609M 2009ApJ...700.1609M). Hubs
are small networks of converging interstellar filaments, at the centre
of which active star formation is often observed (e.g. Liu et al.
2012ApJ...756...10L 2012ApJ...756...10L; Kirk et al. 2013ApJ...766..115K 2013ApJ...766..115K; Peretto et al.
2013A&A...555A.112P 2013A&A...555A.112P, Peretto et al. 2014A&A...561A..83P 2014A&A...561A..83P,
Cat. J/A+A/561/A83; Trevino-Morales et al. 2019A&A...629A..81T 2019A&A...629A..81T). They
are found in all types of region, from low-mass star-forming clouds
(e.g. Myers P.C. 2009ApJ...700.1609M 2009ApJ...700.1609M; Kirk et al.
2013ApJ...766..115K 2013ApJ...766..115K), to high-mass star-forming regions (e.g. Peretto
et al. 2014A&A...561A..83P 2014A&A...561A..83P,; Schworer et al. 2019A&A...628A...6S 2019A&A...628A...6S), and
have even been observed in our closest neighbouring galaxy (Fukui et
al. 2019ApJ...886...14F 2019ApJ...886...14F; Tokuda et al. 2019ApJ...886...15T 2019ApJ...886...15T).
In this study, we aim at constraining the efficiency of hubs at
concentrating their mass into their MMC, and this for a large range of
clump masses. The end goal is to disentangle the effects of clump mass
to those related to clump morphology. We do this by analysing new
Atacama Large Millimeter/submillimeter Array (ALMA band 3) observations of a
sample of hubs. We achieve an angular resolution of ∼2.8-4.7 arcsec,
which at the distance of the targets corresponds to a linear resolution
of 0.029-0.073 pc. This is at least a factor of two smaller than the Jeans
length (which ranges between 0.10 and 0.21 pc). The data were
reduced and calibrated using the same casa (McMullin et al.
2007ASPC..376..127M 2007ASPC..376..127M) versions as used by the ALMA pipeline, using the
standard pipeline scripts. (Please see the section 1 Introduction and
2.2 ALMA observations).
For the purpose of this study, we selected six infrared dark clouds
(IRDCs), all part of the Peretto & Fuller (2009A&A...505..405P 2009A&A...505..405P, Cat.
J/A+A/505/405) catalogue these six clouds have been selected to
exhibit a well-defined hub morphology seen in extinction at 8 µm,
with an easily identified filament convergence point. They all have
high extinction contrast against a relatively uniform mid-infrared
background. They have been selected so that their distances lie within
a narrow range, i.e. from 2 to 3.2 kpc, so that their properties can
easily be compared to each other. Finally, they have been chosen so
that they cover a large range of masses, from a few hundred to a few
thousand solar masses, to try to evaluate the impact of the hub
morphology on core formation independently of the clump mass, (Please
see the section 2.1 sample selection).
In order to extract cores properties from our 6 IRDCs, we complete our
data with available Spitzer GLIMPSE 8 µm data (Churchwell et al.
2009PASP..121..213C 2009PASP..121..213C) and WISE 12 µm data (Wright et al.
2010AJ....140.1868W 2010AJ....140.1868W), at an angular resolution of ∼2.4 and ∼6.5 arcsec,
respectively. We use temperature and column density maps presented in
Peretto et al. (2016A&A...590A..72P 2016A&A...590A..72P, Cat. J/A+A/590/A72) at a
resolution of ∼18 arcsec, which were constructed from 160 and 250
µm data from the Herschel Hi-GAL (Molinari et al.
2010A&A...518L.100M 2010A&A...518L.100M). Finally, we also make use of the Molinari et al.
(2016A&A...591A.149M 2016A&A...591A.149M, Cat. J/A+A/591/A149) 70 µm compact source
catalogue, (i.e see the section 2.3 Spitzer, WISE, and Herschel data).
Then, we proceed core extraction as explained in the section 3.1, we
use a dendrogram-based method astrodendro, a python package based on
the Rosolowsky et al. (2008ApJ...679.1338R 2008ApJ...679.1338R) implementation of
dendrograms to analyse astronomical data. Core candidates with at
least npix,min pixels with an SNR ≥ 3 are classed as detections.
Extracted structures that do not satisfy this condition are discarded.
After applying this criteria we obtain a set of 67 cores as showed in
the the table a2021.dat, (please refers to the section 3.2 Core sizes
and masses to see definitions of cores properties).
Finally, we compare our hub sample to those from a less biased
Galactic plane population of clumps, we use the Csengeri et al.
(2017A&A...600L..10C 2017A&A...600L..10C, Cat. J/A+A/600/L10) sample of high-mass ATLASGAL
sources observed with ALMA and logically we produce the same analysis
as for our sample to extract cores and their properties. Results are
available in the table cores.dat, (i.e section 4.1 Broader sample of
clumps and cores). Last, we focus our attention on MMCs and HBS by
classifying the 35 clumps in two categories HFS or no-HFS (refers to
sections 3.3 Core formation efficiencies and 4.2 Clump
classification), results are presented in the table mmcs.dat.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
a2021.dat 383 67 Our sample of clump and core properties
cores.dat 279 133 *Cores properties
mmcs.dat 262 35 Clump classifications and MMCs properties
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Note on cores.dat: This sample contains 35 clumps that have been observed with
ALMA ACA at 878 µm (Band 7). These ACA data have similar angular resolution
as ours, with a mean beam size of 3.8 arcsec. Also, the distance of these
clumps span a very similar range (1.3 kpc < d < 4.2 kpc) to our set of sources.
Note that as our 7 + 12 m observations are Band 3, and hence the dust emission
we are comparing between data sets may arise from slightly different layers of
the cores.
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See also:
J/A+A/561/A83 : SDC13 infrared dark clouds spectra (Peretto+, 2014)
J/A+A/505/405 : A catalogue of Spitzer dark clouds (Peretto+, 2009)
J/A+A/590/A72 : Herschel counterparts of SDC (Peretto+, 2016)
J/A+A/591/A149 : Hi-GAL. inner Milky Way: +68≥l≥70 (Molinari+, 2016)
J/A+A/600/L10 : Massive cluster progenitors from ATLASGAL (Csengeri+, 2017)
J/MNRAS/422/3178 : Distances of 793 BGPS sources (Eden+, 2012)
J/A+A/642/A87 : Hub-filament candidates (Kumar+, 2020)
J/ApJ/783/130 : Parallaxes of high mass star forming regions (Reid+, 2014)
J/ApJS/179/249 : Low-luminosity embedded protostar population (Dunham+, 2008)
J/A+A/547/A49 : Herschel EPoS: high-mass overview (Ragan+, 2012)
J/MNRAS/471/100 : Hi-GAL compact source catalog. -71.0<l<67.0 (Elia+, 2017)
J/A+A/487/993 : MAMBO Mapping of c2d Clouds and Cores (Kauffmann+, 2008)
Byte-by-byte Description of file: a2021.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 16 A16 --- Clump Clump name from Galactic coordinates
(GLLL.llll+B.bbbb) (clump_name) (G3)
18- 21 I4 pc d Estimated distance (d) (G4)
23- 25 I3 pc e_d Mean error on d (d_err)
27- 32 F6.1 Msun Mclump Mass of the clump (M_clump) (G5)
34- 53 A20 --- Core Core name from Galactic coordinates of the
clump (LLL.llll+B.bbbb-MMNN) and a number
between 1 and 19 (core_name)
55- 70 F16.12 deg RAdeg Right ascension (J2000) (RA)
72- 88 F17.13 deg DEdeg Declination (J2000) (Dec)
90-106 F17.15 Jy Snu Integrated flux density of the source
around 2890 µm (Sν) (G6)
108-127 E20.15 Jy Snuclip Integrated flux density of the source
with the clipped paradigm around 2890 µm
(Sνclip) (G6)
129-148 E20.15 Jy e_Snu Mean error on Sν (Sνerr)
150-166 F17.15 Jy/beam Inupeak Integrated flux density of the source pear
beam size around 2890 µm (18 pixels)
(Inu_peak)
168-185 F18.14 --- SNR Signal to noise ratio calculated
at the maximum peak values (peak_snr)
187-203 F17.15 deg BeamFWHM FWHM of the beam area (beam_FWHM) (G7)
205-217 E13.8 deg2 Acore Size of the core in the square degrees unit
1deg2=(π/180)2sr (A_core)
219-235 F17.15 pc Req Equivalent radius (R_eq) (G8)
237-253 F17.15 pc Rsource Deconvolved source radius (R_source) (G9)
255 I1 --- f_Rsource [0/1] Flag on Rsource, 1 for the resolved
sources (resolved) (G9)
257-265 F9.6 K Tcol First estimated temperature (Tcol) (G10)
267-269 F3.1 K e_Tcol [0.5] Mean error on Tcol (Tcolerr)
271 I1 --- 70um [0/1] Availability of an associated 70 µm
source, 1 if it's the case (70micron) (G11)
273-288 F16.13 K Td ?=- Second estimated temperature
(Td) (G12)
290-306 F17.15 K e_Td ?=- Mean error on Td (Tderr)
308-317 F10.7 K Tcore Estimated core temperature (Tcore) (G13)
319-323 F5.3 K e_Tcore Mean error on Tcore (T_err)
325-343 F19.15 Msun Mcore Core mass (Mcore) (G14)
345-363 F19.15 Msun E_Mcore Mcore error upper value (Merrpos) (G15)
365-383 F19.15 Msun e_Mcore Mcore error lower value (Merrneg) (G15)
-------------------------------------------------------------------------------
Byte-by-byte Description of file: cores.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 16 A16 --- Clump Clump name from Galactic coordinates
(GLLL.llll+B.bbbb) (clump_name)
18- 22 A5 --- Sample [C2017/A2021] sample origin (sample) (G1)
24- 45 E22.17 Hz Freq Observed frequency (nu) (G2)
47- 64 F18.16 arcsec BeamFWHM FWHM of the beam area (beam_FWHM)
66- 69 I4 pc d Estimated distance (d) (G4)
71- 88 F18.12 Msun Mclump ?=- Mass of the clump (M_clump) (G5)
90-109 A20 --- Core Core name from Galactic coordinates of
the clump (LLL.llll+B.bbbb-MMNN) and a number
between 1 and 19 (core_name)
111-126 F16.12 deg RAdeg Right ascension (J2000) (RA)
128-144 F17.13 deg DEdeg Declination (J2000) (Dec)
146-163 F18.15 Jy Snu Integrated flux density of the source
around 878 µm (Sν) (G6)
165-182 F18.15 Jy Snuclip Integrated flux density of the source
with the clipped paradigm around 878 µm
(Sνclip) (G6)
184-200 F17.15 pc Req Equivalent radius (Req) (G8)
202-218 F17.15 pc Rsource Deconvolved source radius (Rsource) (G9)
220 I1 --- f_Rsource [0/1] Flag on Rsource, 1 for the resolved
sources (resolved) (G9)
222-230 F9.6 K Tcol ?=- First estimated temperature
(Tcol) (G10)
232 I1 --- 70um [0/1] Availability of an associated 70 µm
source, 1 if it's the case (70micron) (G11)
234-249 F16.13 K Td ?=- Second estimated temperature (Td) (G12)
251-259 F9.6 K Tcore ?=- Estimated core temperature
(Tcore) (G13)
261-279 F19.15 Msun Mcore ?=- Core mass (Mcore) (G14)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: mmcs.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 16 A16 --- Clump Clump name from Galactic coordinates
(GLLL.llll+B.bbbb) (clump_name)
18- 22 A5 --- Sample [C2017/A2021] sample origin (sample) (G1)
24- 25 I2 --- ClumpID [1-35] Clump identifier number (clump_ID)
27- 48 E22.17 Hz Freq Observed frequency (nu) (G2)
50- 68 A19 --- Core Core name from Galactic coordinates of the
clump (LLL.llll+B.bbbb-MMNN) and a number
between 1 and 19 (core_name)
70- 85 F16.12 deg RAdeg Right ascension (J2000) (RA)
87-103 F17.13 deg DEdeg Declination (J2000) (Dec)
105-108 I4 pc d Estimated distance (d) (G4)
110-126 F17.15 pc Req Equivalent radius (R_eq) (G8)
128-144 F17.15 pc Rsource Deconvolved source radius (R_source) (G9)
146-154 F9.6 K Tcol First estimated temperature (T_col) (G10)
156 I1 --- 70um [0-1] Availability of an associated 70 µm
source, 1 if it's the case (70micron) (G11)
158-173 F16.13 K Td ?=- Second estimated temperature (T_d) (G12)
175-183 F9.6 K Tcore Estimated core temperature (T_core) (G13)
185-201 F17.13 Msun Mcore Core mass (M_core) (G14)
203-220 F18.12 Msun Mclump Mass of the clump (M_clump) (G5)
222-238 F17.15 --- fMMC The fraction of the clump mass contained
within its MMC (f_MMC) (1)
240-256 F17.15 --- CFE The core formation efficiency (CFE) (2)
258 I1 --- HFS Hubs filament system classification (HFS) (4)
260-262 F3.1 --- IRclass Brightness category (IR_class) (3)
--------------------------------------------------------------------------------
Note (1): As far as massive star formation is concerned, another quantity of
interest is the fraction of the clump mass contained within its MMC
(most massive core), so we express fMMC = MMMC/Mclump,
(i.e equation 7 in the section 3.3 Core formation efficiencies)
Note (2): As discussed in the introduction, the ability of a clump to
concentrate its mass within cores is a fundamental, but poorly
understood characteristic of star-forming regions. In this paper,
we refer to parsec-scale dense molecular cloud structures as clumps,
within which stellar clusters and large systems can form
(Eden et al. 2012MNRAS.422.3178E 2012MNRAS.422.3178E, Cat. J/MNRAS/422/3178; Motte et al.
2018ARA&A..56...41M 2018ARA&A..56...41M). Here, we calculate the core formation
efficiency (CFE) as CFE = ∑iMcore,i/Mclump which is the sum
of core masses in a given clump, divided by the clump's mass. This
tells us how much of a clump's mass is contained within compact
sources. The clump masses are obtained from Herschel column density
maps (Peretto et al. 2016A&A...590A..72P 2016A&A...590A..72P, Cat. J/A+A/590/A72),
(i.e equation 6 in the section 3.3 Core formation efficiencies).
Note (3): We first classify the clumps based on the mid-infrared brightness
within the NH2 = 3*1022 cm-2 contour used to define the clump
boundaries. Infrared brightness has recently been shown to be a
reliable time evolution tracer (Rigby et al. 2021MNRAS.502.4576R 2021MNRAS.502.4576R). We
classify clumps into three infrared brightness category, from the less
evolved to the more evolved as follows:
0.0 = IR-dark, no 8 µm extended emission within clump, prominent
extinction features
1.0 = IR-bright, significant 8 µm extended emission within the
clump, without prominent extinction features
0.5 = Intermediate, having both clear extinction and emission features
within the clump
This classification is made by eye, and is therefore subject to some
subjectivity, especially for borderline cases. However, it still
provides a reasonable classification of the inner star formation
activity of a clump. Out of the 35 clumps, we classify 13 as IR-dark,
16 as Intermediate, and 6 as IR-bright.
Note (4): Clumps are then further classified as either HFS or non-HFS according
to the location of the MMC with respect to its local network of
filaments. For that purpose we utilize a Hessian-based method, similar
to Schisano et al. (2014ApJ...791...27S 2014ApJ...791...27S) and Orkisz et al.
(2019A&A...624A.113O 2019A&A...624A.113O), to extract filamentary structures from Herschel
250 µm images of the clumps. We then classify a clump as an HFS if
there are at least three filaments pointing towards the location of
the MMC.
One caveat of this method is the relatively low angular
resolution of the Herschel 250 µm image compared to the ALMA data
(∼18 arcsec versus ∼3 arcsec) which prevents us from making a robust
association between filaments and cores. Also, for the same reason,
a lot of the filamentary structures within the clumps will not be
resolved or even identified. We therefore use the Spitzer 8 µm
images in conjunction with our extracted filaments to inform our final
classification, by checking each one of the clumps for filamentary
structures seen in extinction at 8 µm.
Out of the 35 clumps, 28 are classified as hubs and 7 as non-hubs,
making our sample hub-dominated. This is likely to be a consequence
of how the sample has been built: the merging of 6 infrared dark hubs
with a sample of 29 massive clumps, which are known to often be
associated with hubs (Kumar et al. 2020A&A...642A..87K 2020A&A...642A..87K,
Cat. J/A+A/642/A87).
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Global notes:
Note (G1): Sample are as follows:
C2017 = Csengeri et al. (2017A&A...600L..10C 2017A&A...600L..10C, Cat. J/A+A/600/L10)
A2021 = Our work
Note (G2): Central observed frequency for our study is 103.6 GHz corresponding
to ∼ 2890 µm in radio ALMA Band 3 while for C2017 they have used
the central observed frequency at 878 µm in infrared ALMA Band 7,
(i.e https://www.eso.org/public/italy/teles-instr/alma/
receiver-bands/).
Note (G3): The six infrared dark cloud/clumps (IRDC) names are G326.4745+0.7027,
G335.5857-0.2906, G338.3150-0.4130, G339.6080-0.1130,
G340.9698-1.0212, G345.2580-0.0280.
Note (G4): We use the Revised Kinematic Distance Calculator5 (Reid et al.
2009ApJ...700..137R 2009ApJ...700..137R, Reid et al. 2014ApJ...783..130R 2014ApJ...783..130R,
Cat. J/ApJ/783/130) to estimate the distances to the IRDCs, using
the LSR velocities for each clump.
Note (G5): The clump masses are obtained from Herschel column density maps
(Peretto et al. 2016A&A...590A..72P 2016A&A...590A..72P, Cat. J/A+A/590/A72), where the
clump boundary is defined by the H2 column density contour at
NH2 = 3*1022 cm-2.
Note (G6): The integrated flux density of the cores comes from our dendrogram
extraction, following the 'clipped' paradigm (see Rosolowsky et al.
2008ApJ...679.1338R 2008ApJ...679.1338R). Since we care about the cores as being
overdensities, by using a clipped method we minimize the contribution
from the background on the mass estimates, which could be
particularly large for the crowded areas at the centre of the
Hubs-filament systems.
Note (G7): The corresponding six FWHM values of the beam in arcsec are
2.30163, 2.34363, 2.35196, 2.36576, 2.45926, 4.12388 stands
in degrees respectively for the six values
0.000639342369822, 0.000651007869300, 0.000653322580431,
0.000657156178693, 0.000683127999712, 0.001145522451164 linked
respectively for the six IRDCs G326.4745+0.7027,
G335.5857-0.2906, G338.3150-0.4130, G339.6080-0.1130,
G340.9698-1.0212, G345.2580-0.0280 .
Note (G8): The equivalent radius Req of a core, which is the radius of a
circle with equal area to the core's corresponding dendrogram mask,
(i.e see the section 3.1 Core extraction).
Note (G9): We calculate a deconvolved source radius which is given by
sqrt(Req2 - θmaj*θmin/4) where θmaj
and θmin are the major and minor beam axes.
Upper limits for the radii of unresolved sources are indicated
instead of the real value. We denote a 1 for a resolved source and
a 0 for an unresolved source.
Note (G10): To estimate core temperatures we use a combination of two methods.
Our primary method is to use dust temperature maps derived from
column density maps presented in Peretto et al.
(2016A&A...590A..72P 2016A&A...590A..72P, Cat. J/A+A/590/A72) which were constructed
from 160 and 250 µm data from the Herschel Hi-GAL survey
(Molinari et al. 2010A&A...518L.100M 2010A&A...518L.100M). We simply take the
temperature at the position of each core's intensity-weighted
centroid.
These maps cover a temperature range of around 12-30 K for our set
of fields. Note that because we assume a unique temperature along
the line of sight and that the typical background temperature of the
Galactic Plane is ∼ 18 K, we may overestimate the temperatures of
dense clumps colder than this background value (Peretto et al.
2010A&A...518L..98P 2010A&A...518L..98P; Battersby et al. 2011A&A...535A.128B 2011A&A...535A.128B;
Marsh et al. 2015MNRAS.454.4282M 2015MNRAS.454.4282M).
Note (G11): For warmer sources (such as massive protostellar cores), this may be
significantly underestimating their temperature, and hence
overestimating their mass. To try and counter this effect, we use
the Hi-GAL 70 µm Compact Source Catalogue (Molinari et al.
2016A&A...591A.149M 2016A&A...591A.149M, Cat. J/A+A/591/A149) to see which cores in
our sample have an associated 70 µm source, as the 70 µm
flux density is known to be a good tracer of the luminosity of
embedded sources (Dunham et al. 2008ApJS..179..249D 2008ApJS..179..249D,
Cat. J/ApJS/179/249; Ragan et al. 2012A&A...547A..49R 2012A&A...547A..49R,
Cat. J/A+A/547/A49). If a 70 µm source is present within the
equivalent radius Req of a core, which is the radius of a circle
with equal area to the core's corresponding dendrogram mask, we say
they are associated.
Note (G12): We then convert the 70 µm flux densities to bolometric internal
luminosities using the equation (3) in the section 3.2 Core sizes
and masses (Elia et al. 2017MNRAS.471..100E 2017MNRAS.471..100E, Cat. J/MNRAS/471/100).
Assuming that the dust emission from a protostellar core is
optically thin and is predominantly in the far-infrared, we
calculate the mean mass-weighted temperature of the core Td with
the equation (4) in the section 3.2 Core sizes and masses
(Emerson 1988ASIC..241..193E 1988ASIC..241..193E; Terebey et al. 1993ApJ...414..759T 1993ApJ...414..759T).
Note (G13): If a 70 µm flux density derived temperature can be obtained for a
core, we assign the core Tcore = Td and otherwise assign
Tcore = Tcol. We assume that the temperature of the gas and
dust is coupled as the cores have a density at least ∼ 106 cm-3,
the threshold at which Goldsmith (2001ApJ...557..736G 2001ApJ...557..736G) states that
the dust and gas temperatures become essentially equal.
Note (G14): Assuming that the cores are in local thermodynamic equilibrium (LTE)
and that the dust emission is optically thin, the core masses can
then be calculated using the equation (1) in the section 3.2 Core
sizes and masses, Mcore = d2*Sν/κν*Bν(T),
where d is the distance to the IRDC, Sν is the integrated flux
density of the source, κν is the specific dust opacity,
and Bν(T) is the Planck function at a given dust temperature T,
(Kauffmann et al. 2008A&A...487..993K 2008A&A...487..993K, Cat. J/A+A/487/993).
Note (G15): The errors in the core masses were calculated using Monte Carlo
methods, by randomly sampling over each variable in equation (1)
(section 3.2 Core sizes and masses) assuming Gaussian errors.
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History:
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(End) Luc Trabelsi [CDS] 31-Jul-2024