Distance biases in the estimation of the physical properties of Hi-GAL compact sources-I. Clump properties and the identification of high-mass star forming candidates

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by  Adriano Baldeschi

MNRAS000,000–000(0000) Preprint30January2017 CompiledusingMNRASLATEXstylefilev3.0
Distance biases in the estimation of the physical properties
of Hi-GAL compact sources-I. Clump properties and the
identification of high-mass star forming candidates.
Adriano Baldeschi1,2 (cid:63), D. Elia 1, S. Molinari 1, S. Pezzuto 1, E. Schisano 1,
M. Gatti 3, A. Serra 4, M. Merello 1, M. Benedettini 1, A. M. Di Giorgio 1, J. S. Liu 1
1Istituto di Astrofisica e Planetologia Spaziali - INAF, Via Fosso del Cavaliere 100, I-00133 Roma, Italy
7 2Dipartimento di Fisica, ˆaA˘Y¨SapienzaaˆA˘Z´Universita` di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
1 3Institut de Fisica d’Altes Energies (IFAE). Edifici Cn, Universitat Autonoma de Barcelona (UAB), E-08193 Bellaterra (Barcelona), Spain
0 4IBM Italia - Via Sciangai 53, I-00144 Roma, Italy
2

n
a 30January2017
J

7
2 ABSTRACT
The degradation of spatial resolution in star-forming regions observed at large dis-
] tances (d (cid:38)1 kpc) with Herschel, can lead to estimates of the physical parameters of
A
the detected compactsources (clumps)which do notnecessarilymirrorthe properties
G
oftheoriginalpopulationofcores.Thispaperaimsatquantifyingthebiasintroduced
. intheestimationoftheseparametersbythedistanceeffect.Todoso,weconsiderHer-
h
schel mapsofnearbystar-formingregionstakenfromtheHerschel-Gould-Beltsurvey,
p
- and simulate the effect of increased distance to understand what amount of informa-
o tionislostwhenadistantstar-formingregionisobservedwithHerschel resolution.In
r the maps displaced to different distances we extract compact sources, and we derive
t
s theirphysicalparametersasiftheywereoriginalHi-GALmapsoftheextractedsource
a
samples. In this way, we are able to discuss how the main physical properties change
[
withdistance.Inparticular,wediscusstheabilityofclumpstoformmassivestars:we

1 estimate the fraction of distant sources that are classified as high-mass stars-forming
v objects due to their position in the mass vs radius diagram, that are only“false posi-
5 (cid:16) (cid:17)1.42
tives”.Wegivealsoathresholdforhigh-massstar-formation M >1282 r M .In
3 [pc] (cid:12)
0 conclusion, this paper provides the astronomer dealing with Herschel maps of distant
8 star-forming regions with a set of prescriptions to partially recover the character of
0 the core population in unresolved clumps.
.
1
Key words: ISM: clouds, stars: formation, infrared: ISM, methods: statistical.
0
7
1
:
v
i 1 INTRODUCTION (Elia et al. 2010; Veneziani et al. 2013; Beltra´n et al. 2013;
X Olmi et al. 2013; Molinari et al. 2014).
The impact of massive stars in the Milky Way is predomi-
ar nant with respect to low-mass stars: they produce most of Star forming regions observed in Hi-GAL span a wide
the heavy elements and energize the interstellar medium range of heliocentric distances (1 kpc (cid:46) d (cid:46) 15 kpc, Rus-
(ISM) through the emission of ultraviolet photons. There- seil et al. 2011; Elia et al. 2016), therefore the physical size
fore, understanding massive star formation is one of the of the detected compact sources (i.e. not resolved or poorly
mostimportantgoalsofmodernAstrophysics(see,e.g.,Tan resolved) could correspond to quite different types of struc-
et al. 2014). The Herschel infrared Galactic Plane Survey tures, depending on the combination of their angular size
(Hi-GAL,Molinarietal.2010),basedonphotometricobser- and distance.
vations in five bands between 70 and 500 µm, was designed ThesmallestanddenseststructuresintheISM,consid-
tostudytheearlyphasesofstarformationacrosstheGalac- ered as the last product of cloud fragmentation, then pro-
tic plane, with particular interest in the high-mass regime genitorsofsinglestarsormultiplesystems,arecalleddense
cores(D(cid:46)0.2pcBergin&Tafalla2007),whilelargerunre-
solved overdensities in Giant Molecular Clouds which host
these cores are called clumps (0.2 pc (cid:46) D (cid:46) 3 pc). In few
(cid:63) E-mail:[email protected] cases, very distant unresolved Hi-GAL sources may have a
(cid:13)c 0000TheAuthors
2 Baldeschi et al.
Figure 1.Original(a)andmoved(b-e)mapsofPerseusat250µm.Hereonlyafewofthesimulateddistancesareshown.
Figure 2. Perseus map at 250µm as it appears at the original distance (panel a) is the same as panel a) of Fig. 1 and how it would
looklikeatthedistanceof7kpc(panelb).Thislatterpanelhasbeenenlargedtomakethefigurehavethesamesizeofpanela).The
lossofspatialresolutionat7kpcisevident.
diameter D>3 pc (Elia et al. 2016), even fulfilling the def- Observationsathigher resolutionwouldbeneeded(for
inition of cloud. Correspondingly, other distance-dependent examplebymeansofsub-mminterferometry)tofullyresolve
sourceproperties,asmassandluminosity,arefoundtospan any individual clump identifying all its single components,
a wide range of values, from typical conditions of a core to but this would require very large observing programs with
those of an entire cloud. different facilities, to cover the entire Galactic plane.
Unfortunately, for distant sources Herschel is not able to To overcome empirically the lack of spatial resolution, we
resolve the internal structure and the contained population pursuedacompletelydifferentapproach,namelytoconsider
of cores (e.g. Elia et al. 2013), therefore only global and/or Herschel maps of nearby star forming regions and degrade
averagedparameterscanbequotedtodescribethephysical their spatial resolution to simulate the view of the same
conditions of the source and the characteristics of possible regioniflocatedatalargerheliocentricdistance.Weimple-
star formation ongoing in its interior. mentedthisideausingsomenearby(d<0.5kpc)molecular
MNRAS000,000–000(0000)
Distance bias affecting Hi-GAL source properties 3
clouds observed in the Herschel Gould Belt survey (HGBS, clump catalogue of the inner Galaxy (Elia et al. 2016) only
Andr´e et al. 2010), where the compact sources correspond 166 sources out of 36644 having a distance estimate are lo-
to dense cores. Obviously, these maps do not represent the cated at d < 500 pc. Furthermore, each HGBS region has
“reality”, in turn being those regions located at a heliocen- theadvantageofbeingself-consistentindistance,whichisa
tric distance of some hundred pc. However they constitute basicrequirementforourkindofanalysis.Insteadtheafore-
theclosest,thenbestresolved,availableviewofstar-forming mentionednearbyHi-GALsourcesaregenerallyfoundtobe
regions on which to base our analysis.“Moving away”these mixed, in the same maps, with sources belonging to other
regions to farther distances, we aim to understand not only distance components, which would represent an irreparable
how a region would appear if it were placed at a distance contaminationofourdataset.Ontheotherhandthedisad-
farther than the actual, but mainly at linking the physical vantage of using HGBS data consists of a limited statistics
propertiesofthecompactsourcesdetectedinthenewmaps duetolimitedmapsizeatthefurthestsimulateddistances.
with those of the underlying source populations present in HGBSobservationsweretakenat60(cid:48)(cid:48)/sinparallelmode
theoriginalmaps.Inthiswaywecanevaluatethedegreeof with the two cameras PACS (Poglitsch et al. 2010) and
informationlostasafunctionofdistance,inotherwordsthe SPIRE (Griffin et al. 2010): the observed wavelengths were
distance bias affecting the estimation of Hi-GAL compact 70 µm and 160 µm for PACS, and 250 µm, 350 µm and 500
source physical properties. To reach this goal, we probed a µm for SPIRE.
set of different simulated distances for each considered re- Maps were generated using the Unimap (Piazzo et al.
gion, and at each distance we repeated the typical proce- 2015)map-makerforbothinstruments.Theareaconsidered
dures applied to Hi-GAL maps for extracting the compact forourworkisthatcommontothePACSandSPIREfields
sources (e.g. Elia et al. 2013), treating the simulated maps of view.
asacompletelynewdataset,withnoreminiscenceeitherto We assumed the following distances to the selected re-
the original map or to those“moved”at other distances. gions:150pcand200pc(Comero´n2008)forLupusIVand
The first paper is organized as follows: in section 2.1 we III, respectively; 235 pc (Hirota et al. 2008) for Perseus;
present the regions of the Gould Belt survey that we use in 230 pc for Serpens (Eiroa et al. 2008), 415 pc for Orion A
thispaper,insection2.2wedescribetheprocedureof“mov- (Mentenetal.2007).ThedistanceoftheSerpensmolecular
ing away”the regions, and in section 2.3 we report how the cloud has been a matter of controversy: some authors place
detection and the photometry of the sources in all the pro- theSerpensmolecularcloudatapproximately400pc.Inap-
duced maps has been carried out. In section 3.1 and 3.2 we pendix C we discuss, briefly, how the physical properties of
describehowthenumberofdetectedsourcesandthefraction theSerpensmolecularcloudchangeifweassumeadistance
starless-to-protostellarchangeswithdistance.Insection3.3 of436pc(Ortiz-Leo´netal.2016).Theseregionswillbethe
we present the distribution of the size of the detected ob- subject of dedicated papers to be published by the HGBS
jects as a function of distance. Section 3.4 shows a proce- consortium: in this respect we stress that in this paper we
duretoassociatethesourcesdetectedatdifferentdistances. are not interested in deriving the physical properties of the
Section 3.5 describe describe uncertainties in the average sourcesatthenominaldistances,butwewanttoderivehow
temperature for protostellar and prestellar objects due to the intrinsic properties of the sources change with the dis-
distance effect Section 4 describes the distance bias in the tance. For this reason we do not provide any catalogue of
mass vs radius relation. A summary of main conclusions is cores.
reported in section 6. In a second paper we will discuss the
effects of the distance bias on the the luminosity vs mass
diagram and on the derived star-formation rate. 2.2 The simulation of increased distance
Themethodologyadoptedinthispapersimulatestheview,
throughHerschel,ofaregionoftheGould-Beltasifitwere
placed at a distance larger than the actual one. Of course,
2 OBSERVATIONS AND METHODOLOGY
thisprocedureimpliesalossofspatialresolutionanddetail
2.1 Observations and data reduction since the angular size of the moved maps (MM) decreases.
The pipeline adopted to obtain a MM is the following:
TheobservationsusedinthispaperweretakenfromtheHer-
schel (Pilbratt et al. 2010) Gould Belt survey (Andr´e et al. (i) Rescaling/rebinning the original map.
2010)forthestudyofnearbystarformingregions.Afullde- (ii) ConvolvingthenewrescaledmapwiththePSFofthe
scriptionoftheHGBSisgivenbyK¨onyvesetal.(2015).For instrument at the given wavelength.
this paper we concentrated on a few regions among those (iii) Adding white Gaussian noise to the map.
observed in the HGBS, namely: Orion A, Perseus, Serpens
In detail,
and Lupus III and IV.
(i) A structure of spatial size L placed at distance d sub-
We selected these regions both because they are close, 0
tendsanangleϕ = L,whileifthesameobjectismovedtoa
sothatwecanreasonablyassumethatmostofthecoreswe 0 d0
detect are not blended, and because they cover a range of distanced1>d0 itsangulardimensionbecomesϕ1= dL1 <ϕ0.
different core masses: Orion A is a high-mass star forming Therefore ϕ = ϕ d0, so an image rebinned by a factor d0
1 0d1 d1
region, Perseus is an intermediate-to-low mass star-forming mimics the movement of the region from d to d .
0 1
region,whileLupusandSerpensareforminglow-massstars. (ii)Toreproducemorerealisticallytheeffectofaregionob-
Other similar Herschel programs, such as HOBYS (Motte servedwithHerschel,therescaledmapmustbere-convolved
etal.2010)andHi-GALitself,observedfartherregions,for withthePSFoftheinstrument.However,onemusttakeinto
which confusion is an issue: for example, in the Hi-GAL accountthefactthattheoriginalmapalreadyresultsfroma
MNRAS000,000–000(0000)
4 Baldeschi et al.
convolutionoftheskywiththePSF,i.e.akernelwhichcan require a CuTEx set-up similar to the Hi-GAL one for the
be approximated with a Gaussian of width, θ , which is outerGalaxy.OrionAandPerseushavealargermedianflux
beam
equalto8.4,13.5,18.2,24.9,36.3arcsecat70,160,250,350, (∼ 70 MJy/sr) respect to the others. Furhermore Serpens,
500 µm, respectively (Molinari et al. 2016). So the width of Lupus III and IV have a median absolute deviation compa-
the kernel we use to re-convolve the map is: rable (∼11 MJy/sr) with the outer Galaxy regions such as
(cid:115) the 2◦×2◦ field centred at l ∼ 160◦, showing the lack of an
θconv= θb2eam1−(cid:32)dd0(cid:33)2. (1) extenTdheedrebfaocrekgwreouunsedd. theinnerGalaxysetupofCuTExfor
1
OrionAandPerseuswhileweusedtheouterGalaxysetup
(iii)Thenoiseinthemapscanbewellmodeledasacombi-
for Serpens, Lupus III and Lupus IV. The fluxes measured
nation of correlated noise (which is strongly attenuated by
withCuTExarethencorrectedwiththeproceduredescribed
themapmakingalgorithm,seePiazzoetal.2015)andwhite
in Pezzuto et al. (2012) to take into account for the fact
noise.Themaprescaling,ofcourse,reduceswhitenoisewith
√ that the instrumental PSF is not a Gaussian, while CuTEx
respect to the original map by a factor d /d . The sample
0 1 performs a Gaussian fit.
standard deviation of the noise in the original and rescaled
√ After the source detection and flux measurement in all
mapare s and s ( d /d ),respectively,thentorestorethe
N N 0 1 fiveHerschel bands,weselectthegoodcompactsourcecan-
noise level of the original map one has to add a white noise
didates(band-merging)byapplyingtheproceduredescribed
image to the rebinned map. In this noise image, each pixel
in Elia et al. (2010, 2013) as well as Elia et al. (2016). The
is the realization of a Gaussian process with 0 mean and a
√ bandmergingmakesitpossibletobuildtheSpectralEnergy
standarddeviationof s 1−d /d (tokeepinallthesimu-
N 0 1 Distribution(SED)ofthesources.ASEDeligibleforagrey
lated maps the same white noise level of the original one).
bodyfitmustsatisfythefollowingcriteria:1)atleastthree
The s was estimated in a box of the original map where
N consecutive fluxes between 160 and 500 µm, 2) showing no
no sources and quite low diffuse emission are found, and
dips (negative second derivative), 3) not peaking at 500µm.
therefore where the signal is essentially due to statistical
An additional issue in our case is that the absolute as-
fluctuation.
trometry of the MMs has no physical meaning because the
This procedure is applied to every map at each band.
rescalingoftheimageshrinkstheirsize.Inthebandmerging
Wedecideto“move”themapsofeachregionforeachbandto
procedure we take care of this issue, to ensure that the co-
thefollowingvirtualdistances:0.75,1,1.5,2,3,5and7kpc.
ordinates of the detected sources, at different wavelengths,
Fig.1showstheoriginalandMMsofthePerseusnebulaat
are consistent with each other.
250µm while in the Appendix A the maps of the remaining
We address this issue as follows: the function that we
regions are shown. Fig. 2 displays how the MM of Perseus
used to execute the band merging works with Equatorial
lose detail at increasing distance, and correspondingly, how
coordinates. For this reason we had to perform the band
sources resolved at the original distance become unresolved
merging considering the pixel coordinates and the angular
at large distances.
extentoftheobjectsintheMMs,thenrescaledthemtothe
original map and then finally convert them into the equa-
torial system. With these quantities it is finally possible to
2.3 Source extraction and catalogue compilation
perform the band merging.
The detection and photometry of compact sources on the This procedure is repeated for all maps at each wave-
original and moved maps is carried out with CuTEx (Cur- length. Once the SEDs are built, it is possible to perform a
vature Thresholding Extractor, presented in Molinari et al. modifiedblackbody(hereaftergrey-body)fit(e.g.Eliaetal.
2011). This algorithm detects the sources as local maxima 2010) described by the equation:
in the second derivative images and then fits an elliptical M (cid:32)ν(cid:33)β
Gaussiantothesourcebrightnessprofiletoestimatethein- Fν = d2k0 ν Bν(T), (2)
tegratedflux.Themainoutputparametersofthefitare:the 0
peak position, the minimum and maximum FWHM (φmin, where Fν is the flux at frequency ν; M is the mass of the
φflmuaxx.)Soifnctheeinfitthtiinsgpaepllieprswe,etihnetepnedaktoflturexaatntdhethmeovinetdegrreagtioedn sqouuerncceyloνc0.atWedeaatdothpetdk0is=ta0n.c1ecdm,2k0g−is1tahteνo0p=ac1i0ty00atGtHhze(fir.ee-.
ateachsimulateddistanceasanindependentdataset,tobe λ0=300µm,Beckwithetal.1990); Bν(T)isthePlanckfunc-
analysed according to typical procedure applied to Hi-GAL tion at the temperature T. We fixed β to 2 as in Elia et al.
fields(e.gEliaetal.2016),werunCuTExonallthemapsat (2013). The flux at 70 µm, where present, is not considered
each simulated distance for each region. Depending on the for the fit since it is mostly due to the protostellar content
brightness level of the region, we adopted a CuTEx set-up ofaclump,ratherthanitslarge-scaleenvelopeemittingasa
moresuitablefortheinnerGalaxy(Molinarietal.2016)or grey-body(Eliaetal.2013).Inthiswayweobtainestimates
fortheouterGalaxy(Merelloetal.,inprep).Regionsinthe oftemperatureandmassforeachsourceinboththeoriginal
outer Galaxy have in general a lower median flux per map and moved maps.
with respect to the inner part, due to much lower back-
ground emission. Moreover the detection of sources in the
outer Galaxy is more sensitive to pixel-to-pixel noise. For 3 DISCUSSION OF DISTANCE BIAS
maps in the outer Galaxy, the CuTEx set-up also includes
3.1 Number of sources as a function of distance
the smoothing of the PACS image and a lower detection
threshold for SPIRE and PACS 160µm. We therefore made The amount of objects detected by CuTEx in Herschel
a check on our set of HGBS maps to ascertain which ones maps is expected to decrease whith increasing simulated
MNRAS000,000–000(0000)
Distance bias affecting Hi-GAL source properties 5
distance (for each band). In this section we analyse this
Table 1.Valuesoftheslopeδofthepowerlawrelationbetween
effect from a quantitative point of view. Notice that, since thenumberofsourcesandthedistance.Uncertaintyonthevalues
in this section we study each band separately, not all the ofδisalmostalways0.1(seeFig.3).Thevaluesofδforthe70µm
sources discussed here constitute a regular SED as those band for Lupus III and Lupus IV are not very reliable since the
considered in the following sections. numberofdetectedsourcesisverylow.
Thedecreaseofthenumberofobjectswithdistance(see 70µm 160µm 250µm 350µm 500µm
Fig.3)isduetotwomaincombiningeffects.Thefirstoneis
Perseus 1.3 1.1 1.5 1.7 1.7
related to the decrease of the flux with distance (F ∝d−2):
λ Orion 1.4 1.4 1.5 1.7 1.7
if the flux goes below the sensitivity limit at a given band LupusIII 0.9 1.3 1.5 1.6 1.5
the source is not detected any more. The second one is due LupusIV 0.9 1.5 1.6 1.7 1.5
to blending of sources that are close to each other in the Serpens 1.1 1.6 1.8 1.9 1.9
original map and hence are not resolved any more at larger
distances.Theblendingeffectmayalsopreventlosingsome
sources(sincethefluxisanadditivequantity)thatwouldbe Certainly Equation 4 requires to confirmation by in-
undetected when their flux would be below the sensitivity dependent observational evidence, such as interferometric
limit. measurements aimed at exploring the real degree of frag-
In principle since the flux decreases quadratically with mentation of clumps.
distanceandsinceinalog-logplot,datashowsaremarkable
linear correlation, we fit a power law to the data:
N (d)∝d−δ, (3) 3.2 Starless and protostellar fraction vs distance
s
where N is the number of sources at distance d. The best- After assembling the SEDs the sources are classified as fol-
s
fitting power-laws with the corresponding values of the δ lows: if a 70µm counterpart is present, the source is clas-
exponent are shown in Fig. 3 and reported in Table 1. This sified as protostellar candidate (e.g. Giannini et al. 2012),
exponent is smaller for the 70µm and 160 µm bands and is hereafter protostellar, otherwise it is considered a starless
found generally to be between 1 and 1.9. If we assume that object. The starless sources can be further subdivided into
the decreasing of sources is due to the decrease of the flux bound (objects that can form stars and which are usually
with distance, and assuming a power-law relation between calledprestellar)orunbound(transientobjectsthatwillnot
the number of detected sources and the flux (N ∝ F−η) it form stars) whether their mass is larger or smaller, respec-
s λ
turnsoutthat N(d)∝d2η−2.Togetthevalueofη,wefitthe tively,thanthemassgivenbytherelationofLarson(1981)
s
distribution of the fluxes, for the different regions at 70 µm.
We find that 2η−2 is equal to 1.6, 1.0 and 1.0 for Orion (cid:32) r (cid:33)1.9
A, Serpens and Perseus respectively. There sample is too M =460 M . (5)
Lars [pc] (cid:12)
smallfortheLupusIIIandIV.Wedidthisanalysisonlyat
70µm because in the other bands the effects of the blending We define the starless and protostellar fraction as n /n
sl
are more prominent. These values are in good agreement and n /n, respectively, where n and n are the number
pro sl pro
with the values of δ in table 1, considering that we make of starless and of protostellar sources respectively and n =
the simple assumption that the distribution of the fluxes is n +n isthetotalnumberofsources.InFig.4weshown /n
sl pro sl
a power-law. andn /nwhileinFig.5weshown andn asafunctionof
pro sl pro
Knowingtheslopeδcanturnouttobeveryinteresting distance, respectively. The general trend for n /n in Orion
pro
for practical purposes, as shown by the following example: A, Perseus and Serpens is to increase with distance until it
suppose we detect N objects at a certain wavelength in a reaches a plateau. A different behaviour is found in Lupus
Hi-GALregionlocatedatadistanced>1kpc;itispossible III, where n /n decreases and in Lupus IV where n = 0
pro pro
to obtain an estimate of the number of“real”sources (at a to all moved distances due to the complete lack of detected
specificband)thatonewouldexpecttoobserveifthecloud protostellar sources.
was located at a distance d0<d, using the formula: The increase of npro/n with distance is explained with
(cid:32)d (cid:33)δ thefactthatasourcedetectedatalargerdistanceisanun-
N =N . (4) resolved object that probably contains multiple cores (pro-
0 d
0 tostellarbutalsostarless).Supposetherewereanunresolved
Acriticalpointisrepresentedbythechoiceofd ,which source,classifiedasprotostellar,detectedatasimulateddis-
0
can lead to quite different values of N . We suggest using tanced ,andactuallycontainingacertainamountofsources
0 1
valuesintherange200pc<d <400pcsincethiscorresponds attheoriginaldistanced ,andsupposethatoneofthemisa
0 0
to compact source scales typical of cores. For example, let protostellarandtheremainingonesarestarless:inthatcase
us consider a star-forming region located at d = 5000 pc, one would assign a protostellar character to a source which
whoseHi-GALmapat250µmcontains20sources:howmany actually contains also a certain number of prestellar cores.
sources we would see if the region was located at d = 300 Thissimpleexamplesuggesttousthatinprinciplen /nis
0 pro
pc? Using equation 4 we can give a rough estimate of this expectedtoincreasewithdistance,aslongasn /nreaches
pro
number assuming δ = 1.6 (see Table 1) namely N = 1802. a plateau where the number of detected objects is very low
0
Applying instead equation 4 to a larger d (e.g. d > 1000 due to of the sensitivity effect. The decrease of n /n with
0 0 pro
pc) would imply to deal with clumps also at the original distance found for Lupus III and IV may, instead be due
distance (i.e. with still unresolved structures). to a weak emission at 70 µm at the original distance, which
MNRAS000,000–000(0000)
6 Baldeschi et al.
Figure 4.Fractionofstarlessandprotostellarobjects(nsl/nand
npro/n)asafunctionofthedistanceforthefiveconsideredregions
respectively.
Figure 5. Number of starless and protostellar objects (nsl and
npro)asafunctionofthedistance.
leadstoadecreaseinthenumberofprotostellaratthelarger
virtual distances (Fig. 5).
Ragan et al. (2016) found that the behaviour of n /n
pro
as a function of the heliocentric distance, in the Hi-GAL
catalogue (Molinari et al. 2016), is in agreement with that
wederivedfromFig.4.Indeedtheyfoundthatn /ngrows
pro
upto2kpcandthenn /nreachesaplateau.IntheirFig.4
pro
theyfoundthatn /n(cid:46)0.2upto2kpcbuttheorderof0.2
pro
forlargerdistances.Thissignificantlysupportstheresultwe
obtained here.
3.3 Size distribution vs distance
A common feature of molecular clouds is the hierarchical
structure they show, containing bright agglomerates called
clumps, that in turn are formed by smaller condensations
called dense cores (see section 1). In Fig. 6 the distribution
of the radii (at 250 µm) of the detected sources is shown,
Figure 3. Number of sources detected by CuTEx at various
bands for each region as a function of the virtual distance at for the Perseus and Orion A maps, at different distances.
which the map is moved. The power-law exponents δ estimated We do not show the same for the Lupus III, Lupus IV and
throughthebestfitarereportedintheupperrightcornerofeach Serpensduetopoorstatistics.Asonecanseefromthesefig-
panel.
MNRAS000,000–000(0000)
Distance bias affecting Hi-GAL source properties 7
ures,thephysicalradiusincreasesonaverage,andhencethe
fraction of cores in the overall population of detected com-
pactsourcesdecreaseswithdistance.Asitemergesfromthis
figure, up to d = 1000 pc most of the detected sources are
classified as cores, while at larger distances they are gener-
ally classified as clumps. Of course the threshold r(cid:46) 0.1 pc
is not so strict and the transition between core and clump
definitionisnotsosharp.Furthermore,adifferenceisfound
between the prestellar and protostellar source distribution:
the former is characterized on average by larger radii than
thelatter,asfound,e.g.,byGianninietal.(2012).InFig6
thebehaviouroftheaverageradiusforeachofthetwopopu-
lations is also reported (top right corner): that of prestellar
(cid:68) (cid:69) (cid:68) (cid:69)
objects R is larger than R for protostellar sources,
pre pro
but this gap appears to get smaller at larger distances. If
(cid:68) (cid:69) (cid:68) (cid:69)
we define q such that R =q R , q is found to be 0.68,
pro pre
0.77, 0.88, 0.89 and 1.08 for the Perseus region at 235, 750,
1000, 1500 and 2000 pc, respectively, while q is 0.82, 0.92,
0.89,0.89and0.95fortheOrionAregionat415,750,1000,
1500 and 2000 pc, respectively.
3.4 Association of the“moved”sources with the
original ones
In section 3.3 we have seen that for d (cid:38) 1.5 kpc the source
sizes are such that the objects are classified as clumps. For
furtheranalysisitbecomesimportanttoidentifyandcount
the cores present in the original map that are contained in
clumpsfoundintheMM.Thisinformationcanbeused,for
example, to estimate which fraction of mass of such clumps
comes from the contained cores, and what comes from the
diffuse “inter-core” material. To associate the sources de-
tected at a given distance d with the original population
of objects, we projected the ellipse, found at 250 µm at dis-
tance d, back to the original distance d , and consider the
0
sources falling within such ellipse: an example is shown in
Fig.7.Atthispointitispossibletoassociatethesourcesof
the moved map and those of the original one in two ways:
1) by doing band-specific associations, including those
without regular SEDs. For example, suppose to consider
an object, detected at 250µm at 5 kpc and then count the
sources that, in the map corresponding to the original dis-
tance and to the same band, lie inside the area occupied
by this object. 2)Association using only sources with regu-
lar SEDs. As an example, let us suppose there is a clump
with a regular SED at 5 kpc and then count the number of
coreswitharegularSEDthatarecontainedintheclump,in
theoriginalmap.Thisassociationbetweenaclumpandthe
contained cores is very useful because one can decompose
an unresolved object (clump) into its smaller components
(cores). Therefore, from a practical point of view, this cor-
responds to observing an unresolved object with a higher
resolution and hence revealing its internal structure. Figure 6. Radii distribution of the protostellar and prestellar
Theformerapproachwillbeusedinsection3.4.1where sourcesfordifferentdistancesfortheOrionAandPerseusregions.
wediscussthecontributionofthediffuseemissionseparately The vertical magenta line represents the separation between the
forthevariousdifferentwavelengths,whilethelatterwillbe cores/clumps according to the classification of Bergin & Tafalla
used both in the following and in section 3.4.2, where we (2007), namely Rsep = 0.1 pc. The values of the mean radius for
all regions at each simulated distance are also reported. Dashed
will discuss the relation between the physical properties of
histogramrepresentsthedistributionoftheradii,intheoriginal
the moved sources and the original core population.
map, for Perseus if it was located at an original distance of 415
Fig. 8 shows the average number of cores (cid:104)N(cid:105), at the
pc(sameasOrionA)insteadof235pc(seeappendixC).
originaldistance,thataremergedintoonesinglesourcewith
MNRAS000,000–000(0000)
8 Baldeschi et al.
Figure 7. Example of association between a source detected in
amovedmapandthepopulationofcorespresentintheoriginal
map. A portion of the original Perseus map at 250 µm is shown,
withblueellipsesrepresentingthesourcesdetectedwithCuTEx.
The magenta ellipse represents a source detected in the MM at
5kpcandprojectedontotheoriginalmap.
aregularSED,atthemoveddistances.Asonecanseefrom
this figure, (cid:104)N(cid:105) increases slowly, with distance, up to 1500
pcandthentendstoincreasefaster.Wefitthedatawitha
powerlaw(cid:104)N(cid:105)∝dζ,startingfrom1500pcandwefindvalues
forζ between1and1.5forthedifferentregions.Theslower Figure 8. Average number of cores that are contained within a
increaseof(cid:104)N(cid:105)atsmallerdistancesissimplyduetothefact clumpatthemoveddistancesforeachregion.Thebestpower-law
thatthesizesoftheobjectsintheMMsaremoresimilarto fit is plotted as a dashed line, and the corresponding exponent,
the sizes of the original cores. estimatedfromd≥1500pc,isalsoreported.Greendashedthick
line:areferencepowerlawwithexponent2.
Moreover,thevaluesofζarealwayssmallerthan2,that
istheexpectedvalueifthedistributionofcoresinthemaps
wasuniform.Since,ontheotherhand,theactualcoredistri- original map, and F = (cid:80)n f the sum of the flux of the
bution is far from being uniform, but rather it is clustered, λ∗d i=1 λi
sourcesthatarewithinthemovedsourceattheoriginaldis-
it is reasonable to find values of ζ <2.
tance. Fig. 9 shows F vs F for different regions at each
The values of (cid:104)N(cid:105) depend both on the original average λ(d) λ∗d
wavelength:itappearsthat,asexpected,thecontributionof
surface density Σ (measured as the number of sources per
the diffuse emission F -F increases with distance. This
pc2) of the core population, and on the minimum spatial λ(d) λ∗d
is not surprising since the objects in the map are patchily
scalepresentintheoriginalmaps.Thelattereffectexplains,
distributed (see Fig.7) and since the size of the sources in-
forexample,whythevaluesof(cid:104)N(cid:105)intheOrionAaresmaller
creaseswithd(seesection3.3).Astheradiusbecomeslarger,
than in the other regions: the spatial detail corresponding
the contribution of the diffuse inter-core emission, which is
to the Herschel resolution in Orion A is coarser than in
expected to be more uniformly distributed, increases quite
Lupus,SerpensandPerseusduetothelargerdistance.The
regularlywiththeincreasingareaofthesource(inaddition
former effect, is instead, related to Σ which is 93.0, 56.4,
to this, an increasing amount of background emission is in-
50.4,39.7,129.8pc−2 forOrionA,Perseus,LupusIII,Lupus
cluded in such flux estimate, as shown at the end of this
IV and Serpens, respectively. Considering two regions with
section through Fig. 11). On the contrary, the contribution
comparable original distance, namely Serpens and Perseus,
ofemissionfromcoresincreaseswithdistancedependingon
this effect can be appreciated, since Σ is larger in Serpens
the degree of clustering.
and,correspondingly,larger(cid:104)N(cid:105)aresystematicallyfoundfor
Figure.10showstheaveragefractionofthediffuseemis-
Serpens than for Perseus. (cid:68) (cid:69)
sion (cid:15) = (F −F )/F vs distance. As one can see
λ(d) λ(d) λ∗d λ(d)
from this figure, the contribution of the diffuse emission at
70 µmislowerthanatlargerwavelengthsforalltheconsid-
3.4.1 Diffuse emission
eredregions;thisisduetothefactthatthe70µmemissionis
Afirstcomparisonbetweenthepropertiesofthesourcesde- typicallyassociatedwithprotostellaractivity(e.g.Dunham
tected in the MM and those of the sources at the original et al. 2008; Elia et al. 2013) and is therefore more concen-
distance that are within the rescaled object can be carried tratedincompactstructuresthantheemissionintheother
out looking at the total fluxes. We perform such analysis bands, which appears instead arranged in a diffuse network
separatelyateachwavelength,thereforewealsoincludede- of cold filaments. Furthermore, (cid:15) increases with distance
λ(d)
tectionsthatdonotcontributetobuildregularSEDs.There- up to a certain point, which depends on the region, after
fore we associate sources through the method 1) described which it tends to reach a plateau. In conclusion this analy-
in section 3.4. Let F the flux of a source detected in a sissuggeststhatthecontributionofthediffuseemissionfor
λ(d)
MM at a wavelength λ and at distance d rescaled to the large distances (d (cid:38) 1 kpc), i.e. a typical case for Hi-GAL
MNRAS000,000–000(0000)
Distance bias affecting Hi-GAL source properties 9
sources,goesfrom50%upto95%(dependingontheregion) 3.4.2 Physical properties of the“moved”clump and those
exceptforthe70µmbandwhereitgoesfrom50%upto80% of the original core population
(see Fig. 10). These large values of (cid:15) suggest that most
λ(d) In this section we consider the mass of those sources of the
of the clump emission is due to the diffuse inter-core emis-
MM for which we performed the grey-body fit, to under-
sion when the clump is located far away (d ≥ 1 kpc). This
stand how these quantities for a moved source mirror those
hastobetakenintoaccounttodistinguishthewholeclump
of the original core population rather than those of the dif-
mass from the fraction of it contained in denser substruc-
fuse material. We define with M the mass of the moved
tures, possibly involved in star formation processes. Such d
detected sources (protostellar and prestellar) at distance d,
behaviour can not be simply explained with the increasing and with M = (cid:80)n m the sum of the masses of all the
physicalsizeofthesource,butitmustbetakeintoaccount ∗d i=1 id
originalsources(protostellarandstarless)thatlieinsidethe
how the background level estimate changes with distance.
source when it is reported in the original map. Figure 12
Indeed we expect that the background level for the sources
showstheaveragevaluesof M vs M atdistanced:wefind
detected in the original map is higher than that generally d (cid:68) ∗(cid:69)d
that (cid:104)M (cid:105) is always larger than M . A similar conclusion
foundinthemovedmaps,sincethebackground,intheorig- d ∗d
canbeobtainedifoneusesthemedianstatistics,insteadof
inalmap,isduetotheinter-coreemission,whileintheMM
themean:themedianmassoftheclumpsatlargedistances
it is the weaker cirrus emission on which the entire clump
isbyfarlargerthanthesumofthemassesofthecontained
lies.
cores, as weel.
SinceCuTExderivesthefluxofasourcebyfittinga2-
DGaussianwiththeformula F =4.53abF ,whereaandb We want to know the effect of distance on the deter-
λ p mination of the core formation efficiency. The average core
arethesemi-axesathalfmaximumoftheellipticalGaussian (cid:68) (cid:69)
formation efficiency, that we define as (cid:104)CFE(cid:105) = M /M ,
andFp isthepeakfluxmeasuredinMJy/sr,withincreasing can be derived from the values plotted in Fig. 12 (pa∗ndel ad).
distance, a and b are constrained to have physical plausible
InFig.13weshow(cid:104)CFE(cid:105)asafunctionofdistanceforeachof
size as in general is done with the extraction tool, so the
theconsideredregions.Itcanbeseenthatthe(cid:104)CFE(cid:105)changes
physical area we use to scale F increases quadratically, on
λ from region to region and tends to decrease with d for dis-
average.Moreoverthebackgroundlevelisgenerallyexpected
tances below 1500 pc while, at large distances, it becomes
to be estimated lower and lower (see above), producing an
independent of d. The decrease of the (cid:104)CFE(cid:105) with d below
increaseofF .Toshowthat,wecomputedthemeanvalueof
p 1500 pc is due to the fact that the size of the clumps and
thebackgroundandofF foralltheregionsmergedtogether
p thecontainedcoresarequitesimilarandhencethefraction
asafunctionofdistance:inFig.11thebackgroundisfound
of diffuse material remains low. In fact, this effect is partic-
on average to become smaller with d, and correspondingly
ularly prominent in Orion A, because it is located at 415
F becomes larger.
p pc while we do not see this effect in the Lupus IV which is
Therefore, the derived values of (cid:15) may be explained
λ(d) locatedat150pc.Thevaluesofthe(cid:104)CFE(cid:105)atlargedistances
roughly with the following considerations: the value of (cid:15)
λ(d) are between 1% and 20%, depending on the region.
for one source can be modeled by the formula
(cid:80)N abF 3.5 Mean temperature vs Distance
(cid:15) =1− i=1 i i pi (6)
λ(d) abF Let us consider now the effects of the distance on the mean
p
temperature of the sources detected in each region at all
virtual distances, comparing it with the temperature of the
where a, b, F are the parameters of the objects in the originalpopulationofcoresthatfallwithineachclump.We
i i pi
original map that are contained within a larger object at fit the average temperature with a power-law
the moved distance d having a, b, Fp parameters in turn. (cid:104)T(cid:105)d∝dξ .Theuncertaintiesof(cid:104)Td(cid:105)aregivenby S√Tnd,where
Theproductabisproportionaltothesquareofthedistance S is the sample standard deviation of the temperature at
and we roughly assume that the peak flux of the sources diTsdtance d, and n is the sample size. Fig. 14 shows (cid:104)T (cid:105) for
d
at the original distance is the same for all sources. The each d together with the best power-law fit and the val-
peak flux Fp is weakly dependent on distance (Fig. 11): on ues of ξ. We find that (cid:104)T(cid:105)d increases slowly with distance
one hand, the dramatic drop of the background emission for the prestellar objects while it decreases slowly for the
at increasing distance should be expected to produce cor- protostellar ones. The values of ξ for the prestellar objects
respondingly, by subtraction, a strong increase of Fp. How- (see Fig. 14, lower panel) are 0.06, 0.03, 0.2, 0.04, 0.05 for
ever this is not observed mostly due to the fact that the Perseus, Orion A, Lupus III, Lupus IV and Serpens respec-
distance increase implies the averaging of boxes of pixels tively.Theseslopesareveryshallowbutarepositiveanyway.
implied by the map rebinning we impose to simulate the Anoppositetrend(i.e.temperatureweaklydecreasingwith
distance effect. In particular we find that Fp at the largest distance) is found for the protostellar objects: the values of
probed distance is at most 1.5 times the average peak flux ξ are -0.1, -0.02 and -0.1 for Perseus, Orion A, and Serpens
for smaller distances, therefore adopting this value we get respectively. The statistics are not sufficient at large dis-
that (cid:15) =1−(cid:16)d0(cid:17)2N(d)/1.5 where N is the number of con- tancetoperformthefitfortheLupusIIIandIVregions.It
λ(d) d
tained sources within the moved source. For example, if we appears unlikely that both of those behaviours are due by
consider the Perseus region observed at 250 µm at 5000 pc chance, since we systematically find these trends in all the
assuming N(d)=22 (as in Fig. 7), we get (cid:15) =0.97, which considered regions.
λ(d)
isingoodagreement,despitethenaivetyofthemodel,with Wearequiteconfidentthatthedecreasingbehaviourof
the result of Fig. 10, namely (cid:15) =0.9. temperature for the protostellar sources and the increasing
λ(d)
MNRAS000,000–000(0000)
10 Baldeschi et al.
Figure 9. Flux of a source in the MM (Fν(d)) vs the sum of the flux Fν∗d of the sources in the original map that are within the moved
source.ThecolumnscorrespondtofivedifferentHerschelbands,whiletherowscorrespondtothefiveconsideredregions.
one for the prestellar ones is due to the effect of confusion contained in protostellar clumps (for all the regions merged
and can be possibly explained by taking into account two together).Theprestellarcontamination,asexpected,isclose
main factors likely to be concomitant in most cases. to 0 up to 1000 pc and then starts to get larger, in particu-
larbetween5000and7000pctheaveragenumberoforiginal
The first is related to the fact that the protostellar ob-
prestellar cores contained in the protostellar moved clumps
jectsaretypicallywarmerthantheprestellarones(e.g.Elia
becomes the same as the original protostellar objects. On
etal.2013).Aprotostellarclumpdetectedatalargedistance
the other hand, if we take an unresolved prestellar clump
is probably an unresolved object containing in turn some
at large distance this can contain some protostellar cores,
smallerobjectsthatcanbestarlessorprotostellar.Ifinside
whosefluxat70µmgoesbelowthesensitivitythreshold(and
the unresolved protostellar clump there are some prestellar
hencenotdetected),thatcancontributeanywaytoincrease
onesthiscandecreasetheglobalaveragetemperature.Inthe
the average temperature. Indeed, although the signature of
lowerpanelofFig.15weshowtheprestellarcontamination
the presence of a protostellar component would remain un-
of sources, namely the average number of prestellar cores
MNRAS000,000–000(0000)