A spectral line survey of the starless and proto-stellar cores detected by BLAST toward the Vela-D molecular cloud

1.9 MB·English

by  Jorge L. Morales Ortiz

Astronomy&Astrophysicsmanuscriptno.paper˙VelaD˙ATNF˙v15 (cid:13)c ESO2012
January27,2012
A spectral line survey of the starless and proto-stellar cores
detected by BLAST toward the Vela-D molecular cloud
JorgeL.MoralesOrtiz1,2,†,LucaOlmi3,2,MichaelBurton4,MassimoDeLuca5,DavideElia6,TeresaGiannini7,
7 2 8
DarioLorenzetti ,FabrizioMassi ,andFrancesco Strafella
1 UJF-Grenoble1/CNRS-INSU,InstitutdePlane´tologieetd’AstrophysiquedeGrenoble(IPAG)UMR5274,Grenoble,F-38041,
Francee-mail:[email protected]
2 OsservatorioAstrofisicodiArcetri-INAF,LargoE.Fermi5,I-50125,Firenze,Italy
2
3 UniversityofPuertoRico,RioPiedrasCampus,PhysicsDepartment,Box23343,UPRstation,SanJuan,PuertoRico(USA)
1
4 SchoolofPhysics,UniversityofNewSouthWales,SydneyNSW2052,Australia
0
5 LERMA-LRA,UMR8112duCNRS,ObservatoiredeParis,E´coleNormaleSupe´rieure,UPMC&UCP,24rueLhomond,75231
2
ParisCedex05,France

n 6 IstitutodiFisicadelloSpazioInterplanetario-INAF,viaFossodelCavaliere100,I-00133Roma,Italy
a 7 OsservatorioAstronomicodiRoma-INAF,ViaFrascati33,I-00040MonteporzioCatone,Roma,Italy
J 8 DipartimentodiFisica,Universita´delSalento,CP193,I-73100Lecce,Italy

3
Received;accepted
2

ABSTRACT
]
A
Context. Starlesscoresrepresentaveryearlystageofthestarformationprocess,beforecollapseresultsintheformationofacentral
G
protostaroramultiplesystemofprotostars.
. Aims. Weusespectrallineobservationsofasampleofcolddustcores,previouslydetectedwiththeBLASTtelescopeintheVela-D
h
molecularcloud,toperformamoreaccuratephysicalandkinematicalanalysisofthesources.
p
Methods. Wepresenta3-mmand1.3-cmsurveyconductedwiththeMopra22-mandParkes64-mradiotelescopesofasampleof
-
o 40colddustcores,includingbothstarlessandproto-stellarsources.20objectswerealsomappedusingmoleculartracersofdense
r gas.TotracethedensegasweusedthemolecularspeciesNH3,N2H+,HNC,HCO+,H13CO+,HCNandH13CN,wheresomeofthem
t tracethemorequiescentgas,whileothersaresensitivetomoredynamicalprocesses.
s
a Results. Theselectedcoreshaveawidevarietyofmorphologicaltypesandalsoshowphysicalandchemicalvariations,whichmay
[ beassociated todifferent evolutionary phases. Wefindevidence of systematicmotionsinbothstarlessandproto-stellar cores and
wedetectlinewingsinmanyoftheproto-stellarcores.Ourobservationsprobelineardistancesinthesources>∼0.1pc,andarethus
1
sensitivemainlytomoleculargasintheenvelopeofthecores.Inthisregionwedofindthat,forexample,theradialprofileofthe
v N H+(1−0)emissionfallsoffmorequicklythanthatofC-bearingmoleculessuchasHNC(1−0),HCO+(1−0)andHCN(1−0).We
2
8
alsoanalyzethecorrelationbetweenseveralphysicalandchemicalparametersandthedynamicsofthecores.
9
Conclusions. Dependingontheassumptionsmadetoestimatethevirialmass,wefindthatmanystarlesscoreshavemassesbelow
7
theself-gravitatingthreshold,whereasmostoftheproto-stellarcoreshavemasseswhicharenearorabovetheself-gravitatingcritical
4
value. An analysis of the median properties of the starless and proto-stellar cores suggests that the transition from the pre- to the
.
1 proto-stellarphaseisrelativelyfast,leavingthecoreenvelopeswithalmostunchangedphysicalparameters.
0
Keywords.submillimeter:ISM—stars:formation—ISM:clouds—ISM:molecules—radiolines:ISM
2
1
:
v 1. Introduction rived luminosities and masses. Recent surveys with the MIPS
i
X instrumentof the Spitzer Space Telescope are able to constrain
Starlesscoresrepresenta veryearlystageofthestar formation the temperaturesof warmer objects(Careyetal. 2005), but the
r
a process,beforecollapseresultsintheformationofacentralpro- youngestand coldest objects are potentially not detected, even
tostar or a multiple system of protostars. The physical proper- inthelong-wavelengthSpitzerbands.
tiesofthesecorescanrevealimportantcluesabouttheirnature.
On the other hand, the more recent surveys with both
Mass, spatial distributions, and lifetime are importantdiagnos-
the BLAST (“Balloon-borne Large-Aperture Submillimeter
tics of the main physicalprocesses leading to the formationof
Telescope”, Pascaleetal. 2008) and Herschel telescopes (see,
thecoresfromtheparentmolecularcloud.
e.g., Netterfieldetal. 2009, Olmietal. 2009, Molinarietal.
In the past, (sub)millimeter continuum surveys performed 2010) have demonstrated the ability to detect and characterize
withground-basedinstrumentshaveprobedtheRayleigh-Jeans colddustemissionfrombothstarlessandproto-stellarsources,
tail of the spectral energy distribution (SED) of these cold ob- constraining the low temperaturesof these objects (T <∼ 25K)
jects,farfromitspeakand,atshortsubmillimeterwavelengths, using their multi-band photometry near the peak of the cold
havebeenaffectedbylowsensitivityduetoatmosphericcondi- coreSED. Thebolometricobservationsalone,however,cannot
tions.Therefore,thesesurveyshavebeenlimitedbytheirsensi- fullycontrainthedynamicalandevolutionarystatusofthecores.
tivityorbytheirrelativeinadequacytomeasurethetemperature Spectrallinesfollow-upsarenecessaryinordertoinvestigatethe
(e.g.,Motteetal.1998),producinglargeuncertaintiesinthede- physical,dynamicalandchemicalstatusofeachdetectedcore.
1
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
Table2.MolecularspeciesobservedwiththeParkesandMopra
telescopes
Spectralline E n a RestFrequency
u eff
[K] [×103cm−3] [MHz]
NH (1,1) 23.4 − 23694.496
3
NH (2,2) 64.9 − 23722.633
3
N H+(1 −0 ) 4.47 2.5 93172.053
2 21 32
HNC(1 −0 ) 4.35 9.5 90663.574
2 1
HCO+(1−0) 4.28 2.5 89188.526
H13CO+(1−0) 4.16 2.2 86754.330
HCN(1 −0 ) 4.25 28 88631.847
2 1
H13CN(1 −0 ) 4.14 20 86340.167
2 1
Notes. (a) SeeSection4.4.2foradefinitionofn .
eff
BLAST has identified more than a thousand new star-
less and proto-stellar cores during its second long duration
balloon science flight in 2006. BLAST detected these cold
cores in a ∼ 50deg2 map of the Vela Molecular Ridge
(VMR) (Netterfieldetal. 2009). The VMR (Murphy&May
1991, Liseauetal. 1992) is a giant molecular cloud complex
within the galactic plane, in the area 260◦ <∼ l <∼ 272◦ and
−2◦ <∼ b <∼ 3◦, hence located outside the solar circle. Its
mainpropertieshavebeenrecentlyrevisitedbyNetterfieldetal.
(2009)andOlmietal.(2009).
Fig.1. The gray-scale image shows the BLAST 250µm map
In particular, Olmietal. (2009) used both BLAST and
of Vela-D, with galactic coordinates in degrees. Superimposed
archivaldatatodeterminetheSEDsandthephysicalparameters
arethelocationsofbothstarless(opencircles)andproto-stellar
ofeachsourcedetectedbyBLASTinthesmallerregionofVela-
(crosses) cores (see Olmietal. 2009). The size of the symbols
D (see Figure 1), where observations from IR (Gianninietal.
indicatesthemassrange[M ]ofeachcoreandcolor-codingin-
2007) to millimeter wavelengths (Massietal. 2007) were al- ⊙
dicatesthecoretemperature[K](seelegend).
ready available. Olmietal. (2010) then used the spectral line
dataofEliaetal.(2007)toperformafirstanalysisofthedynam-
icalstateofthecorestowardVela-D.Theyfoundthat∼30−50%
oftheBLASTcoresaregravitationallybound,andthatasignifi-
increasingtemperatureanddifferentmorphology.Thisselection
cantnumberofcoreswouldneedanadditionalsourceofexternal
criterionisquitearbitrarybutaimedatidentifyingdifferentevo-
confinement.
lutionarystageswithineachsub-sample.
In this work we will use spectral line observations, both
InordertoprobethedenseandcoldgasdetectedbyBLAST
single-points and maps, of a sample of BLAST sources from
toward the cores in Vela-D we needed appropriate molecular
Vela-D to perform a more accurate physical and kinematical
tracers.We thusselected severalrotationaltransitionswith low
analysisofthestarlessandproto-stellarcores.Thispaperisthus
quantum numbers to be observed at Mopra in the 3-mm band,
organizedasfollows:inSection2we describethe selectedtar-
andwealsoobservedtheNH (1,1)and(2,2)inversionlineswith
getsandmolecularlines. InSection3 we presenttheresultsof 3
theParkestelescope.Inthefollowingsections,ouranalysiswill
the analysis of the observed molecular line spectra and maps,
bebasedontheammonialinesandonthemainspectrallinesob-
describingthederivedphysicalandkinematicalparameters.We
servedatMopra,i.e.,N H+(1−0),HCN(1−0),HNC(1−0)and
then further discuss these results in Section 4 and conclude in 2
HCO+(1−0)(andtwooftheirisotopologues,seeTable2).This
Section5.
choice of molecular tracers ensured that we would be able to
trace the dense as well as the more diffuse gas, and we would
also be able to detect molecular outflows. Furthermore, these
2. Observationsandarchivaldata
molecules should also be able to give out clues about the dif-
2.1.Targetsandlinesselection ferentchemicalstatesofthesources.
TheobservationswereperformedinJune2009withtheMopra
and Parkes telescopes of the Australia Telescope National 2.2.Mopra
Facility(ATNF).Althoughoriginallyouraimwastoobserveall
sourcesinthecatalogofOlmietal.(2009),becauseoftimecon- During the spectral line mapping or single-pointing mode ob-
straintswewere abletoobservea totalof40sourcesatMopra servations with the Mopra telescope the system temperatures
and 22 sources at Parkes, in either mapping or single-pointing were typically comprised in the range ∼ 170− 280K and we
mode(or both,see Table 1 and Figure1). We have selected an reacheda RMSsensitivity inT⋆ unitsofabout∼ 30−40 mK
A
almostequalnumberofstarless(19)andproto-stellar(21)cores after rebinning to a 0.22 kms−1 velocity resolution. The beam
where,followingOlmietal.(2009),wedefinetheBLASTcores full width at half maximum (FWHM) was about38arcsec and
as proto-stellar when they turned out to be positionally asso- thepointingwascheckedeveryhourbyusinganSiO maseras
ciated with one or more MIPS sources at 24µm, and starless a reference source. Typically, pointing errors were found to be
otherwise.Eachsub-sampleiscomposedbyobjectsthatpresent ∼5−10arcsec.
2
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
Table1.BLASTsourcesinVela-DobservedwiththeMopraandParkestelescopes
BLAST Mopra Parkes
Source#a Sourcename l b Starless Observation Observation
[deg] [deg] orProto-Stellar typeb typeb
3 BLASTJ084531-435006 263.6001 −0.5302 P SP SP
9 BLASTJ084546-432458 263.3005 −0.2341 S SP&M SP
12 BLASTJ084552-432152 263.2707 −0.1886 S SP –
13 BLASTJ084606-433956 263.5331 −0.3425 S M –
14 BLASTJ084612-432337 263.3322 −0.1585 S SP&M SP
23 BLASTJ084633-432100 263.3370 −0.0827 P SP –
24 BLASTJ084633-435432 263.7742 −0.4309 P SP&M SP
26 BLASTJ084637-432245 263.3685 −0.0899 P SP –
31 BLASTJ084654-431626 263.3177 0.0149 S SP&M SP
34 BLASTJ084718-432804 263.5147 −0.0496 S SP&M SP
38 BLASTJ084731-435344 263.8713 −0.2886 P SP SP
40 BLASTJ084735-432829 263.5521 −0.0141 S SP&M SP
41 BLASTJ084736-434332 263.7488 −0.1699 S SP&M SP
43 BLASTJ084738-434931 263.8305 −0.2277 P SP SP
44 BLASTJ084739-432623 263.5322 0.0167 P SP –
45 BLASTJ084742-434347 263.7637 −0.1582 P SP SP
47 BLASTJ084744-435045 263.8591 −0.2249 S SP&M SP
50 BLASTJ084749-434810 263.8349 −0.1861 S SP&M SP
52 BLASTJ084754-432748 263.5802 0.0387 P SP –
53 BLASTJ084759-433942 263.7428 −0.0757 P SP –
54 BLASTJ084801-435108 263.8947 −0.1907 P SP –
55 BLASTJ084803-433051 263.6369 0.0281 S M –
56 BLASTJ084805-435415 263.9430 −0.2138 S SP&M –
57 BLASTJ084813-423730 262.9644 0.6103 S SP&M SP
59 BLASTJ084815-434714 263.8713 −0.1166 P SP SP
63 BLASTJ084822-433152 263.6856 0.0609 S SP&M SP&M
65 BLASTJ084823-433858 263.7799 −0.0106 S SP –
71 BLASTJ084834-435455 264.0059 −0.1538 P SP –
72 BLASTJ084834-432430 263.6126 0.1657 S SP –
77 BLASTJ084842-431735 263.5392 0.2584 P SP SP
79 BLASTJ084844-433733 263.8007 0.0525 P SP –
81 BLASTJ084847-425423 263.2482 0.5133 P SP&M SP
82 BLASTJ084848-433225 263.7415 0.1155 P SP&M SP
88 BLASTJ084910-441636 264.3543 −0.2984 P SP –
89 BLASTJ084912-431353 263.5480 0.3668 S SP&M SP
90 BLASTJ084912-433618 263.8379 0.1312 P SP SP
93 BLASTJ084925-431710 263.6165 0.3645 P SP SP
97 BLASTJ084932-441046 264.3206 −0.1857 P SP SP
101 BLASTJ084952-433808 263.9381 0.2058 S M –
109 BLASTJ085033-433318 263.9551 0.3532 S M –
Notes. (a) Wefollowthesourcenumbering(0to140)definedbyOlmietal.(2009).(b) “SP”standsforsingle-pointobservationand“M”stands
formap.
The parameter η to convert from antenna temperature to tically thick and thus two isotopologues, H13CO+ and H13CN,
mb
main-beambrightnesstemperaturehasbeenassumedtobe0.44 werealso observedto provideopticaldepthandlineprofilein-
at 100GHz and 0.49 at 86GHz (Laddetal. 2005). The Mopra formation.Unfortunately,theirintensitywasingeneraltooweak
spectrometer (MOPS) was used as a backend instrument in its toallowderivationofcolumndensitiesthroughoutthemapsand
“zoom”mode,whichallowedtosplitthe8.3GHzinstantaneous otherusefulphysicalandkinematicalparameters,andthusmost
band in up to 16 zoom bands; each sub-band was 137.5 MHz ofouranalysiswillbebasedonthefourmostintensemolecular
wide and had 2×4096 channels. The single-point observations tracers.
were performedin position-switchingmode,whereasthe spec-
trallinemaps,ofsizemostly3×3arcmin2,wereobtainedusing
2.3.Parkes
theMopraon-the-flymappingmode,scanninginbothrightas-
censionanddeclination.
A total of 22 sources where observed with the Parkes tele-
ThemostintenselinesobservedwereN H+(1−0),HCN(1− scopeinsingle-pointingmode(seeTable1),andonlyonesource
2
0),HNC(1−0)andHCO+(1−0).Theselinesareallgoodtrac- (BLAST063)was mappedusingthe NH3(1,1)and (2,2)transi-
ersofdensegas,andarealsooftenusedtodetectvelocitygradi- tions1.Thesystemtemperaturesweretypically∼40−50Kand
ents.N H+isknowntobemoreresistanttofreeze-outongrains we reachedaRMS sensitivityinT⋆ unitsof∼ 10mKafterre-
2 A
than the carbon-bearingspecies. HNC is particularly prevalent
incoldgas(Hirotaetal.1998),whileHCO+ oftenshowsinfall 1 Thesignal-to-noiseratio(SNR)inthismapwasverylowandthus
signaturesandoutflowwings.Thesestronglinescanallbeop- wewillnotconsideranyfurtherthismap.
3
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
binningtoa≃0.2kms−1velocityresolution.ThebeamFWHM Table4.NH (1,1)lineparameters.
3
was about 1.3arcmin and the pointing errors were found to be
< 20arcsec. The Parkes Multibeam correlator, in single-beam Source# NH (1,1)
3
high resolution mode, was used as a backend. A simultaneous T⋆τ V FWHM τ
A lsr
band of 64MHz was observed, with a total of 8192 channels, [K] [kms−1] [kms−1]
which allowed to observe the NH (1,1) and (2,2) lines within 3 0.15 5.3 1.9 1.40
3
thesamebandwidth. 9 0.04 10.7 1.1 0.66
14 0.13 3.0 0.7 2.63
24 0.38 3.5 2.6 0.51
2.4.BLAST 31 0.06 10.7 1.3 2.77
40 0.07 1.3 0.9 0.22
BLAST is a 1.8m Cassegrain telescope, whose under- 41 0.05 11.1 0.7 0.10
illuminated primary mirror has produced in-flight beams with 47 0.04 5.5 1.5 0.77
FWHMof36′′,42′′,and60′′ at250,350,and500µm,respec- 57 0.07 14.0 1.5 1.73
tively.More details on the instrument,calibrationmethodsand 63 0.11 12.4 1.7 0.94
map-making procedure can be found in the BLAST05 papers 77 0.05 2.0 0.8 0.10
81 0.06 12.3 3.1 0.10
Pascaleetal. (2008), Patanchonetal. (2008), and Truchetal.
82 0.11 11.7 2.0 0.22
(2008).
90 0.10 11.4 1.7 0.10
The Vela-D region, shown in Figure 1 and defined by
93 0.13 2.4 1.2 0.70
Olmietal. (2009) as the area contained within 262◦.80 < l <
97 0.31 9.4 1.6 1.28
264◦.60 and −1◦.15 < b < 1◦.10, was part of a larger map
of the Galactic Plane obtained by BLAST toward the VMR Notes. Parametersderivedfrommethod“nh3”oftheCLASSprogram.
(Netterfieldetal.2009).InVela-DOlmietal.(2009)foundato- SourceswherethehyperfinestructureoftheNH3(1,1)couldnotbefit-
talof141sources,bothstarlessandproto-stellar,andinthenext tedarenotlistedhere.
sectionswewillfollowthesourcenumbering(0to140)defined
bytheseauthors. Table5.NH (2,2)lineparameters.
3
Source# NH (2,2)
3
3. Results T⋆dV V FWHM
A lsr
[KR kms−1] [kms−1] [kms−1]
Inthissectionwewilldiscussthederivationofvariousphysical
3 0.06 5.3 1.1
parameters such as column density, mass and kinetic tempera-
24 0.54 3.6 3.1
ture, that are fundamental for the analysis of the sources. We
47 0.03 5.3 2.9
willalsoanalysethekinematicsofthesources,determiningve- 63 0.03 10.3 1.8
locitygradientsandlineasymmetries.Theestimateofthevirial 81 0.08 12.2 2.7
masses will also allow us to determine which sources are cur- 82 0.07 11.7 1.9
rentlygravitationallyboundandwhicharenot. 90 0.06 11.4 2.5
93 0.07 2.4 1.8
97 0.14 9.3 2.1
3.1.Morphologicalcharacteristicsofspectrallinemaps
Notes. Parameters derived from a standard Gaussian fit to the main
Thespectrallinedataandmapswerereducedandanalyzedus- componentoftheNH (2,2)hyperfinestructure.
3
ingthestandardIRAMpackageCLASS,andtheXSpackageof
theOnsalaSpaceObservatory.Thesingle-pointspectraobtained
with the Mopra telescope towards the nominal position of the
BLASTcoresareshowninFiguresB.1toB.7oftheAppendix. integratedintensity,particularlyinthemapsoftheHCO+(1−0)
Thepeakintensitiesofthedetectedlines,orthespectrumRMS line. We can also see that in source BLAST082 two separate,
in case of nodetection,are listed in Table 3. TablesC.1 to C.4 smaller cores have been identified. In terms of the molecu-
intheAppendixlistseveralphysicalandkinematicalparameters lar tracers observed, we note that there are clear differences
ofthesources. in the spatial distribution of emission from different molecular
Themulti-lineintegratedintensitymapsobtainedatMopra, species. These morphological differences are more evident in
with the mostsignificantSNR, are shownin FigureA.1to A.4 thestarlesscores(butalso,forexample,intheproto-stellarcore
oftheAppendix,wherethewhitecontoursrepresenttheBLAST BLAST081)andsuggestbothphysicalandchemicaldifferences
emissionat250µm.Onecanseethatingeneralthelineemission amongtheobservedsources.
followsthedustcontinuumemission,evenwhentheemissionis We may summarize the wide variety of spatial morpholo-
morediffuseandfilamentaryasobserved,forexample,insource giesobservedas follows:veryearlyandcold starlesscoresap-
BLAST063.Butwealsonotethatinseveralsources(forexam- pear to have an irregular shape (e.g., BLAST009) in most or
ple, BLAST055, BLAST056, BLAST081 and BLAST101) the all molecular tracers mapped at Mopra. Some warmer cores
dustcontinuumandsomeofthe lineemissionpeakatdifferent (e.g., BLAST031) and cores at the transition phase from star-
positions. less to proto-stellar (BLAST063,see Section 4.5) appear to be
One can immediatelynote that the three proto-stellarcores morecompact.Finally,proto-stellarcoresallshowa morereg-
that were mapped (BLAST024, BLAST081 and BLAST082) ularshapeandnarrowradialintensityprofiles(seeSection3.6).
haveamuchmoreregularshapethanthestarlessones.Wealso Throughoutthe rest of the paper we will thus discuss how,be-
note that the maps of sources BLAST024 and BLAST081 are sidestomorphologicaldifferences,thesecoresalsoshowphysi-
partlyaffectedbyartefacts,likelycausedbybadweatherduring calandchemicalvariations,whichmaybeassociatedtodifferent
theobservationsatMopra,whichshowupassharpdropsofthe evolutionaryphases.
4
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
Table3. PeakintensityofmaindetectedlinesorthermsLevelofthespectrum.
Source# N H+ HCN H13CN HNC HC Na HCO+ H13CO+
2 3
3 0.17 0.81 <0.03 0.58 – 0.70 0.13
9 0.09 0.06 <0.03 0.20 – 0.22 0.06
12 <0.02 0.05 <0.02 <0.03 – 0.07 <0.02
23 <0.02 0.10 <0.03 0.25 – 0.38 <0.03
24 1.33 2.97 0.23 2.23 – 3.20 0.32
26 <0.02 0.07 <0.02 0.08 – 0.14 <0.02
26b – – – 0.10 – 0.13 –
31 <0.02 0.11 <0.02 0.15 – 0.34 <0.02
34 <0.02 0.08 <0.02 0.07 – 0.23 <0.02
34c – – – – – 0.15 –
38 0.07 0.11 <0.02 0.15 – 0.19 <0.02
40 0.20 0.31 <0.02 0.45 – 0.73 0.28
41 <0.02 0.27 <0.03 0.20 – 0.41 <0.02
43 <0.05 0.11 <0.05 0.26 – 0.42 <0.05
44 0.21 0.35 <0.04 0.57 – 0.88 0.13
45 0.13 0.24 <0.02 0.24 – 0.52 <0.02
47 <0.02 0.19 <0.02 0.12 – 0.14 <0.02
47c – – – – – 0.13 –
50 <0.02 0.10 <0.02 0.07 – 0.16 <0.02
52 <0.02 0.11 <0.02 0.10 – 0.18 <0.02
53 0.07 0.20 <0.02 0.28 – 0.19 0.07
54 <0.02 0.14 <0.02 0.12 – 0.12 <0.02
56 <0.02 0.14 <0.03 0.08 – 0.16 <0.02
57 0.12 0.13 <0.03 0.21 – 0.33 0.13
59 0.12 0.18 <0.03 0.22 – 0.23 0.08
63 0.11 0.44 <0.02 0.55 – 0.76 0.09
65 <0.02 0.12 <0.02 0.09 – 0.15 <0.02
71 <0.04 0.11 <0.04 <0.05 – <0.08 <0.04
72 <0.02 0.15 <0.02 0.14 – 0.39 <0.02
72c – – – – – 0.19 –
77 0.06 0.26 <0.02 0.23 – 0.45 <0.03
79 <0.05 0.17 <0.05 0.23 – 0.22 <0.05
81 1.49 4.32 0.39 2.42 – 4.31 0.25
82 0.50 0.65 <0.03 0.74 – 1.30 0.23
88 <0.02 0.26 <0.03 0.18 – <0.02 <0.03
89 <0.02 0.16 <0.02 0.09 – 0.22 <0.03
90 0.50 1.32 0.12 1.30 0.16 2.19 0.38
93 0.50 0.75 0.11 1.03 0.26 1.45 0.44
97 0.19 0.54 <0.03 0.62 – 0.79 0.12
Notes.Onlysourceswithasingle-pointobservationarelisted(seeTable1).AllvaluesareinunitsofT⋆[K].
A
(a) ThetypicalnoiseRMSinthespectrawhereHC Nwasnotdetectedis≃ 0.03K. (b) Thissourcehastwoseparatevelocitycomponentsin
3
HNCandHCO+andonlytheselinesarelistedforthisvelocitycomponent. (c) ThesesourceshavetwoseparatevelocitycomponentsinHCO+
andonlythislineislistedforthisvelocitycomponent.
3.2.Temperatureandopticaldepthfromhyperfinestructure HCO+wasdetectedbutnotH13CO+,thevaluesofbothT andτ
ex
fits foragivenmolecularspecieswereassumedtobetheaveragesof
theparametersestimatedfromthedetectedmoleculartransitions
The excitation temperature, Tex, and the line optical depth, τ, inthesamesource.
which are required to estimate the molecular column densi-
ties(seeSect.3.5.1)couldonlybedeterminedinthosesources
wheremoleculeswithahyperfinestructure(hfs,hereafter)were 3.3.TemperatureandopticaldepthfromNH3
detected, i.e., N H+, HCN and H13CN, and/or when both the
2 The single-point spectra of the NH (1,1) inversion line, ob-
HCO+(1−0)andH13CO+(1−0)linesweredetected. 3
tainedwiththeParkestelescope,areshowninFigureB.8ofthe
In the molecules with a hfs, we used method “hfs” of Appendix.The(2,2)linehasbeendetectedtowardsninesources
the CLASS program to determine both Tex and τ. In those (mostlyproto-stellar).We attemptedtomap theNH3(1,1)tran-
cases where both HCO+ and H13CO+ were detected, the opti- sition towardBLAST063,butwe did notdetectthe line due to
caldepthwasestimatedfromtheirlineintensityratio,assuming insufficientSNRintheindividualscanningpositions.
the same excitation temperaturefor the two isotopic molecular Method “nh3” of the CLASS program, similar to method
species and using the abundance ratio [HCO+]/[H13CO+]≃ 40 “hfs”describedabove,wasusedtofittheNH (1,1)lineandre-
3
(Zinchenkoetal.2009). sulted in the parameters T⋆τ, τ and FWHM listed in Table 4.
A
For the purpose of estimating the column density later, in Due to the fact that the hfs components of the NH (2,2) line
3
those sources where the hfs method could not be used for one were not detected (with the exception of source BLAST024),
ormoremolecules(forexamplebecauseoflowSNR),orifonly thelineparameterswerederivedfromastandardGaussianfitto
5
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Table6.Resultsofvelocitygradientfitting.
Source# HNC(1−0) HCO+(1−0)
V dV/dr θ a V dV/dr θ a
o v o v
[kms−1] [kms−1pc−1] [deg] [kms−1] [kms−1pc−1] [deg]
9 − − − 12.2 0.8 88.5
13 1.0 2.3 21.1 0.9 1.5 18.1
24 5.5 1.9 60.7 5.3 1.7 57.7
34 − − − 2.6 1.6 224.1
40 2.5 0.2 16.7 2.6 1.2 71.5
41 − − − 12.1 1.2 289.9
47 6.6 2.7 240.1 − − −
63 13.0 1.6 55.2 13.2 1.3 86.8
81 13.5 1.4 256.9 13.3 1.9 312.6
82 13.6 2.1 15.7 13.0 1.5 334.5
Notes. (a) Theangleθ ismeasuredpositivefromtheaxisofpositivelongitudeoffsetstowardtheNorth.
v
the NH (2,2) transition was not detected, we could only deter-
3
mineanupperlimittoT (showninFigure2).However,inor-
k
dertoobtainanestimateofthecolumndensity,andthusofthe
mass,forthesesourcesweadoptedtheBLAST-derivedtemper-
ature, T , as an approximation for T , which turns out to be a
d k
reasonablygoodassumption,asdiscussedbelow.
For those sources with an independent estimate of T we
k
compared the resulting kinetic temperatures with the BLAST-
deriveddusttemperatures,asobtainedbyOlmietal.(2009),and
weshowtheresultsinFigure2.ThiscomparisonbetweenT and
k
T ,whenappliedseparatelytostarlessandproto-stellarcores,is
d
affectedbythefewdetectionsofNH (2,2)towardstarlesscores,
3
andbytherelativelyhighspreadinthevaluesoftheT /T ratio.
k d
Infact,forthetwostarlesscores(BLAST047andBLAST063;
seealsoSection4.5)wherethisratiocouldbemeasuredweob-
tain a mean value hT /T i = 1.4, whereas for the proto-stellar
k d
coreswegetamedianvalueT /T =1.2±0.2.
k d
When all cores are considered together, we get a median
Fig.2. Kinetic temperature, Tk, as derived from the NH3(1,1) valueTk/Td = 1.2±0.2,i.e.,themedianvalueisdominatedby
and (2,2) inversion transitions, vs. the BLAST-derived dust the proto-stellar cores. A tentative explanationfor the fact that
temperature, Td. Sources are identified through their ID (see Tk tends to be slightly higher than Td could be that the NH3
Table 1), and the vertical arrows indicate that the correspond- observations are sampling regions that are somewhat warmer
ingTk isanupperlimit. ThedashedlineindicatestheTk = Td comparedto the BLAST-derivedTd measurements.In fact, the
locus. BLAST observations are likely to average the temperature on
muchlargervolumesof dustand,in addition,in the less dense
regions there could be a systematic difference between T and
themaincomponentoftheNH (2,2)hyperfinestructureandare d
3 T .Intheliteraturebothcasesofsystematicdeparturesbetween
listedinTable5. k
dustandgastemperature,i.e.T < T orT > T ,canbefound
We then determined the kinetic temperature, T , and NH k d k d
k 3 (e.g., Kruegel&Walmsley 1984, Pirogov&Zinchenko 1993).
column density using both NH (1,1) and (2,2) transitions, in
3 Thedustandgastemperaturemaybeaffectedbyvariouseffects,
thosesourceswherethe(2,2)linewasindeeddetected.Inthese
and a more detailed analysis of these effects in our sources is
cases we were able to determine the rotational temperature,
beyondthescopesofthepresentwork.
T (and thus T ), and the column density using the method
12 k
of Ungerechtsetal. (1986) and Bachilleretal. (1987). In this
methodthe requireddata were: (i) the productτ(Tex −Tbg) for 3.4.Kinematics
the (1,1) line, where T and T = 2.725K are the excitation
ex bg
and backgroundtemperatures,respectively,and τ is the optical 3.4.1. Velocitygradients
depth;(ii)thelinewidth∆V(1,1);and(iii)the(2,2)integratedin-
Weinvestigatedthepresenceofsystematicvelocitygradientsin
tensity.OnceT hasbeenestimated,thekinetictemperaturecan
12
thosesourceswhichcouldbemapped.Inparticular,thevelocity
be determined using the analytical expression of Tafallaetal.
gradientofagasclumpcanbedeterminedbyusingallormost
(2004):
ofthedatainamapatonce,byleast-squaresfittingmapsofline-
T = T12 (1) centervelocityforthedirectionandmagnitudeofthebest-fitve-
k 1− T12 ln[1+1.1exp(−16)] locitygradient(seeGoodmanetal.1993andreferencestherein).
42 T12 Acloudundergoingsolid-bodyrotationwouldexhibitalin-
whichisanempiricalexpressionthatfitstheT −T relationob- ear gradient, dV/dr, across the face of a map, perpendicularto
12 k
tainedusingaradiativetransfermodel.Forthosesourceswhere therotationaxis.Thus,wehaveappliedtheproceduredeveloped
6
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Fig.3. InthetoppanelsweshowthemapsoftheV fortheHNC(1−0)(left)andHCO+(1−0)(right)linestowardtheproto-stellar
lsr
coreBLAST081,asobtainedfromGaussianfitstothespectraateachmapposition.Thearrowsshowthedirectionofthevelocity
gradient,withtheirlengthproportionaltothemagnitudeslistedinTable6.Thebottompanelsshowtheposition-velocityplots,with
thehorizontalaxisrepresentingtheangularoffsetalongadirectionparalleltothevelocitygradientshownbythearrowsinthetop
panels.Notethedifferentdirectionofthevelocitygradientinthetwomoleculartracers.
byGoodmanetal.(1993)andOlmi&Testi(2002)todetermine molecularoutflow,assuggestedbythepresenceofline-wingsin
themagnitudeanddirectionofthevelocitygradientinourspec- theHCO+(1−0)spectra(seeTableC.4).
trallinemaps.OurbestresultsarelistedinTable6,andarere-
strictedtotheHCO+(1−0)andHNC(1−0)lines.Wenotethat
3.4.2. Lineasymmetries
formostsourceswithmeasuredvelocitygradientsinbothlines,
the two separately estimated values of dV/dr and θv are con- The HCO+(1− 0) line is generally the most intense transition
sistent,withina50%difference.However,thevelocitygradient
observed with the Mopra telescope in each source, and it does
measuredintheHNCmapofcoreBLAST040isquitesmalland nothaveahyperfinestructure.Therefore,itrepresentstheideal
thusitsdirectioncanbeaffectedbylargeuncertainties.Thusthe candidate to identify and analyze asymmetries of the line pro-
largestdiscrepanciesbetweenthetwotracersareobservedinthe file.Infact,theHCO+(1−0)lineshowsanon-Gaussianprofile
twoproto-stellarcoresBLAST081andBLAST082,andalsoin towardseveralsources(seeTableC.4),andinsomecasesunam-
thestarlesscoreBLAST013. biguouswingemissionisdetected,indicatingthelikelypresence
ofamolecularoutflow.By inspectingTableC.4we alsonotea
The position-velocity plots for the proto-stellar core moderateshift,upto∼ 1kms−1,betweenthepeakpositionsof
BLAST081areshowninFigure3.Thetoppanelsshowthemaps thegenerallyopticallythickHCO+(1−0)lineandopticallythin
of V forthe HNC(1−0) andHCO+(1−0) lines, asobtained H13CO+(1−0)transition.Wecangiveaquantitativeestimateof
lsr
fromGaussianfitstothespectraateachobservedposition.The thisasymmetryinordertogetsomeindirectinformationabout
arrowsrepresentthedirectionandmagnitudeofthevelocitygra- dynamicalprocessesinthecores.
dientasobtainedfromtheproceduredescribedabove.We note A widely used methodto extractline asymmetriesis based
the significantdifferencebetweenthe directionsofthe velocity on the comparison of optically thin and optically thick line
gradients as measured in the HNC and HCO+ maps. It is not velocities, i.e., determining the parameter δV = (V −
thick
clear whether this discrepancy is real or may be caused by the V )/∆V (Mardonesetal. 1997). In this way we can divide
thin thin
presenceofsomeartefactsintheHCO+ mapofBLAST081,as ourcoresin“blueshifted”cores,withδV <0,and“redshifted”
notedinSection3.1.Ontheotherhand,sourceBLAST082has coreswithδV >0.TheblueshiftedvaluesofδVcouldbecaused
no visible artefacts, and it is thus possible that in both proto- by infall motions and the red excess by expanding motions or
stellar cores the different velocity gradients in the HNC and outflow.
HCO+ maps are real and are tracing different systematic mo- We identified 13 sources where the HCO+(1 − 0) and
tions.Oneofthesevelocitygradientscouldbeassociatedwitha H13CO+(1−0) linewidths could be measured and in Figure 4
7
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
we show the distribution of their δV parameter,with V and
thick
V beingdeterminedfromtheHCO+(1−0)andH13CO+(1−0)
thin
lines,respectively.WealsoestimatedthetypicalerroronδVand
then used the same ±5σ threshold as Mardonesetal. (1997)
δV
to excludethose sourceswhere the V differenceswere domi-
lsr
nated by measurementerrors. We estimated 5σ ≃ 0.4−0.6,
δV
thusin Figure4 a typicalvalue5σ ≃ 0.5is used.Onlythree
δV
coresshowasignificantblueshift(BLAST044,BLAST090and
BLAST093),andtwoaredshift(BLAST003andBLAST053).
FromtheredexcesscandidateswehavetoexcludeBLAST053
whichhasaweakandnoisyH13CO+(1−0)spectrum.
3.5.Derivationofmasses
From our spectralline data we can derive masses from the gas
column density, M , as well as virial masses, M , which we
cd vir
canthencomparewiththeBLAST-derivedmasses, M ,esti-
blast
matedfromthedustcontinuum.Clearly,whilethevirialmasses
refer to the total gas mass, with M we can only determine
cd Fig.4. HistogramofδV =(V −V )/∆V ,whereV and
the mass of a given molecular species. The total gas mass can thick thin thin thick
V weredeterminedfromtheHCO+(1−0)andH13CO+(1−0)
onlybedeterminedbyassumingspecificmolecularabundances; thin
lines,respectively.Theverticaldashedlinesindicatethe±5σ
or,alternatively,wecangiveacoarseestimateofthemolecular δV
level.
abundancebytakingtheratio M /M (seeSection4.1).The
cd blast
isotopologuesobserved by us, H13CO+ and H13CN, are gener-
allytooweaktoallowderivationofcolumndensitiesthroughout whereN (x,y)representsthecolumndensityinasinglepixel
mol i i
themaps,andthusweuseonlythemainmolecularspecies,at- (x,y) of the map, with n representing the total number of
i i pix
temptingtocorrectforfirst-orderopticaldeptheffects. pixels, and ∆Ω represents the solid angle covered by a sin-
pix
gle pixel. The map pixels selected are those that have an in-
tegrated intensity I ≥ σ , and also lie within an 1/e radius
3.5.1. Massderivedfromcolumndensity map
fromthecenterofa2DGaussianfittothecore,foreachspecific
The calculation of masses from the column density assumes molecule.Assumingthatalineisdetectedifatleasttwoadjacent
LTE and we determine the molecular gas mass integrating the velocitychannelslieabovethe3σrmslevelofthespectrum,then
moleculecolumndensityovertheextentofthesource.Thenwe wecalculatetheRMSoftheintegratedintensityinthemapsim-
canwrite: ply as σmap = 2(3σrms)∆v, where ∆v is the channelwidth. We
thusselectonlythosepixelsthatbelongto theactual“core”of
M =d2m N dΩ (2) the source,and removepixelsthatcome fromextendeddiffuse
cd mol mol
Z envelopes.TheresultingmassesarelistedinTable7.
where N dΩisthemoleculecolumndensityintegratedover
mol
theregRionenclosedbythechosencontourlevel,mmolisthemass 3.5.2. Virialmass
ofthespecificmoleculebeingconsidered,andd isthedistance
Wethenestimatethevirialmassofthecoresassumingtheyare
tothesource.ThecolumndensityN correspondingtoa J →
mol simplesphericalsystemswithuniformdensity(MacLarenetal.
J−1rotationtransitioncanbecalculatedas:
1988):
4.0×1012 E
N [cm−2]= Zexp J × M [M ]=210R [pc](∆V [kms−1])2 (6)
mol J2µ2[D]B[K] T ! vir ⊙ dec av
ex
η1mb1−τe−τ Z TA⋆dv[Kkms−1] (3) wtshuhemelrioenfeRtFhdeWectiHhseMtrhmeoadfletachnoednmvtouolrlvbeeucdulelsneotoucfrocmmeerpaaondnimuensatasssn:,dc∆alVcuavlarteepdreassetnhtes
where B denotes the rotational constant, E is the upper state
J
1 1
energy,µisthe dipolemoment(inDebye)andwe usedthe es- ∆V2 =∆V2 +kT8ln2 − (7)
cape probability τ/[1− exp(−τ)] to account for first-order op- av mol m m !
av mol
tical depth effects. The derivation of both T and τ has been
ex where ∆V is the line FWHM of the molecular transition
discussedinSection3.2.ForkT >> hBthepartitionfunction, mol
ex being considered and m = 2.3 amu is the mean molecular
Z,ofalinearmoleculeisgivenby: av
weight (with respect to the total number of particles), assum-
kT ing a mass fraction for He of 25%. We note that according to
Z = ex (4)
MacLarenetal.(1988),Eq.(6)mayleadtoamassoverestimate
hB
if the density distribution is not uniform. For example, in the
wherehandk arethePlanckandBoltzmannconstants,respec- caseofaspherewithadensitydistributionρ ∝ r−2 thenumeri-
tively.
calfactorinEq.(6)shouldbereplacedby126.
Eq.(2)isactuallyimplementedbywriting:
As the deconvolved source radius we used the BLAST-
derived values of Olmietal. (2009). We decided to use the
npix
M =d2m ∆Ω N (x,y) (5) BLAST sizes, to estimate the virial masses, instead of the
cd mol pix mol i i
Mopra-derived sizes for two main reasons: (i) the linewidths
Xi=1
8
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Table7.Massestimates.
Source# M b
cd
M M a N H+ HNC HCO+ HCN NH c
blast vir 2 3
[M ] [M ] [×10−9M ] [×10−9M ] [×10−9M ] [×10−9M ] [×10−7M ]
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
3 23.2 68.1 − − − − −
9 3.1 15.9 − 2.6 1.6 0.3 7.9
13 6.4 − − 3.7 7.6 3.5 −
14 7.7 8.9 − − − − −
24 98.0 87.3 5.4 25.7 54.1 17.8 5.8
31 4.0 26.4 − 0.02 2.3 0.6 31.8
34 4.6 − − 2.1 1.9 − −
38 2.2 32.4 − − − − −
40 6.3 11.3 0.13 4.9 13.9 2.5 2.1
41 2.8 10.8 − − 7.4 − 0.8
44 5.8 19.1 − − − − −
45 2.1 17.6 − − − − −
47 2.6 44.7 − 2.2 2.7 5.7 4.6
50 2.3 − − − 6.0 9.9 −
53 11.6 25.9 − − − − −
56 1.8 − − 0.1 1.5 0.6 −
57 14.0 27.0 − − 8.7 − −
59 1.8 17.5 − − − − −
63 13.4 64.6 1.5 4.7 10.3 8.3 9.0
77 3.7 12.3 − − − − −
81 69.9 88.8 2.2 13.4 40.4 14.2 0.6
82 16.5 42.2 2.4 8.1 29.8 4.2 1.4
89 2.4 − − − 6.7 − −
90 22.2 43.9 − − − − −
93 15.2 17.7 − − − − −
97 24.4 54.5 − − − − −
101 2.1 − − 1.0 3.5 0.9 −
109 1.0 − − − 0.9 − −
Notes. (a) M isdeterminedassumingauniformdensitysphericalsource. (b) M isdeterminedonlywhenaspectrallinemapwasavailable,
vir cd
withtheexceptionofNH . (c) M[NH ]islistedonlyforthosesourceswhereanestimateoftherotationaltemperature,T ,waspossible,and
3 3 12
whereanestimateofthesourcediametercouldbeobtainedfromatleastoneofthemoleculartracers.
aremostlymeasuredfromthesingle-pointspectraofNH , and
3
where NH was not observed or not detected we used the ob-
3
servationsofN H+,forwhichonlyafewmapswereavailable;
2
(ii) the BLAST mapsare not affected by spatial variationsthat
mayinsteadaffectspecificmoleculesandthuslikelygiveabet-
terrepresentationofthemassdistributionineachsource.
Aspreviouslystated,thelineFWHMiscalculatedfromthe
NH (1,1) single-pointspectra toward each source, if available,
3
orfromtheN H+(1−0)lineotherwise,sincethesemoleculesare
2
lesslikelytobeaffectedbydepletion,theytracethedensergas
andaremostlyopticallythin.Thelinewidthsdeterminedbythe
fitprocedureareartificiallybroadenedbythevelocityresolution
of the observations, and thus we subtracted in quadrature the
resolutionwidth, ∆V , from the observedline FWHM, ∆V ,
res obs
suchthat∆V = ∆V2 −∆V2 .
mol obs res
q
The resulting virial masses are listed in Table 7 and a plot
of the total core mass, M , as derived from BLAST, vs. the
blast
virial mass is shown in Figure 5. We note that nearly all of
the starless cores lie below the self-gravitating line, indicating
Fig.5. Totalcoremass,M = M ,vs.thevirialmass,M ,
core blast vir thattheyareunlikelytobegravitationallybound,whereasmore
calculated using the velocity linewidths of the NH (1,1) and
3 than half of the proto-stellar cores lie near or above that line,
N H+(1−0)transitions(see text).Yellow,filled squaresrepre-
2 confirming that they are gravitationally bound (about 30% of
sentproto-stellarcoresandred,filledtrianglesrepresentstarless
all sourceshave M /M > 0.5).However,as we mentioned
cores.ThesolidlineindicatestheminimumM =0.5M for core vir
core vir above,foranon-uniformdensitydistribution(seeSection3.6),
whichthecoresshouldbeself-gravitating.Individualvaluesof
e.g. of type ρ ∝ r−2, all virial masses should be multiplied by
M arelistedinTable7.
vir a factor 0.6. In this case, most of the proto-stellar cores would
moveabovetheself-gravitatinglineandalsomostofthestarless
9
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Fig.6. ExamplesofnormalizedradialprofilesforsourcesBLAST063(starless,toppanels)andBLAST082(proto-stellar,bottom
panels).Thepointsanderrorbarsrepresentthering-averagedintegratedintensityinthemolecularlines(fromlefttoright)N H+(1−
2
0), HNC(1−0), HCO+(1−0) and HCN(1−0). The black solid line representsthe fit obtainedusing Eq. (8). The red solid line
showstheradialprofileoftheaveragedBLASTintensityat250µm,andthegreensolidlinerepresentsthe3-mmbeamprofileof
theMopratelescope.Eachpixelcorrespondsto15arcsec.
Table8.Parametersforfittotheradialprofileofcolumndensity.
Source# N H+ HNC HCO+ HCN
2
R η R η R η R η
flat flat flat flat
[arcsec] [arcsec] [arcsec] [arcsec]
9 − − 67.5 1.2 15.0 0.3 34.5 0.9
13 − − 69.0 3.4 16.5 0.6 19.5 0.5
24 28.5 1.1 48.0 1.5 15.0 0.8 22.5 1.1
31 − − 37.5 3.3 27.0 1.8 15.0 0.4
34 − − 57.0 1.4 16.5 0.7 − −
40 27.0 2.7 45.0 1.0 16.5 0.3 16.5 0.2
41 − − − − 33.0 0.8 − −
47 − − 30.0 0.8 16.5 0.4 15.0 0.4
50 − − − − 15.0 0.3 18.0 0.6
56 − − 58.5 2.3 39.0 1.9 16.5 0.5
57 − − − − 20.0 0.6 − −
63 70.0 2.0 30.0 0.9 18.0 0.4 24.0 0.5
81 24.0 2.6 21.0 1.3 15.0 0.7 18.0 1.1
82Aa 31.5 2.4 22.5 0.7 16.5 0.5 21.0 0.5
82B 31.5 2.4 16.5 0.6 16.5 0.5 16.5 0.5
89 − − − − 36.0 1.1 − −
101 − − 22.5 0.7 27.0 1.2 33.0 1.6
109 − − − − 36.0 2.8 − −
Notes. (a) TheparametersforthetwospatialcomponentsinBLAST082arelisted.
coreswouldbelocatednearthatline(about60%ofallsources and that a central flattening is always needed to reproduce the
haveM /M >0.5inthiscase). data(e.g.,Tafallaetal.2002andreferencestherein).Amongthe
core vir
standardanalyticprofilesthatcombinethe power-lawbehavior
of column density for large radii r and a central flattening at
3.6.Radialprofilesofcolumndensity
smallr,isthefollowingfunction:
In orderto identifysignificantdifferencesin the distributionof
η
bothmoleculargasanddustcontinuum,wehavederivedradial N(r)= N Rflat (8)
profiles of the column density from both the BLAST maps at flat(R2 +r2)1/2
250µmandfromtheMopramapsoftheintegratedintensityof  flat 
the different molecular transitions. While the BLAST 500µm where the columndensity is approximatelyuniform,with N ∼
measurementswouldbesomewhatlessaffectedbyopticaldepth N ,forr≪R ,anditfallsoffasr−η forr≫R .
flat flat flat
effects, we have chosen to compare our molecular data to the Inthefitting procedurewe firstcircularlyaveragethemaps
BLAST 250µm measurements since they are closely matched of the integrated intensity of selected molecular transitions
totheMoprabeam. aroundthepeak,andthenuseaχ2routinetofitthecolumnden-
Previous work has shown that single-power-lawdensity, or sity profile,obtainedfromtheintegratedintensitywithEq.(3),
columndensity,profilesdonotfittheemissionfromdensecores using the model given by Eq. (8), after convolution with a 2D
10