A possible far-ultraviolet flux-dependent core mass function in NGC 6357
J. Brand, A. Giannetti, F. Massi, J.G.A. Wouterloot, C. Verdirame
AAstronomy & Astrophysics manuscript no. Brand_AA_2020_39506_final © ESO 2021February 11, 2021
A possible far-ultraviolet flux-dependent core mass function inNGC 6357 (cid:63)
J. Brand , A. Giannetti (cid:63)(cid:63) , F. Massi , J.G.A. Wouterloot , and C. Verdirame INAF - Istituto di Radioastronomia & Italian ALMA Regional Centre, via P. Gobetti 101, 40129 Bologna, Italye-mail: [email protected] INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy East Asian Observatory, 660 N. A’ohoku Place, Hilo, Hawaii 96720, USA Dip.to di Fisica e Astronomia, Università di Bologna, via P. Gobetti 93 /
2, 40129 Bologna, ItalyReceived date; accepted date
ABSTRACT
Context.
NGC6357 is a galactic star-forming complex ( d ∼ . ii regions, a few young stellar clusters,and giant molecular clouds. In particular, the H ii regions G353.2 + + + Aims.
We aim to derive the properties of the densest compact gas structures (cores) in the region as well as the e ff ects of an intensefar-ultraviolet (FUV) radiation field on their global properties. Methods.
We mapped the NGC6357 region at 450 and 850 µ m with SCUBA-2 and in the CO(3-2) line with HARP at the JCMT. Wealso made use of the Herschel Hi-GAL data at 70 and 160 µ m. We used the algorithm Gaussclumps to retrieve the compact coresembedded in the di ff use sub-millimetre emission and constructed their spectral energy distribution from 70 to 850 µ m, from which wederived mass and temperature. We divided the observed area into an ’active’ region (i.e. the eastern half, which is exposed to the FUVradiation from the more massive members of the three clusters) and a ’quiescent’ region (i.e. the western half, which is less a ff ected byFUV radiation). We compared the core mass functions and the temperature distributions in the two areas to look for any di ff erences thatcould be due to the di ff erent levels of FUV radiation. Results.
We retrieved 686 dense cores, 411 in the active region and 275 in the quiescent region, with an estimated mass completenesslimit of ∼ (cid:12) . We also attempted to select a sample of pre-stellar cores based on cross-correlation with 70 µ m emission and red WISEpoint sources, which unfortunately is biased due to distance, emission at 70 µ m from the dust on the surface of the cores that is heated bythe FUV radiation, and saturation in the WISE bands. Most of the cores above the mass completeness limit are likely to be gravitationallybound. The fraction of gas in dense cores is very low, 1 . M / M (cid:12) ) ∼ a × log( D / arcsec), with a inthe range 2 . .
4, depending on the precise selection of the sample. The temperature distributions in the two sub-regions are clearlydi ff erent, peaking at ∼
25 K in the quiescent region and at ∼
35 K in the active region. The core mass functions are di ff erent as well,at a 2 σ level, consistent with a Salpeter initial mass function in the quiescent region and flatter than that in the active region. Thedense cores lying close to the H ii regions are consistent with pre-existing cores being gradually engulfed by a photon dominated regionand photoevaporating. A comparison of the obtained distribution of core masses with those derived from simulations of cloud-cloudcollisions yields no conclusive evidence of ongoing cloud-cloud collisions. Conclusions.
We attribute the di ff erent global properties of dense cores in the two sub-regions to the influence of the FUV radiationfield. Key words.
Stars: formation – Submillimeter: ISM – ISM: structure – ISM: HII regions – ISM: individual objects: NGC6357 – Stars:massive
1. Introduction
The ionising radiation of early type (massive) stars generates aphoton dominated region (PDR) where it hits a nearby molecu-lar cloud. Molecular clouds are complex entities, having a self-similar structure over a wide range of scales (e.g. Ossenkopf et al.2007). With increasing spatial resolution molecular clouds ap-pear fragmented in substructures of smaller angular dimensions.Hence, the molecular material is typically very clumpy, imply-ing that a large part of the molecular cloud can be exposed tofar-ultraviolet (FUV) radiation (6 < h ν < . (cid:63) Table 2 is only available in electronic form at the CDS via anony-mous ftp to cdsarc.u-strasbg.fr(130.79.128.5) or via http: // cdsarc.u-strasbg.fr / viz-bin / qcat?J / A + A / ..... (cid:63)(cid:63) Present address: Energy Way s.r.l., Modena, Italy; [email protected] penetrate much deeper than if the cloud were homogeneous, mak-ing the PDR volume vastly larger. The radiative and mechanical(winds) action of massive stars can evaporate existing structures,but it may also trigger the formation of a new generation of starsin the surrounding material, for example through radiation-drivenimplosion (RDI; see e.g. Bisbas et al. 2011).The importance of gas fragmentation in star-forming regionshas been reinforced by the discovery that the smallest ( ∼ . > ∼ − cm − ), named cores, insidegiant molecular clouds follow a well-defined mass distribution(core mass function: CMF) resembling the stellar initial massfunction (IMF; see Rathborne et al. 2009; Ikeda & Kitamura2009; André et al. 2014a and references therein). We note thatcores are embedded in molecular clumps, which are larger (0 . − − cm − ) gas concentrations (see e.g. Article number, page 1 of 16 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. Brand_AA_2020_39506_final
Bergin & Tafalla 2007). Although the link between the CMF andthe IMF is still debated, there seems to be growing consensusthat the IMF derives from the CMF through further fragmentationand star formation (taking into account the formation of binariesand multiple systems; Goodwin et al. 2008), provided that thestar-forming e ffi ciency (SFE) of each core is less than ∼ −
50% (Alves et al. 2007). On the other hand, Motte et al. (2018) haverecently found that the CMF in the mini-starburst galactic regionW43-MM1 challenges this scenario of direct proportionality, inthat its slope is "markedly shallower" than that of the IMF, forcore masses greater than about a solar mass; variations in theCMF are indeed possible in di ff erent environments.If the CMF does in fact evolve into the stellar IMF, thenthe distribution of stellar masses will be linked to the origin ofdense cores, and di ff erent CMFs may significantly a ff ect the massdistribution of the final stellar population. The characteristics ofthe CMF (its slopes as well as the presence of a turn-over andits location in mass) are likely to depend on conditions in themolecular clouds in which the cores are embedded, the propertiesof which, in turn, depend on the environment in which theywere formed. Therefore, it has to be expected that if intense UVradiation has any e ff ect on star formation, it must be by primarilya ff ecting the CMF in the exposed molecular cloud(s).The region of interaction between young massive stars and amolecular cloud is thus of great interest. Hydrodynamical simula-tions (e.g. Dale et al. 2007; Bisbas et al. 2011; Arthur et al. 2011;Wall et al. 2020; González-Samaniego & Vazquez-Semadeni2020) have shown that star formation may be either triggeredor halted in clouds exposed to intense FUV radiation. The FUVflux intensity is possibly a key element in determining one of thetwo scenarios. Feedback from young massive stars is believedto be instrumental in regulating the SFE in galaxies (Krumholz2014; MacLachlan et al. 2015). Lucas et al. (2017) propose thatthe removal of molecular cloud envelopes by stellar feedback cansignificantly decrease a cloud’s SFE. Thermal feedback a ff ectsthe way in which a molecular cloud fragments and can lead toa top-heavy IMF (Krumholz 2014). A way of observationallyassessing the e ff ects of intense FUV radiation fields on moleculargas is therefore to determine whether the CMF near to a PDRsignificantly di ff ers from that observed in more quiescent regions(i.e. in regions less exposed to intense stellar FUV radiation).NGC6357 is a galactic complex of molecular clouds and H ii regions that hosts several active star-forming sites. Massi et al.(2015) discussed the issue of distance, concluding that NGC6357is located 1.7 kpc away. A more reliable assessment can now bebased on GAIA DR2 data (Gaia Collaboration et al. 2018). Xuet al. (2018) retrieved the parallaxes of a large sample of OB starsfrom the GAIA DR2 catalogue. Those associated with NGC6357lie in the range 1 . − . ∼ . ± .
12 kpc and Maíz Apellániz et al. (2020) a distanceof 1690 + − pc, both using GAIA data. This definitely rules out adistance as large as 2 .
56 kpc, which was derived by Massey et al.(2001). Thus, we will safely continue using d = . ∼
10 %.Figure 1 in Giannetti et al. (2012) shows that the molecu-lar gas in NGC6357 is arranged in a ring surrounding a large( ∼
15 pc ×
10 pc) cavity (or a collection of connected smallercavities), possibly shaped by feedback from one or more starclusters (Wang et al. 2007). In the northern part of this complexis located G353.2 + + + ii region seen nearly face-on, with an extended ionisation front(IF) or PDR on the side facing the ionising stars and with an ele-phant trunk seen prominently against the ionised gas. South-eastof G353.2 + + ii region with an IF orPDR, seen edge-on, associated with the cluster AH03J1725–34.4(Massi et al. 1997; Massi et al. 2015). East of these two is an-other H ii region, G353.2 + + + + (cid:48) × (cid:48) area around G353.2 + ∼ (cid:12) ).An analysis of the complex molecular emission profiles led tothe identification of at least 14 clumps in the area mapped, indi-cating that the gas is indeed fragmented. However, the angularresolution (21–54 (cid:48)(cid:48) ) of these single-dish observations is insu ffi -cient to resolve some clumps for which there are indications ofsmaller-scale structures. Near-infrared ( J , H , and K ) images ofG353.2 + µ m (Schuller et al. 2009b), showing the most prominent clumpsseen at millimetre lines. However, although its spatial resolution( ∼ (cid:48)(cid:48) , ∼ . / beam), and most of the clumps found at millimetre lineswent undetected.NGC6357 / G353.2 + ∼ ff ect thenearby gas, for example by rapidly photoevaporating the smallestcores and thus producing a flatter CMF. Other parts of the com-plex are more quiescent and have no clear signs of star formation,and therefore no intense FUV-radiation field is expected there.Because of this contrast, NGC6357 may be one of the best loca-tions to study the influence of FUV radiation on star formation.In this paper we identify dense cores from dust-continuum datain an area of about 0.5 square degrees in NGC6357. Combiningthese data with Herschel Hi-GAL (Molinari et al. 2010) imageswe construct the spectral energy distribution (SED) for each core.Fitting a greybody to those SEDs yields temperatures and massesfor all cores, from which a mass function is derived. By divid-ing the field into a sub-field where a more intense FUV fieldis expected and a sub-field less exposed to FUV radiation, wecarry out a comparison between the mass functions from the twosub-fields.The layout of the paper is the following. In Sect. 2 we describeour observations and data reduction. Our results are presented inSect. 3 and discussed in Sect. 4. Finally our conclusions are listedin Sect. 5.
2. Observations and data reduction
We used the Submillimetre Common-User Bolometer Array 2(SCUBA-2: Holland et al. 2013) at the James Clerk MaxwellTelescope (JCMT) to observe 12 partially overlapping fields, si-
Article number, page 2 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357
Table 1.
Adopted flux conversion factors (FCFs).
Field date 850 µ m 450 µ m(ddmmyy) (Jy pW − beam − )1 − Fig. 1.
Herschel HiGAL 160 µ m map (colour scale) with fields observedin 2012 (1–6; green) and 2015 (7–12; blue). The location and approxi-mate size of star clusters are marked in yellow (Massi et al. 2015). Thelinear size of the region shown is approximately 22 ×
17 pc . multaneously at 450 µ m and 850 µ m: on 13 July 2012 (fields1–6; project m12an004) and on 6 and 23 April and 22 May 2015(fields 7–12; project m15ai093). The observations were carriedout using a so-called CV Daisy pattern ; each daisy-field obser-vation took 30 minutes. Each field has a radius of about 8 ar-cmin, and together they cover the entire ring-like structure ofNGC6357, including three star clusters, as illustrated in Fig. 1.The images were reduced using SMURF and associated pack-ages contained in STARLINK , following the Cookbook versionSC / (Chapin et al. 2013). After reduction, the fields weremosaicked together. The resulting sensitivity varies with location,and except at field edges is ∼ < −
15 mJy / beam (at 850 µ m), and60-400 mJy / beam (at 450 µ m). We used the flux conversion fac-tors (FCFs; see Dempsey et al. 2013) listed in Table 1. These werederived from measurements of CRL2688 taken close in time toeach series of observations. The Starlink SDF files were then con-verted into FITS format for further analysis. The (e ff ective) beamsize of SCUBA-2 is 9 (cid:48)(cid:48) ± (cid:48)(cid:48) at 450 µ m and 14 (cid:48)(cid:48) ± (cid:48)(cid:48) at 850 µ m(i.e. ∼ .
07 pc and ∼ .
12 pc, respectively). To complement theseobservations and construct SEDs, we used the 70 µ m and 160 µ mimages from the Herschel / Hi-GAL survey (Molinari et al. 2010),with beam sizes of 5 (cid:48)(cid:48) and 11. (cid:48)(cid:48)
5, respectively. https: // / jcmt / instrumentation / continuum / scuba-2 / observing-modes / http: // http: // / docs / sc21.htx / sc21.html The 850 µ m emission is potentially contaminated by CO(3–2)line emission at 345.8 GHz. The continuum band is very wide(ca. 39 GHz, see Naylor et al. 2014) and lines have to be brightand broad in order to significantly a ff ect the continuum emis-sion. Several studies (e.g. Sadavoy et al. 2013) show that thecontamination is typically less than ∼
70 mJy / beam, but mayreach ∼
150 mJy / beam (10 −
30 times the rms level in our map),and would thus a ff ect especially the lower-level emission andhence the lower-mass cores, which are important to define thelow-mass turnover point in the CMF. As there are numerous lo-cations with star formation in NGC6357, outflow emission, andtherefore contamination at relevant levels, is to be expected.On the other hand, CO(6–5) falls at the edge of the 450 µ mband. No significant contamination is expected (also consideringthe high noise level of the 450 µ m continuum data).We used the HARP receiver at the JCMT (see Buckle et al.2009) to map the CO(3–2) emission in the ∼ (cid:48)(cid:48) × (cid:48)(cid:48) region covered by the SCUBA-2 observations on 2, 7, and 20May and 9 and 18 July 2014 (project m14au032). Observationswere made in ’basket-weave’ raster-scanning mode. HARP has16 SIS receptors, 14 of which were operational at the time ofthe observations. The reference position (17:25:36.2 − = T ∗ A ) at 0.3 km s − resolution. Weused the ACSIS backend with a bandwidth of 1000 MHz, whichprovided 2048 channels with a spectral resolution of 0.488 MHz(0.423 km s − at 345.796 GHz). The data were reduced usingthe ORAC-DR pipeline (Jenness et al. 2015); the maps were thenconverted into CLASS format for further analysis. The main-beam e ffi ciency of HARP is 0.64, and all line intensities wereconverted into a T MB scale. The average rms in the CO map is2.0 K, on the T MB scale. The beam size of HARP at 345 GHz is14 (cid:48)(cid:48) .We followed the procedure outlined by Parsons et al. (2018)to correct continuum data for line contamination, using the HARP CO(3-2) integrated intensity map as a negative fake map to becombined with the SCUBA-2 data in the map maker (see alsoDrabek et al. 2012). For this we made use of a script kindlyprovided by Dr. Parsons.
3. Results
The CO(3–2) map used to correct the 850 µ m continuum emis-sion is shown in Fig. 2. Following the procedure outlined inSect. 2.1, we obtained CO-corrected 850 µ m maps for each of the12 observed fields. The individual fields at each wavelength werethen combined into the single map shown in Fig. 3 using the task’wcsmosaic’. The 850 µ m map has the best combination of sensitivity andangular resolution (see Sect. 2), and we used this to identifyand extract the cores. Because we wanted to identify cores inthis complex, we needed to isolate the most compact structures,which are more likely to collapse and form a single star or a closemultiple system, depending on the level of fragmentation, and aretherefore more closely connected with the IMF. To facilitate theidentification, we first removed the extended 850 µ m emissionin which the cores are embedded. We therefore performed amulti-scale decomposition of the image, using a median filter(see Belloche et al. 2011). We used seven levels of decomposition Article number, page 3 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final
Fig. 2. CO(3–2) integrated emission ( (cid:82) T MB dV; −
20 to +
20 km s − ).Contours values are 80(80)470 K km s − (low(step)high). on S / N maps, using only those with scales (cid:46) (cid:48)(cid:48) in the imagereconstruction, thus filtering out any structure more extended thanthat. This procedure results in the image shown in Fig. 4. We notethat the spatial resolution at 850 µ m is ∼ . S / N map was then visuallyinspected to identify and remove spurious sources, confirmed assuch by a comparison with the Herschel Hi-GAL maps. We alsoexcluded cores outside of the region observed in CO with HARP,and at the noisy edges of the continuum mosaic. A minimum sizethreshold was set at 13 (cid:48)(cid:48) ( ∼ beam at 850 µ m). The final cataloguecontains 1221 cores.The distributions of fluxes and sizes of the cores in this cat-alogue are shown in Figure 5 and 6, respectively. In the latterfigure, we have also made a distinction between cores in regionswith and without intense FUV-flux, as defined in Sect. 3.2. To investigate how the enhanced FUV radiation fields from newlyborn massive stars a ff ect the molecular environment and the on-going star formation activity, and to avoid e ff ects due to possibledust opacity di ff erences in intense and moderate FUV environ-ments (see Sect. 3.5), we divided the mapped region into twosub-regions, hereafter the ‘active’ and the ‘quiescent’ regions.The active region includes the parts of the cloud complex moreexposed to a high FUV-photon flux, such as G353.2 + ii region G353.2 + ii region G353.1 + ii region G353.2 + ff ected by FUV radiation and has been labelled as quiescent region. We note that we are onlyinterested in finding out if a global signature of di ff erent levels inthe FUV is apparent in the core populations in the two areas thatmay be further investigated in future works. Thus we do not needvery accurate selection criteria to define the two regions at thisstage. Because we are interested in the CMF, we need to transformthe fluxes of the cores into masses. Making use of the Hi-GALimages we constructed the core SEDs by complementing ourSCUBA-2 850 µ m and 450 µ m flux densities with those from the160 µ m and 70 µ m frames taken at the central pixels of the coresidentified in the 850 µ m map. The Herschel- and the 450 µ mmaps were first convolved to the resolution of the 850 µ m mapand had their background subtracted in the same way as donefor the 850 µ m frame. We fitted a greybody to the SEDs forthose cores with at least three data points and a 450 µ m fluxdensity larger than the CO-corrected 850 µ m one, varying thedust temperature between 5 K and 80 K in steps of 0 . − − . g cm − , in steps of0.1 in logarithmic scale. The dust opacity κ ν was assumed tobe 0 . g − at 1 . β equal to 1 .
8, consistent with the dust models used.This yields κ ν = .
85 cm g − at 870 µ m, the value adopted forthe ATLASGAL survey (Schuller et al. 2009a). A more detailedanalysis on the adopted dust opacity is reported in Sect. 3.5We were able to derive a dust temperature for 686 cores; theirlocations are shown in Fig. 7. The active region contains 411cores and the quiescent region 275, out of the 686 considered.The distribution of their temperatures is displayed in Fig. 8. Someexamples of SED-fits are shown in the Appendix.An important di ff erence between the cores populating the tworegions can be seen in Fig. 8. The temperature of cores in thequiescent region peaks at ∼
25 K, whereas that of cores in theactive region peaks at ∼
35 K. Cores in the quiescent region arethus significantly colder than those in the active region. Formalerrors on the temperature from the greybody fits are nearly alwaysless than 1 K. This clearly demonstrates the e ff ect of FUV photonson the gas. This result is contrary to that found by Bobotsis &Fich (2019), who do not find evidence of H ii regions a ff ecting thesurrounding cores in their study of 38 complexes of ionised andmolecular gas. However, their target regions are mostly fartheraway than 2 kpc and do not contain very massive ionising stars. The dust temperatures ( T d ) of the best-fit models are used tocalculate the mass of the cores, from the CO-corrected integrated850 µ m flux densities from Gaussclumps by means of: M = γ D S ν / [ κ ν B ν ( T d )] , (1)where D is the distance to the complex, B ν ( T d ) is the Planck func-tion evaluated at temperature T d , S ν is the total flux density and κ ν is the dust opacity, both at 850 µ m; γ is the gas-to-dust ratio (as-sumed to be 100). In Table 2 we list the properties of all the bonafide cores. The CMF in the NGC6357 region was constructedthrough a kernel density estimate, using an Epanechnikov ker-nel with a bandwidth estimated using the direct plug-in method(Feigelson & Babu 2013). Figure 9 shows the results of this pro-cedure (green dashed line). The slope of the high-mass end ofthe CMF ( M > (cid:12) ; the completeness limit - see Sect. 3.6) is Article number, page 4 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357 T a b l e . P r op e r ti e s o f bon a fi d ec o r e s . O n l y a f e w a r e s ho w n a s e x a m p l e s ;t h e f u llt a b l e i s a tt h e C D S I D α ( J ) δ F ( ) F ( ) F ( ) F ( ) S ( ) σ ( S ( )) s i ze M g a s σ ( M g a s ) T d σ T d χ d e g s d e g s m J y / b ea mm J y / b ea m − e r g s − c m − H z − (cid:48)(cid:48) M (cid:12) K . − . . . . . . . . . . . . . . − . . . . . . . . . . . . . . − . . . . . . . . . . . . . ...... . − . . . . . . . . . . . . . . − . . . − . . . . . . . . . . . − . . . . . . . . . . . . . N o t e s . T h ec o l u m n s c on t a i n t h e f o ll o w i ng i n f o r m a ti on : C o l . : c o r e i d e n ti fi ca ti onnu m b e r ; C o l s . a nd3 : c o r e po s iti on i nd ec i m a l d e g r ee s i n R A a nd D E C ; p ea k fl uxd e n s it y a t , , ( a f t e r c onvo l u ti on t o t h e r e s o l u ti on a t µ m a nd s ub t r ac ti ono f t h ee x t e nd e d e m i ss i on ; − . m ea n s nod e t ec ti on ) a nd850 m i c r on ( a f t e r s ub t r ac ti ono f t h ee x t e nd e d e m i ss i on a nd c o rr ec t e d f o r C O ( ) e m i ss i on ) i n C o l s . - ;i n C o l s . a nd9 t h e t o t a l fl uxd e n s it y a t µ m a nd it s f o r m a l ( pho t o m e t r i c ) e rr o r( e x t e nd e d e m i ss i on s ub t r ac t e d a nd c o rr ec t e d f o r C O ( ) e m i ss i on ) ;i n C o l . :t h e s i ze ( no t d ec onvo l v e d f o r b ea m s i ze ) , w h i c h i s t h e g e o m e t r i ca l m ea no f t h ee lli p s ea x e s ( (cid:112) m a j o r − a x i s × m i no r − a x i s ) a t µ m ; m a ss a nd m a ss f o r m a l e rr o r , bo t hd e r i v e d fr o m t h e t o t a l fl uxd e n s it y a t µ m , i n C o l s . a nd12 ; C o l s . a nd14 : du s tt e m p e r a t u r ea l ong w it h it s f o r m a l e rr o r ; χ - s qu a r e v a l u e fr o m t h e g r e ybody fi t s i n C o l . . Article number, page 5 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final
Fig. 3.
SCUBA-2 observations of the dust emission. Left: 850 µ m mosaic; the emission has been corrected for the integrated CO(3–2) lineemission. Right: 450 µ m mosaic. Units are mJy / beam. Fig. 4. µ m map after filtering out emission from extended structuresas explained in the text. Units are mJy / beam. The black lines indicatethe region mapped in CO(3-2) (see Fig. 2). − . ± .
2, derived by directly fitting a power-law distribution tothe data points using PyMC (Patil et al. 2010).The total gas mass of dense cores is ∼ ∼ (cid:12) in the quiescent and active regions, respectively. Assuminga molecular mass of ∼ . × M (cid:12) for the whole NGC6357complex (Cappa et al. 2011, re-scaled to 1.7 kpc), that implies afraction of gas in dense cores of ∼ . As mentioned above (Sect. 3.3), we adopted a dust opacity of0 . g − at 1 . β = .
8, leading to 1 .
93 cm g − at850 µ m, based on the theoretical work of Ossenkopf & Henning(1994). Their tabulated values are obtained for dense protostellarcores ( ∼ − cm − ) that have remained stable for at least10 years. We have also assumed that the dust opacity is constantthroughout the sample of cores, so it is essential that we shouldcheck whether this is a good approximation before deriving globalproperties such as mass distributions and mass-size relationships.Although Ossenkopf & Henning (1994) note that uncertainties onthe tabulated values should not add up to more than a factor of 2, C oun t s -1 ]10 100 1000 10 Fig. 5.
Distribution of fluxes for the 1221 cores identified in the 850 µ mmosaic. one has to take into account that most of the cores in NGC6357have been exposed to an intense FUV field, a scenario that wascautioned but not modelled by Ossenkopf & Henning (1994).In addition, from Tables 2 and 3 in their paper it is clear thatdust opacity depends on the gas density and that its core-to-corevariations will be much smaller if ice mantles have grown onthe grains. Unfortunately, one can reasonably expect that part ofthese ice mantles either have been removed or did not grow atall in the presence of a FUV field. We note that systematic errorsof even a factor of 2–3 in the dust opacity are acceptable, in thatthey do not a ff ect global properties of the cores such as the shapeof their mass distribution. This is not true for large core-to-corevariations in the dust opacity, which in principle may heavilya ff ect the CMF slope.To test the e ff ects of dust opacity uncertainties in the region,one can then assume the worst case scenario of grains with no Article number, page 6 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357 P r ob a b ilit y d e n s it y Fig. 6.
Distribution of core sizes for all 1221 cores (uncorrected forbeam; black solid line); the red curve indicates the active region and theblue one the more quiescent part.
RA (J2000)
Fig. 7.
All 686 cores with a valid SED fit superimposed on the mosaicat 850 µ m. Darker symbols indicate lower temperatures. The white lineindicates the dividing line between active (to the east) and quiescent (tothe west) regions. ice mantles at all. We derived the dust opacity at 850 µ m as afunction of density from Tables 2 and 3 of Ossenkopf & Henning(1994) by a linear fit in the log-log space. For the 452 cores witha deconvolved size of at least half the telescope beam and usingthe masses derived in Sect. 3.4, we derive a range of averagedensities ∼ × − cm − . Many cores therefore may havedensities less than 10 cm − ; the fit allows us to extrapolate down P r ob a b ilit y d e n s it y Fig. 8.
Temperature distribution for all 686 cores (solid black line), coresin the active region only (411; solid red line), and cores in the quiescentregion only (275; solid blue line). to the lowest values. This may not give the correct dust opacityin those cases, but it should be good enough for our test, takinginto account the limited range spanned by the core densities.Starting from the masses obtained from Eq. 1 with the adopteddust opacity (1 .
93 cm g − at 850 µ m), we computed the densityof each of the 452 cores and recalculated their mass using thedust opacity for their density, as given by the fitted function. Wethen iterated this procedure for each core until convergence wasreached. The masses obtained by assuming a constant opacity (of1 .
93 cm g − ) and the ones obtained with a density-dependentdust opacity are compared in Fig. 10a. For most cores, the massesobtained with a density-dependent dust opacity are within a ∼
30% of the masses obtained by adopting a constant opacity. Onlythree very massive cores exhibit significant di ff erences (with thedensity-dependent opacity always yielding lower masses).We performed another test by constructing and comparing themass distributions, which are shown in Fig. 10b. These are mostlyconsistent with each other within ∼ σ (for a Poisson statistics)and their di ff erence is almost negligible in the log-log space,provided the two most massive bins are excluded. According tothe mass-size relationships derived in Sect. 4.2, it is easy to seethat the most massive cores are also the less dense, so presumablythey are more a ff ected by opacity variations. In fact, a linearfit to the distributions in Fig. 10b (for M ≥ . M (cid:12) ) yields aslope of − . ± .
06 for constant opacity and − . ± .
07 fordensity-dependent opacity, in other words consistent with eachother within 1 σ . So the shape of the core mass distributionis only moderately a ff ected by the choice of the dust opacity. Afurther simple check can be performed to see if the sample massesdepend on the size. We derived mass-size relationships by a linearfit in the log-log space, namely:log( M / M (cid:12) ) = p × log( D / arcsec) . (2)We obtained p = . ± .
15 in the constant opacity case, and p = . ± .
12 in the density-dependent opacity case. Again, thedi ff erence is at a ∼ σ level. Article number, page 7 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final − . − . − . − . − . − . − . Mass (M_sun) l og ( s ou r c e den s i t y ) | | || | | || || ||||| |||| || || || ||| ||| || || || ||| |||| || || || || | |||| |||| || || || ||| ||| ||| || || | | || | || || ||| || || ||| || ||| ||| ||| | || | | ||| | || ||| || | || || || | | |||||| | ||| ||| | | |||| || | || | |||| || ||||| | ||| || ||| |||| | |||| || || ||| ||| || | ||| || || ||| || ||| | || || || || | ||| ||| | | | |||| | || || | ||| |||| | | || | || || || | |||| ||||| | || || | || || || || || || || ||| ||| || || || | || ||| | ||||| | | | | || ||||| ||| | || || ||| || || || || ||| ||| | | ||| ||| ||| | || || | || | ||| || || || || | | |||| || | || || ||||| | | | ||| ||||| || || || ||| | || || ||||| || | || || ||||| || |||| | ||||| | |||| | || | | || ||| ||| | || | | || || |||| || |||| || || | || || | || | || ||| | |||| || |||| | || || || ||| | || | || || | ||| || | || | | | ||||| | | | || || || ||| | ||| | | || | | |||||| | |||| || || | ||| || | | | || | ||| ||| || ||| |||| || | || | || | || | ||| | || || ||| |||| ||| ||| || || | || | || || | ||| || || ||| | | | | || | | || | || | ||||| |||| || | || ||| || | || || |||| || ||| || || || ||||| | || ||| || || ||| || | | |||||| || || || || | || || || || ||| | ||| | || ||| || || || || || ||| | ||| || || || || | | || ||| ||| || | | ||| ||| ||| ||| | | ||| | ||| ||| ||| || ||| || | ||| | || || | || || ||| || || | | |||| ||| | |||| || ||||| ||| |||| || | ||| || ||| || || | | || | |||| || ||| | || || | | ||| || | |||| |||| || ||| || | || | | |||||| | || || || ||| | |||||| || | || || ||| | || ||| ||| |||| || || | || || ||| | || | ||| || || || | | || ||| | | | || || ||||||| | | | || || | ||| || |||| | || || | |||| | | | ||| || | || || ||| | | |||| | ||| || | | || ||| |||| | | ||| | ||| |||| | |||||| | || || | || || ||| || | || || | || ||| || || || ||| ||| ||| ||| || || ||| || | ||| | ||||| || | | | | || || | || | | | || |||| || |||| || || ||| || ||||| ||| | |||| || ||| || || ||| ||| ||| | | || || ||| || | || ||| || | | | || || | || || | || ||| || || | || || || || | | |||||| | || | || ||| | ||||| || | | | Fig. 9.
Core mass function in NGC6357 (dashed green curve for allcores) obtained as density distribution of sources after smoothing with aEpanechnikov kernel. The red curve indicates the active region, and theblue curve indicates the more quiescent part. The vertical line marks the5 M (cid:12) completeness limit (see Sect. 3.6). The small coloured bars showthe masses of the single sources for each sample, following the colourcoding of the distributions.
We note that these results were obtained by using the averagecore densities. However, we expect that significantly higher den-sities are reached only in a small fraction of a core’s total mass.Furthermore, considering that the density-dependent dust opacityis computed for the worst case of grains with no ice mantles, thee ff ects of dust opacity uncertainties on the derived masses may beeven lower. A constant dust opacity is then a good approximation,yielding core-to-core mass uncertainties of <
30 % in most cases.
To evaluate the completeness of our data we followed these steps:Firstly, we inserted a set of 20 artificial cores in the 850 µ m mapwith a FWHM of 14 (cid:48)(cid:48) (the SCUBA-2 PSF at 850 µ m) and a con-stant peak flux. Secondly, the images with the synthetic coreswere filtered as done for the original data. Thirdly, Gaussclumpswas run on this processed image and a catalogue of cores wasproduced, and finally this catalogue was cross-matched with theposition of the artificial cores. If one or more sources were de-tected within a beam, we compared their fluxes and sizes, whichmust be within a factor of 2.5 and 3 of the input values, re-spectively, to decide whether the injected source was detected.This was done for peak flux densities of 5 , , , , ,
80 and100 mJy beam − , and the procedure was repeated 100 times foreach of these values. In this way we obtained the completenessas a function of peak flux density. A completeness of 90% isreached for 60 mJy beam − . This corresponds to a point-likesource with a mass of M compl , point ∼ . M (cid:12) for a dust temper-ature of 20 K and M compl , point ∼ . M (cid:12) for a dust temperatureof 30 K. One way to estimate the mass completeness limits ofextended sources would be by assuming a Gaussian spatial dis-tribution of the emission, and then use the distribution over sizes Fig. 10.
Core masses and core mass distribution. a. Core masses derivedusing a density-dependent opacity (grains with no ice mantles) vs. massesderived using a constant dust opacity of 1 .
93 cm g − (at 850 µ m). Thefull line marks equal masses, whereas the dashed line marks density-dependent opacity masses equal to 70 % of the constant density masses. b. Core mass distributions for masses obtained with a constant dustopacity of 1 .
93 cm g − (at 850 µ m; full line) and for masses obtainedwith a density-dependent opacity (dashed line). The error bars have beencomputed assuming a Poisson statistics. Fig. 11.
Completeness of the cores in our sample, as a function ofmass. Starting from the completeness as a function of flux density forpoint sources, we have used a representative source size of 22 (cid:48)(cid:48) and theobserved temperature distribution (Fig. 8) to derive the distribution inmass shown here (see text). The dashed line indicates the mass wherethe completeness reaches its maximum.Article number, page 8 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357 to see how the completeness of point sources would change; onecan expect that M compl ∼ M compl , point × ( D + B ) / B , (3)where B and D are the beam- and deconvolved source sizes,respectively.We used an alternative method. For each peak fluxdensity value used for the artifical core experiments (i.e.5 , , , , ,
80 and 100 mJy beam − ) we computed a cu-mulative mass distribution from Eq. 1 according to the followingprocedure. Once the peak flux density is fixed, we considereda source size of ∼ (cid:48)(cid:48) , halfway between unresolved sources( ∼ (cid:48)(cid:48) ) and the largest (not beam-deconvolved) size values of ∼ (cid:48)(cid:48) , and derived the mass distribution obtained from the totalflux and the observed distribution of dust temperatures (Fig. 8).Thus, each peak flux density is associated with a range of massesthat reflects the empirical temperature distribution and whosecompleteness was assumed to be that estimated for this peak fluxdensity from the artificial core experiments described earlier. Thefinal mass completeness curve was then computed by averagingthe completeness levels derived for each mass value from theadopted set of peak flux densities, and is shown in Fig. 11.The completeness as a function of mass reaches its maximumaround 5 M (cid:12) . The maximum is not 100% due to confusion e ff ectsthat prevent the recovery of artificial cores that end up in brightand crowded regions. We note that our estimates of the masscompleteness level assume that the e ffi ciency in retrieving a coremostly depends on its peak flux density, irrespective of its size.This appears reasonable. However, one has to consider that alarge fraction of the flux from weak extended cores is likely tobe lost in the noise. So the retrieved total flux density from weakextended sources is bound to be a ff ected by larger errors.
4. Discussion
The CMF for all cores was derived as discussed in Sect. 3.4and shown in Fig. 9. To assess the goodness of both the coreretrieval algorithm and the masses obtained, we compare ourresults to those of previous works. Giannetti et al. (2012) mappedthe area towards G353.2 + ∼ (cid:48)(cid:48) . µ m, overlaid with the positions of thegas clumps found by Giannetti et al. (2012) and with those of ourdust cores.Clearly, the increase in spatial resolution has resulted in beingable to decompose the continuum emission in a much larger num-ber of compact structures. The goodness of the decompositionoperated by Gaussclumps can be confirmed by a visual exam-ination of the figure. Clump C1 corresponds to our core ID 1,clump C2 to our core ID 4, and clump E to our cores ID 2 andID 20 (see Table 2). We note that Giannetti et al. (2012) assumea distance of 2 .
56 kpc, so their masses have to be scaled to ouradopted distance of 1 . µ m mapto the ATLASGAL resolution. Then we performed a rough aper-ture photometry over the areas of the continuum cores found byGiannetti et al. (2012) (which they label 1 to 5; see their table 3).By assuming the same dust temperature (i.e. 30 K), we retrieve Fig. 12.
Continuum emission at 850 µ m towards G353.2 + / beam. Contour levels are 50, 150,and 300 mJy / beam. masses that are a factor of 0 . − . µ m is consistent with that of the ATLASGALdata.As for the gas clumps A to P of Giannetti et al. (2012), wefound that the masses of our cores are a factor of 0 . − . ff erence in mass between our cores andthe gas clumps is not due to the adopted temperatures, but tothe higher spatial resolution and sensitivity of the 850 µ m map,which allow us to retrieve denser and more compact structuresembedded in the gas. This is also confirmed by the fact that a fewgas clumps are only associated with faint compact continuumsources or faint di ff use emission.Our results can also be compared with those of Russeil et al.(2019). These authors used Herschel / PACS and SPIRE data toselect a robust sample of 155 dense cores in NGC6357 with thealgorithm getsources (Men’shchikov et al. 2012). The ranges ofsize and mass that they find are roughly consistent with ours.However, their mass distribution is peaked around 30–50 M (cid:12) ,with a median mass of 22 M (cid:12) and a maximum mass of 386 M (cid:12) ,while our CMF exhibits a maximum mass of 176 M (cid:12) and a peak at ∼ M (cid:12) . Thus we have achieved a much lower mass completenesslimit than Russeil et al. (2019), which is likely to be caused by notonly the di ff erent algorithms used to decompose the continuumemission but also our preliminary filtering out the more extendedemission. We further performed a closer comparison selectingtheir three most massive sources (their MDC 1, 2, and 5). Asshown in Fig. 13, we have retrieved those sources (our coresID 13, 7, and 14, respectively), along with a number of faintercompact structures around them. The masses of our correspondingcores are a factor of 4 − ff erence in the adopted dust Article number, page 9 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final mass opacity (their prescriptions would yield ∼ .
24 cm g − at850 µ m). This clearly indicates that the cores in our sample aresystematically less massive than theirs. As mentioned above, thisdi ff erence is likely to arise not only due to the di ff erent algorithmsused to decompose the emission, but also to our preliminaryfiltering out lower spatial frequency emission. Pre-stellar cores are defined as gravitationally bound cores thatdo not host protostars yet. Separating protostellar and pre-stellarcores is critical, in that the CMF of ‘protostellar’ cores may bea ff ected by mass erosion due to increased turbulence and outflows,and the development of internal temperature gradients, and is lesssuitable to compare with stellar IMFs. Furthermore, dust opacityis sensitive to the physical environment and may vary up to afactor of ∼ ff erent physical environments, as discussed inSect. 3.5. It is then essential that the selected sample contains aclass of objects as homogeneous as possible, with a limited rangein density.Identifying protostellar cores requires probes of protostellaractivity, such as compact emission at 70 µ m. Thus, we cross-checked our 850 µ m data and Herschel Hi-GAL 70 µ m maps forspatial coincidences. All sub-mm cores associated with 70 µ memission have then been labelled as protostellar, whereas allremaining cores have been labelled as ‘starless’. It has beenshown that 70 µ m emission is a sensitive probe of protostellaractivity (see e.g. Koenig et al. 2012). The distribution of thepeak flux densities of the 70 µ m emission associated with thesub-millimetre cores, has a maximum at ∼ / beam. Thisrepresents a rough completeness limit. Assuming that the infraredemission comes from a Gaussian spatial distribution ∼ (cid:48)(cid:48) insize and a FWHM ∼ (cid:48)(cid:48) for the Herschel beam at 70 µ m, thisyields a flux of ∼
24 mJy. Then by using Eq. 2 of Dunham et al.(2008) one can estimate a detection limit for the luminosity of thecentral protostar L int ∼ . L (cid:12) . One problem with this approachis that in the active region, dust is heated from the outside aswell, through FUV radiation, thus increasing the core emissionat 70 µ m possibly mimicking the e ff ects of a central protostar. Infact, we found 129 ‘70 µ m-bright’ sources out of 411 cores inthe active regions, and only ten 70 µ m-bright sources out of 275cores in the quiescent region. All 70 µ m-bright cores in the activeregions are associated with one of the two H ii regions G353.2 + + ii regions.We then applied a further selection filter to the 70 µ m-darkcores, based on the spatial coincidence of cores and red WISEsources. After retrieving all point sources from the WISE SourceCatalog projected towards NGC6357, we selected those withcolours of Class I sources according to Koenig et al. (2012).All contaminants (extragalactic sources, PAH emission, shockemission) were discarded following the criteria of Koenig et al.(2012). We also included sources detected in only two bands withd log( λ F λ ) / d log λ > − . µ m.In addition, we required photometric errors < . µ m-darkcores whose ellipse overlaps the positional uncertainty ellipse ofa WISE source were re-classified as protostellar; this concerned31 cores in the active region and 41 in the quiescent region. Inthe end, we found 251 starless and 160 protostellar cores in http: // wise2.ipac.caltech.edu / docs / release / allsky / the active region and 224 starless and 51 protostellar cores inthe quiescent region. In principle we could also use the WISEsources to verify the nature of the 70 µ m-bright cores in theareas of the active region closest to the H ii regions and in thePDR. Unfortunately this is impossible, due to the saturation ofthe WISE bands; therefore in those areas all 70 µ m-bright coresremain tentatively classified as protostellar.In Fig. 14 we show the temperature distributions for the vari-ous (sub)samples. To avoid e ff ects due to incompleteness, onlycores with M > M (cid:12) have been selected. Fig. 14a shows the dis-tribution for all cores, and emphasizes what we saw in Fig. 8 forcores of all masses. The temperature distributions for 70 µ m-darkand 70 µ m-bright plus WISE-associated cores in the active andquiescent regions are shown in Figs. 14b, c. The temperatures inthe quiescent region for both classes are similar, peaking between15–20 K with an average T ∼
19 K. On the other hand, in theactive region the distribution of 70 µ m-bright cores is clearlyshifted to higher temperatures with respect to that of 70 µ m-darkcores (from an average T ∼
22 K to an average T ∼
28 K).The sensitivity limit for protostellar cores associated withWISE sources can be estimated as follows. We will assume herethat the central protostellar source has an infrared flux increasingwith wavelength, with a spectral index d log( λ F λ ) / d log λ ∼ µ m, we need to derive the WISE sen-sitivity to point sources in this band. The 5 σ sensitivity in the22 µ m band quoted in the explanatory supplement is 5 . µ m ([22]) ∼ µ mand the spectral index are known, we can compute the flux thatsuch a source would exhibit in the other WISE bands. Follow-ing Kryukova et al. (2012), who relate infared spectra to centralbolometric luminosities, F ∼ . ∼ . L (cid:12) . However, WISE is much moresensitive in the other bands, thus central sources with the samespectral index can be undetected at 22 µ m but detected in thelower wavelength bands, increasing the actual sensitivity. On theother hand, due to saturation in the WISE bands there is in fact noway to discriminate between starless and protostellar cores in theareas towards the two H ii regions, that is to say the most criticalones to understand the e ff ects of FUV feedback. Even using theMSX Point Source Catalogue, which has a worse spatial resolu-tion and sensitivity but saturation at higher infrared fluxes, yieldsonly 20 matches near to the H ii regions, still indicating sensitivityproblems. All cores associated with MSX point sources havetemperatures in the range 26–63 K, with only two cores above5 M (cid:12) ( T =
26 and 34 . ∼ . ∼ . . M / M (cid:12) ] > .
8) with a N ∼ M α function,one obtains α = − . ± .
09 for 70 µ m-dark cores and α = − . ± . µ m-dark cores cleaned of WISE-associatedsources in the quiescent regions. In the active regions, one obtains α = − . ± .
09 for 70 µ m-dark cores and α = − . ± . µ m-dark cores cleaned of WISE-associated sources. Thedi ff erence is not statistically significant, probably due to the fact http: // wise2.ipac.caltech.edu / docs / release / allsky / expsup / Article number, page 10 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357
Fig. 13.
Continuum emission at 850 µ m towards the fields of cores MDC 1, 2, and 5 (labelled in figure) of Russeil et al. (2019). Units are mJy / beam.The locations of the cores identified in this work are overlaid (small open squares). Fig. 14.
Distribution of temperatures for cores in the active (full line) and quiescent (dashed line) regions. Only cores with M > M (cid:12) (i.e. abovethe mass completeness limit) have been included. a. All cores. b. Cores with no emission at 70 µ m and no red WISE sources associated. c. Coresassociated with 70 µ m emission and / or red WISE sources. that only a few sources are moved between samples if their massis above the completeness limit.The discussion above highlights the di ffi culties inherent inobtaining a census of real starless cores. Although 70 µ m emissionis in principle a very sensitive probe of protostellar emission,nevertheless we found many cores associated with red WISEsources and no emission at 70 µ m. In addition, we have no wayof checking the nature of 70 µ m-bright cores around the twoH ii regions, which are the sources most a ff ected by the FUVfeedback. On the other hand, we have shown that the associationwith red WISE sources is not a sensitive tool in the whole region,because of saturation. As a result, there is currently no way ofunambiguously separating starless and protostellar cores in largeareas towards NGC6357.For the sake of simplicity, we will refer to the sample of70 µ m-dark cores cleaned of those WISE-associated as the ’star- less’ sample, despite its uncertain degree of contamination fromprotostellar cores. It is composed of 224 sources in the quiescentregion and 251 sources in the active region. On the other hand,there are only 51 candidate protostellar cores in the quiescent partand 160 possible protostellar cores in the active region (31 coresthat are associated with red WISE sources outside the H ii regionsplus 129 70 µ m-bright cores).Not all starless cores are also pre-stellar. Some are just tran-sient, short-lived structures that will dissipate rather than formstars. To check how much our sample of starless cores would alsobe representative of pre-stellar cores we followed the analysis ofAndré et al. (2014b). In Fig. 15, core masses and sizes can becompared to the half-mass loci of Bonnor-Ebert critical mass for T =
30 K and T =
20 K. It is clear that cores with masses largerthan the completeness limits derived from the sub-mm emission,cannot be thermally supported against gravity. Even though tur-
Article number, page 11 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final
Fig. 15.
Mass vs. deconvolved size for a. all cores; b. µ m dark corescleaned from WISE-associated cores; c. µ m bright cores plus coresassociated with WISE sources. Cores with a deconvolved size smallerthan half the beam size have been discarded. Small filled squares markcores in the active region, whereas open green triangles mark cores inthe quiescent region. The critical half-mass loci of Bonnor-Ebert spheresare drawn for T =
20 K and T =
30 K (black dash-dotted lines). Thedotted red line marks the completeness limit for T =
20 K dust (fromEq. 3). Linear (log-log) fits are indicated by a solid (cores in the quiescentregion) and a dashed (cores in the active region) line. bulence and magnetic fields can oppose gravitational collapse, itis unlikely that they will prevent it. So, most of our starless cores,if really starless, would also be pre-stellar in nature, provided thatonly masses above the completeness limit are taken into account.Mass and size of all cores in the two regions are plotted inFig. 15a. We note that only cores with deconvolved sizes greaterthan half the beam size have been used. A linear fit (in log–logspace) to the data according to Eq 2 yields p = . ± . M / M (cid:12) ) ∼ × log( D / arcsec), typical of core populationswith constant column density. Similarly, a linear fit to the massversus deconvolved size of starless cores (shown in Fig. 15b)yields p = . ± . p = . ± . p = . ± . p = . ± . ff erences in the power-law indices areclearly not significant. In addition, one has to be aware that thefit results may be biased due to size-dependent incompleteness,(see Sect. 3.6). Nevertheless, the mass-size relationships derivedin various star-forming regions or from various samples of coresor clumps displays power-law indices in the range 1 . − . Although we were not able to reliably separate protostellar andstarless cores in the molecular gas adjacent to the H ii regions,nevertheless their nature can be assessed if we assume that thosecores are embedded in PDRs. As we said, all 70 µ m-bright coresin the active region lie near either G353.2 + + η c0 (the ratio of the initial clump column densityto that of the FUV-heated clump surface, ∼ cm − ), ν (theratio of sound speed at the surface to that in the innermost clumpregions), and the turn-on time of the heating flux (compared tothe initial sound crossing time in the clump).We computed the deconvolved size for each of the 160 70 µ m-bright cores in the active region and discarded all those smallerthan half the beam size. We then determined volume and columndensity for each of the remaining 102 sources. These were furtherdivided into two subsamples, based on their location either to-wards G353.2 + + ) impingingon each core, in Habing units of 1 . × − erg cm − s − wasderived from Eq. 14 of Giannetti et al. (2012) by scaling to a dis-tance of 1 . ◦ . We adopted a total FUV stellar luminosityof 1 . × L (cid:12) for G353.2 + + ii regions. Furthermore, the relatively high adopted inclination of45 ◦ may partly compensate for extinction.From G and the average density we derived the core surfacetemperature using the PDR model of Kaufman et al. (1999). Inturn, we derived ν for each core from the surface and far-IRtemperatures. It should be noted that ν measures the intensity ofthe FUV field. The dimensionless column density parameter η ,namely the ratio of the current core column density to that of theFUV-heated core surface ( ∼ cm − ), was also computed fromthe mass and the deconvolved size of each core. The results areshown in Fig. 16, adapted from diagnostic diagrams from Gorti& Hollenbach (2002) (see e. g. their Figs. 2 and 7).Gorti & Hollenbach (2002) consider two classes of corespopulating a cloud PDR. One class is represented by turbulentcores in a vacuum that form quickly in the PDR in a time lessthan that needed by the IF to cross the cloud PDR. It shouldbe noted that these authors do not account for gravity in theiranalytical treatment. Assuming a PDR thickness of ∼ ∼ − , the lifetime of these cores would be < ν , the non-thermal to thermal pressure ratio ( α ), andthe magnetic to thermal pressure ratio ( β ); dot-dashed lines inFig. 16 mark the loci of critical density for α = β = α = β =
2, see Eqs. 6-7 of Gorti & Hollenbach (2002).
Article number, page 12 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357
Fig. 16. η - ν (see text) plot for the cores associated with the PDRs aroundthe H ii regions G353.2 + + ff erent values of the non-thermal to thermal pressureratio ( α ) and the magnetic to thermal pressure ratio ( β ), and a frozenmagnetic field. The solid lines mark the evolution of the column densityratio η against the parameter ν (which increases with increasing G ) forpre-existing cores embedded in an interclump medium. The dotted linesindicate the fraction of mass lost by such cores due to photoevaporationwhen exposed to a steadily increasing G . The dashed line marks thecritical density for such cores, i. e. the column density of a core thatwould be completely photoevaporated by a FUV field ν . The second class these authors consider are pre-existing cores.Pre-existing cores much smaller than the thickness of the cloudPDR and embedded in an ICM would enter gradually the PDRand would experience a steadily increasing FUV field (and ν ).The solid lines in Fig. 16 mark the evolution of the column densityparameter η against the parameter ν , which will steadily increaseas the core moves deeper into the PDR (Eqs. 24–25 of Gorti &Hollenbach 2002). The core experiences photoevaporation andthe fraction of mass lost during the evolution is indicated bydotted lines in the figure. The dashed line marks the gas columndensity that would be completely photoevaporated given a FUVfield ν (Eq. 26 of Gorti & Hollenbach 2002).The cores in the PDRs around G353.2 + + has not been corrected for extinction, we notethat the highest ν values always derive from the highest valuesof G . Therefore, these cores represent the ones nearest to theionising sources, which are the least a ff ected by extinction. In thedensity range spanned by the rest of the sample, the core surfacetemperature is not much a ff ected by G and even a decrease ofan order of magnitude would result in a decrease in temperatureby a factor of 2–3. Therefore, log( ν ) would decrease at most by ∼ . ν (i.e. the IF moves closer and closer to thecore) causes the eroded gas column density to decrease below thecritical density, a core will be quickly photoevaporated. However, this is inconsistent with the cores with the highest column densitydisplaying the highest values of ν . In fact, this would imply thatthe cores with the highest column density are located in regionswhere G is the highest, that is to say close to the IFs. But thereis no reason why equally high column densities should not befound closer to the bulk molecular gas (exhibiting low valuesof ν ). Then, either turbulence and / or gas compression becomesimportant close to the IFs and new cores are formed or, morelikely, lack of spatial resolution artificially merges smaller coresincreasing the measured column density (we note that the IF isseen edge-on towards both H ii regions).This analysis suggests that the PDRs preceding the IFs pen-etrate into the molecular clouds through a population of pre-existing molecular cores embedded in a lower density ICM. Someof these cores are then likely to experience an RDI with a subse-quent gravitational collapse (see Bisbas et al. 2011, and referencestherein). This is consistent with the elephant-trunk structures,some associated with IR sources, observed in the region (Massiet al. 2015). Decataldo et al. (2019) numerically modelled thephotoevaporation of Jeans-unstable molecular cores, hence in-cluding gravity, finding that Jeans-unstable cores will remainJeans-unstable after the RDI, although losing part of their mass.This indicates that the most massive cores in the cloud PDRstowards NGC6357 should collapse and host forming stars, ratherthan be just photoevaporated. In other words, accelerated or eventriggered star formation is expected around the H ii regions. We derived the CMF for the samples of cores in the active andquiescent region and estimated the slope of the high-mass end ofthe CMF, α = − d log(d N / d M ) / d log( M ), using only cores with M ≥ M (cid:12) . To minimise statistical biases, which a ff ect simplelinear fits in the log-log space (see Maschberger & Kroupa 2009),we used the python task PyMC and the maximum likelihoodestimator (ML) discussed by Maschberger & Kroupa (2009). Theresults are listed in Table 3.Three trends can be pointed out from Table 3: i) In each region(quiescent and active), all samples and estimates are consistentwith one another within 1 σ , except for the values for pre-stellarcores in the active area yielded by the ML; ii) all estimates inthe quiescent area are consistent with a Salpeter IMF ( α = . σ ; iii) all estimated CMFs in the active area are flatterthan in the quiescent area at least at a 2 σ significance level. Anye ff ect of the FUV field on the dust opacity, discussed in Sect. 3.5,should not significantly a ff ect α in the pre-stellar samples (exceptpossible global shifts in mass, di ff erent for each region), which donot include cores embedded in the PDRs surrounding G353.2 + + α that are consistent with those of the IMFsderived by Massi et al. (2015) for Pismis 24, adopting the smallerextinction range. When the cluster members are selected in theextinction range A V ∼ . − .
8, by assuming the same distanceas in this work, Massi et al. (2015) find slopes in the range α ∼ . − . ∼ − ∼ − M (cid:12) ,depending on the estimator used.The flatter CMF in the active region would be another sig-nature of the e ff ects of an intense FUV field, already discussedfor the cores in the PDRs in Sect. 4.3. The FUV field wouldphotodissociate the smaller cores more quickly, resulting in atop-heavy CMF. However, the e ff ect would be more noticeablein the low-mass end of the CMF, which cannot be probed by ourobservations. This does not necessarily imply that a flatter CMF Article number, page 13 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final
Table 3.
Power index, α = − d log(d N / d M ) / d log( M ), of the CMFs. Only cores with M ≥ M (cid:12) have been used. Quiescent area Active areaSample PyMC fit ML Number of PyMC fit ML Number ofdatapoints datapointsAll cores 2 . ± . . ± . . ± . . ± . a . ± . . ± . . ± . . ± . a . ± . . ± . . ± . . ± .
05 21
Notes. ( a ) See the text on the problems to obtain actual protostellar and pre-stellar samples would in turn result in a flatter IMF as the FUV field may a ff ectthe SFE of the cores as well.We have assumed isothermal cores. The development of tem-perature gradients may impact on core mass determination in twoways. Protostellar cores are heated from the inside, thus using asingle dust temperature, a mean value weighted by the coldestoutermost layers, can lead to overestimating a core mass. Moremassive cores should be more a ff ected than less massive cores,so a residual protostellar contamination of our starless sample inthe quiescent (lower FUV-flux) region may cause the actual CMFto be slightly steeper than found. On the other hand, cores in theactive (high FUV-flux) region are heated from the outside, so asingle dust temperature is a mean value dominated by the warmeroutermost layers, resulting in an underestimate of the mass. Aprototellar contamination of the sample would result in cores withboth outer and inner heating and would probably just mitigatethe e ff ect. Thus the actual CMF in the UV-active region mightbe even flatter than found. Temperature gradients in cores aretherefore likely to enhance the di ff erence between CMFs ratherthan smooth it. Fukui et al. (2018b) (erratum in Fukui et al. 2018a) proposethat the miniburst of star formation in NGC6334 and NGC6357originated in a cloud-cloud collision scenario. It is thereforeinteresting to check whether the CMFs that we have derived showany signature of such a process, provided this is still at work. Thisscenario has been theoretically investigated through numericalsimulations by a number of authors (e.g. Takahira et al. 2014,Balfour et al. 2015, Takahira et al. 2018, Shima et al. 2018, Wuet al. 2018, Fukui et al. 2021) generally finding that cloud-cloudcollisions increase the SFE and boost the birth of high-massstars. Takahira et al. (2018) find a CMF with α = . − ), which isconsistent with our determinations in the active region. However,when the collision speed is increased, a break will develop onthe CMF (300 M (cid:12) at v =
10 km s − shifting to lower massesfor higher collision velocities) above which the CMF steepens.Shima et al. (2018) derived an IMF steeper than a Salpeter onein the high-mass end (at collision velocities of 10 and 20 kms − ). The inclusion of photoionising feedback by these authorsincreases the SFE and results in a slightly flatter IMF, althoughstill steeper than a Salpeter one.Fukui et al. (2018b) find a velocity separation between cloudsof ∼
12 km s − ) towards NGC6357, so a comparison betweensimulations and the results summarised in Table 3 shows thatthe CMF in the active region is consistent with the cloud-cloudcollision scenario simulated by Takahira et al. (2018), but notwith the simulations of Shima et al. (2018). Nevertheless, thelatter agrees with the high-end IMF derived by Massi et al. (2015)in Pismis 24 using the wider extinction range, which is actually steeper than a Salpeter one. In addition, Takahira et al. (2018)predict much higher fractions of gas mass in dense cores than weestimated in NGC6357 (1 . v =
20 km s − , which appears to be flat upto 6–10 M (cid:12) at ≥ . M > −
10 M (cid:12) . Our derived CMFdoes not exhibit such a break, but because of the completenesslimit at ∼ (cid:12) we cannot be conclusive. Fukui et al. (2021) alsopropose that a signature of a cloud-cloud collision can be foundin the distribution of core-core separation. We constructed thisdistribution by using the edges of the minimum spanning tree,as in Fukui et al. (2021). Unfortunately, our spatial resolutiondoes not allow us to resolve their peak at ∼ . ∼
50 pc (the complex radius),with a low peak between 10–20 pc that may resemble the secondpeak yielded by the simulations of Fukui et al. (2021). Ultimately,we cannot draw any clear conclusion on a cloud-cloud collisionscenario in NGC6357 based only on the comparison betweenobserved and theoretical CMFs.
5. Summary and conclusions
We have used JCMT SCUBA-2 observations at 450 and 850 µ m,complemented with Herschel (Hi-Gal) maps at 70 and 160 µ m, tostudy the properties of the dense core population in the galacticH ii regions-young star clusters-star forming complex NGC6357.In particular, we aimed to assess the e ff ect of intense FUV radia-tion on dense cores.We mapped the region in the CO(3-2) line as well, to cor-rect the emission at 850 µ m from line contamination in order toconstruct a map of pure (dust) continuum emission. We then usedthe algorithm Gaussclumps on the map at 850 µ m to identify thedense cores after removing the extended emission..We retrieved 1221 cores. For 686 of these we could derivea dust temperature by fitting greybodies to their SEDs obtainedfrom submm (SCUBA-2) and FIR (Herschel) fluxes. The ob-served (beam-convolved) sizes lie in the range ∼ (cid:48)(cid:48) (the beamsize at 850 µ m) to ∼ (cid:48)(cid:48) ( ∼ . . ii regions G353.2 + + + ff ected by an intense FUVfield. The quiescent region contains 275 cores farther from theionising sources, hence less a ff ected by FUV photons. We there-fore used the quiescent region as a control sample to study thee ff ects of the FUV radiation on dense cores in the active region.Our main results are the following: Article number, page 14 of 16. Brand et al.: A possible far-ultraviolet flux-dependent core mass function in NGC 6357
1. We found di ff erent core temperature distributions in the tworegions, peaking at ∼
25 K (quiescent region) and ∼
35 K(active region), which we attribute to the e ff ects of the FUVradiation.2. We further subdivided our sample into starless and protostellarcores, by exploiting the association with protostellar tracerssuch as WISE point sources and emission at 70 µ m. Wefound 51 candidate protostellar and 224 starless cores inthe quiescent region, and 160 candidate protostellar and 251starless cores in the active region. Unfortunately, the sampleof the active region is biased towards protostellar cores dueto the e ff ects of the external FUV field which heats the dustincreasing its emission at 70 µ m and saturation in the WISEbands towards the H ii regions.3. We derived the core masses by assuming a plausible dustopacity (we also discussed possible e ff ects of FUV radiation).We estimated a mass completeness limit of ∼ (cid:12) . We foundmass-size relations of log( M / M (cid:12) ) ∼ a × log( D / arcsec), with a in the range 2 . − .
4, consistent with those from otherregions or large samples of clumps. The starless cores abovethe mass completeness limit are likely to be gravitationallybound, hence pre-stellar in nature.4. The estimated fraction of molecular gas in dense cores is 1 .
4% in NGC6357. This is consistent with values from mostgalactic star formation regions.5. We showed that the properties of the cores nearer to the H ii regions are consistent with pre-existing cores gradually beingengulfed in a PDR and photoevaporating.6. We constructed the CMFs for M > (cid:12) , finding a Salpeter-like CMF in the quiescent region ( α ∼ . − .
4) and asignificantly flatter (at a 2 σ level) one in the active region ( ∼ . − . α = − d log(d N / d M ) / d log( M )). The di ff erencebecomes even more significant for pre-stellar cores whenusing the maximum likelihood estimator ( α ∼ α ∼ . ff ects of the FUV radiation as well.7. We compared the CMFs with those predicted by simulationsof cloud-cloud collisions, finding no conclusive evidence forcloud-cloud collisions giving rise to the cores, rather thanthem being pre-existing.In conclusion, we found di ff erences in the global properties ofthe cores in the active region and those in the quiescent region.In particular we found a statistically significant di ff erence in theslope of the CMF between the two regions. We attribute thesedi ff erences to the influence of the FUV radiation. Acknowledgements.
The James Clerk Maxwell Telescope was operated by theJoint Astronomy Centre until 2015, on behalf of the Science and TechnologyFacilities Council of the United Kingdom, the National Research Council ofCanada and the Netherlands Organisation for Scientific Research. Additionalfunds for the construction of SCUBA-2 were provided by the Canada Founda-tion for Innovation. The James Clerk Maxwell Telescope has been operated bythe East Asian Observatory since 2015, on behalf of The National Astronomi-cal Observatory of Japan, Academia Sinica Institute of Astronomy and Astro-physics, the Korea Astronomy and Space Science Institute, the National Astro-nomical Observatories of China and the Chinese Academy of Sciences (GrantNo. XDB09000000), with additional funding support from the Science and Tech-nology Facilities Council of the United Kingdom and participating universitiesin the United Kingdom and Canada. We thank Harriet Parsons for the Perl scriptused to correct the 850 µ m data with the CO-emission, and Eugenio Schisanofor providing us with the Herschel 160 µ m map used in Fig. 1. This research hasmade use of NASA’s Astrophysics Data System Bibliographic Services (ADS)and of the SIMBAD database, operated at CDS, Strasbourg, France. This workhas made use of data from the European Space Agency (ESA) mission Gaia ( ), processed by the Gaia
Data Process-ing and Analysis Consortium (DPAC, ). Funding for the DPAC has been provided by na-tional institutions, in particular the institutions participating in the
Gaia
Mul-tilateral Agreement. AG and FM were partly supported by INAF through the grant Fondi Mainstream ’Heritage of the current revolution in star formation: theStar-forming filamentary Structures in our Galaxy’.
References
Alves, J., Lombardi, M., & Lada, C. J. 2007, A&A, 462, L17André, P., Di Francesco, J., Ward-Thompson, D., et al. 2014a, PPVI, 27André, P., Di Francesco, J., Ward-Thompson, D., et al. 2014b, Protostars andPlanets VI, 27Arthur, S. J., Henney, W. J., Mellema, G., de Colle, F., & Vázquez-Semadeni, E.2011, MNRAS, 414, 1747Balfour, S. K., Whitworth, A. P., Hubber, D. A., & Ja ff a, S. E. 2015, MNRAS,453, 2471Belloche, A., Schuller, F., Parise, B., et al. 2011, A&A, 527, A145Bergin, E. A. & Tafalla, M. 2007, ARA&A, 45, 339Bisbas, T. G., Wünsch, R., Whitworth, A. P., Hubber, D. A., & Walch, S. 2011,ApJ, 736, 142Bobotsis, G. & Fich, M. 2019, ApJ, 884, 77Buckle, J. V., Hills, R. E., Smith, H., et al. 2009, MNRAS, 399, 1026Cappa, C. E., Barbá, R., Duronea, N. U., et al. 2011, MNRAS, 415, 2844Chapin, E. L., Berry, D. S., Gibb, A. G., et al. 2013, MNRAS, 430, 2545Csengeri, T., Weiss, A., Wyrowski, F., et al. 2016, A&A, 585, A104Dale, J. E., Clark, P. C., & Bonnell, I. A. 2007, MNRAS, 377, 535Decataldo, D., Pallottini, A., Ferrara, A., Vallini, L., & Gallerani, S. 2019, MN-RAS, 487, 3377Dempsey, J. T., Friberg, P., Jenness, T., et al. 2013, MNRAS, 430, 2534Drabek, E., Hatchell, J., Friberg, P., et al. 2012, MNRAS, 426, 23Dunham, M. M., Crapsi, A., Evans, II, N. J., et al. 2008, ApJS, 179, 249Feigelson, E. D. & Babu, G. J. 2013, Statistical Methods for Astronomy, ed. T. D.Oswalt & H. E. Bond, 445Fukui, Y., Inoue, T., Hayakawa, T., & Torii, K. 2021, PASJ, 73, S405Fukui, Y., Kohno, M., Yokoyama, K., et al. 2018a, PASJ, 70, S60Fukui, Y., Kohno, M., Yokoyama, K., et al. 2018b, PASJ, 70, S41Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1Giannetti, A., Brand, J., Massi, F., Tieftrunk, A., & Beltrán, M. T. 2012, A&A,538, A41González-Samaniego, A. & Vazquez-Semadeni, E. 2020, MNRAS, 499, 668Goodwin, S. P., Nutter, D., Kroupa, P., Ward-Thompson, D., & Whitworth, A. P.2008, A&A, 477, 823Gorti, U. & Hollenbach, D. 2002, ApJ, 573, 215Holland, W. S., Bintley, D., Chapin, E. L., et al. 2013, MNRAS, 430, 2513Ikeda, N. & Kitamura, Y. 2009, ApJ, 705, L95Jenness, T., Currie, M. J., Tilanus, R. P. J., et al. 2015, MNRAS, 453, 73Kaufman, M. J., Wolfire, M. G., Hollenbach, D. J., & Luhman, M. L. 1999, ApJ,527, 795Koenig, X. P., Leisawitz, D. T., Benford, D. J., et al. 2012, ApJ, 744, 130Krumholz, M. R. 2014, Phys. Rep., 539, 49Kryukova, E., Megeath, S. T., Gutermuth, R. A., et al. 2012, AJ, 144, 31Lucas, W. E., Bonnell, I. A., & Forgan, D. H. 2017, MNRAS, 466, 5011MacLachlan, J. M., Bonnell, I. A., Wood, K., & Dale, J. E. 2015, A&A, 573,A112Maíz Apellániz, J., Crespo Bellido, P., Barbá, R. H., Fernández Aranda, R., &Sota, A. 2020, A&A, 643, A138Maíz Apellániz, J., Walborn, N. R., Morrell, N. I., Niemela, V. S., & Nelan, E. P.2007, ApJ, 660, 1480Maschberger, T. & Kroupa, P. 2009, MNRAS, 395, 931Massey, P., DeGioia-Eastwood, K., & Waterhouse, E. 2001, AJ, 121, 1050Massi, F., Brand, J., & Felli, M. 1997, A&A, 320, 972Massi, F., Giannetti, A., Di Carlo, E., et al. 2015, A&A, 573, A95Massi, F., Weiss, A., Elia, D., et al. 2019, A&A, 628, A110Men’shchikov, A., André, P., Didelon, P., et al. 2012, A&A, 542, A81Molinari, S., Swinyard, B., Bally, J., et al. 2010, PASP, 122, 314Mookerjea, B., Kramer, C., Nielbock, M., & Nyman, L.-Å. 2004, A&A, 426,119Motte, F., Nony, T., Louvet, F., et al. 2018, Nature Astronomy, 2, 478Naylor, D. A., Gom, B. G., Abdelazim, S., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9153, Mil-limeter, Submillimeter, and Far-Infrared Detectors and Instrumentation forAstronomy VII, ed. W. S. Holland & J. Zmuidzinas, 915323Ossenkopf, V. & Henning, T. 1994, A&A, 291, 943Ossenkopf, V., Rollig, M., Cubick, M., & Stutzki, J. 2007, in Molecules in Spaceand Laboratory, p.95, ed. J. Lemaire & F. CombesParsons, H., Dempsey, J. T., Thomas, H. S., et al. 2018, ApJS, 234, 22Patil, A., Huard, D., & Fonnesbeck, C. 2010, JStatSoft, 35, 1Ramírez-Tannus, M. C., Poorta, J., Bik, A., et al. 2020, A&A, 633, A155Rathborne, J. M., Lada, C. J., Muench, A. A., et al. 2009, ApJ, 699, 742Russeil, D., Figueira, M., Zavagno, A., et al. 2019, A&A, 625, A134Sadavoy, S. I., Di Francesco, J., Johnstone, D., et al. 2013, ApJ, 767, 126Schuller, F., Menten, K. M., Contreras, Y., et al. 2009a, A&A, 504, 415Schuller, F., Menten, K. M., Contreras, Y., et al. 2009b, A&A, 504, 415Shima, K., Tasker, E. J., Federrath, C., & Habe, A. 2018, PASJ, 70, S54Stutzki, J. & Guesten, R. 1990, ApJ, 356, 513Takahira, K., Shima, K., Habe, A., & Tasker, E. J. 2018, PASJ, 70, S58Takahira, K., Tasker, E. J., & Habe, A. 2014, ApJ, 792, 63Wall, J. E., Mac Low, M.-M., McMillan, S. L. W., et al. 2020, ApJ, 904, 192Wang, J., Townsley, L. K., Feigelson, E. D., et al. 2007, ApJS, 168, 100Wu, B., Tan, J. C., Nakamura, F., Christie, D., & Li, Q. 2018, PASJ, 70, S57Xu, Y., Bian, S. B., Reid, M. J., et al. 2018, A&A, 616, L15 Article number, page 15 of 16 & A proofs: manuscript no. Brand_AA_2020_39506_final
Fig. 17.
Example of SED fits to two cores in the active region. In thetop panel, all flux densities can be fitted with a single greybody; there isno excess at 70 µ m, and this core is recognised as a pre-stellar core. Thecore in the lower panel has an excess flux density at 70 µ m (the point hasnot been excluded from the fit, hence the large χ ). This could be dueeither to the core being heated from the outside by the FUV radiationfield, or to a protostar inside the core (see Sect. 4.2).
6. Appendix
Here we show examples of SED fits to cores in the active andquiescent regions (see Sect. 4.2).