NGC 7538 : Multiwavelength Study of Stellar Cluster Regions associated with IRS 1-3 and IRS 9 sources
K. K. Mallick, D. K. Ojha, M. Tamura, A. K. Pandey, S. Dib, S. K. Ghosh, K. Sunada, I. Zinchenko, L. Pirogov, M. Tsujimoto
MMon. Not. R. Astron. Soc. , 000–000 (0000) Printed 5 December 2018 (MN L A TEX style file v2.2)
NGC 7538 : Multiwavelength Study of Stellar ClusterRegions associated with IRS 1–3 and IRS 9 sources.
K. K. Mallick, (cid:63) D. K. Ojha, M. Tamura, A. K. Pandey, S. Dib, , S. K. Ghosh, , K. Sunada, I. Zinchenko, , L. Pirogov, , and M. Tsujimoto Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba,Mumbai 400 005, India National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Aryabhatta Research Institute of Observational Sciences, Manora Peak, Nainital 263 129, India Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5-7., DK-1350, Copenhagen, Denmark National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007, India Mizusawa VLBI Observatory, NAOJ, 2-12 Hoshi-ga-oka, Mizusawa-ku, Oshu-shi, Iwate 023-0861, Japan Institute of Applied Physics, Russian Academy of Sciences, 46 Uljanov str., Nizhny Novgorod 603950, Russia Lobachevsky State University of Nizhni Novgorod, 23 Prospekt Gagarina, 603950, Nizhni Novgorod, Russia Japan Aerospace Exploration Agency, Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara,Kanagawa 252-5210, Japan
ABSTRACT
We present deep and high-resolution (FWHM ∼ . (cid:48)(cid:48)
4) near-infrared (NIR) imagingobservations of the NGC 7538 IRS 1–3 region (in
JHK bands), and IRS 9 region (in HK bands) using the 8.2 m Subaru telescope. The NIR analysis is complementedwith GMRT low-frequency observations at 325, 610, and 1280 MHz, molecular lineobservations of H CO + ( J =1–0), and archival Chandra
X-ray observations. Usingthe ‘ J − H/H − K ’ diagram, 144 Class II and 24 Class I young stellar object (YSO)candidates are identified in the IRS 1–3 region. Further analysis using ‘ K/H − K ’diagram yields 145 and 96 red sources in the IRS 1-3 and IRS 9 regions, respectively. Atotal of 27 sources are found to have X-ray counterparts. The YSO mass function (MF),constructed using a theoretical mass-luminosity relation, shows peaks at substellar( ∼ M (cid:12) ) and intermediate ( ∼ M (cid:12) ) mass ranges for the IRS 1–3 region.The MF can be fitted by a power law in the low mass regime with a slope of Γ ∼ ii region associated with the IRS 1–3 sources, whose spectral indexof 0 . ± .
11 suggests optical thickness. This compact region is resolved into threeseparate peaks in higher resolution 1280 MHz map, and the ‘East’ sub-peak coincideswith the IRS 2 source. H CO + ( J =1–0) emission reveals peaks in both IRS 1–3 andIRS 9 regions, none of which are coincident with visible nebular emission, suggestingthe presence of dense cloud nearby. The virial masses are approximately of the orderof 1000 M (cid:12) and 500 M (cid:12) for the clumps in IRS 1–3 and IRS 9 regions, respectively. Key words:
ISM: individual objects: NGC 7538 – infrared: ISM – ISM: molecules –radio continuum: ISM – stars: luminosity function, mass function – X-rays: stars
NGC 7538, an optically visible H ii region (Fich & Blitz1984, also known as Sh2-158), is a part of the Cas OB2 (cid:63) E-mail: [email protected] complex and located at l = 111 . o , b = +00 . o , at adistance of 2.65 kpc (Moscadelli et al. 2009). Early infraredobservations of this region by Wynn-Williams et al. (1974)and Werner et al. (1979) revealed the presence of infraredsources IRS 1-11 associated with and in the neighbourhoodof the optical nebula. This region has been studied in prolific c (cid:13) a r X i v : . [ a s t r o - ph . GA ] J u l K. K. Mallick et al. detail using various techniques such as high-frequency radioobservations, line emission observations, maser observations,outflows, and so on. However, most of these studies as well asmany recent ones concentrate on the individual features ofluminous IRS and candidate high-mass sources. Even then,the bulk deals with the sources around IRS 1–3 stellar clus-ter region, and the IRS 9 region analyses have been sparse.Recently, an NIR study of the overall NGC 7538 region byOjha et al. (2004a), reddening and cluster related studiesusing NIR by Balog et al. (2004), a spectroscopic study ofthe luminous sources by Puga et al. (2010), and a multi-wavelength study of clusters (using statistical techniques)with a focus on high-mass stars by Chavarr´ıa et al. (2014)have been carried out. Other large scale studies have beencarried out at far-infrared
Herschel bands and at submil-limetre wavelengths to identify cold clumps and filamentarystructures (Sandell & Sievers 2004; Fallscheer et al. 2013).According to Ojha et al. (2004a) and McCaughreanet al. (1991), there appear to be three distinct sub-regionswhich can be separated based on the stellar population andmorphology, namely the IRS 1–3, IRS 4–8, and IRS 9 sub-regions. Although the previous works identified a rich clustermembership in a wide field, encompassing all the major star-forming sites in this complex, none of the optical/infraredsurveys were deep enough to reach the substellar regime.Hence the works available in the literature were not ableto have a detailed study of these stellar cluster sub-regions,which need to be analysed separately due to their veritabledifferences. Recent advanced instruments on 8–10 m classtelescopes now make it feasible to conduct imaging and spec-troscopic studies of low-mass populations in distant high-mass star-forming regions, where the star-forming environ-ment may be different from their low-mass counterparts.Moreover, in the case of stars in a distant cluster, high res-olution imaging is also needed to recognize individual stars.Since most of the available studies of low-mass populationsare mainly based on nearby star-forming regions and thesample of substellar sources is small to draw definitive con-clusions, we considered it worthwhile to focus on the stellarclusters of the NGC 7538 region observed using the 8.2 mSubaru telescope - the deepest and highest-resolution NIRdata till date. The NIR data has been used to study theluminosity function and initial mass function (IMF) of theregion. In young massive star-forming regions, a gamut ofcomponents are present which could affect further evolution,and thus we have complemented our deep NIR observationswith : previously unexamined low-frequency bremsstrahlungto ascertain the ionizing gas characteristics, molecular lineH CO + ( J =1 - 0) observations for the dense gas morphol-ogy, and Chandra
X-ray observations for stellar populationanalysis.In this paper, therefore, the aim is to continue withour multiwavelength study of star-forming regions (Ojha etal. 2004a, 2011; Samal et al. 2007, 2010), as well as ourinvestigations to detect and characterize the young browndwarfs (BDs) in distant massive star-forming regions (cf.Ojha et al. 2004b, 2009). In Section 2, we present details ofthe observations and data reduction procedures. The YSOselection procedure is dealt with in Section 3. The spatialdistribution, morphology, and physical characteristics of theregions are discussed in Section 4. In Section 5, we elaborateupon the luminosity and mass functions obtained for differ- ent clusters. Discussion and final conclusions are presentedin Sections 6 and 7, respectively.
Deep NIR imaging observations of the NGC 7538 IRS 1-3 re-gion (centered on α = 23 h m s , δ = +61 o (cid:48) (cid:48)(cid:48) )in J ( λ =1.25 µ m), H ( λ =1.64 µ m), and K ( λ =2.21 µ m) bands, and the NGC 7538 IRS 9 region (centered on α = 23 h m s , δ = +61 o (cid:48) (cid:48)(cid:48) ) in H and K bandswere obtained on 2005 August 19, using the Cooled InfraredSpectrograph and Camera for OHS (CISCO) mounted atthe Cassegrain focus of the 8.2 m Subaru telescope. Theseobservations were done in the service mode of the telescope.CISCO is equipped with a 1024 × (cid:48)(cid:48) pixel − at the f/12focus of the telescope provides a field-of-view (FoV) of ∼ (cid:48) × (cid:48) (Motohara et al. 2002). Observations were car-ried out in a 3 × ∼ (cid:48)(cid:48) offsets - witha varying number of images (three upto ten) being obtainedat each dithered position. Individual image exposure timeswere 40 s, 20 s, and 10 s for the J , H , and K bands, respec-tively, finally yielding a total integration time of 12, 12, and13.5 minutes in these respective bands. All the observationswere done under excellent photometric sky conditions. Theaverage seeing size was measured to be 0.4 (cid:48)(cid:48) full-width-at-half-maxima (FWHM) in all three filters, and the air massvariation was between 1.34 and 1.44. Off-target (located ∼ (cid:48) east of the target position) sky-frame observations, iden-tical in area to the target FoV, were taken just after thetarget observations using a similar procedure.Data reduction was done using the Image Reductionand Analysis Facility ( iraf ) software package. The sky flatswere generated by median-combining individual ditheredsky frames for respective filters. These median-combinedsky-flats were applied for both flat-fielding and sky subtrac-tion. Identification of the point sources and their photometrywas performed using the daofind and daophot packages of iraf . Because of source confusion and nebulosity within theregion, photometry was performed using the point spreadfunction (PSF) algorithm allstar in the daophot package(Stetson 1987). An aperture radius of 4 pixels ( ∼ (cid:48)(cid:48) ) wasused for the final photometry, with appropriate aperture cor-rections applied for the respective bands. Since no standardstar was observed during the observations, the photomet-ric calibration was carried out using sources (about 10-12,cross-matched within 0.4 (cid:48)(cid:48) of the Subaru catalogue) from theTwo Micron All Sky Survey (2MASS) , selected on the ba-sis of their ‘phqual’ and ‘ccflg’ flag values, as well as vi-sual examination, to avoid artifacts and contaminations. Fi-nally, the photometric calibration rms was ∼ This publication makes use of data products from the Two Mi-cron All Sky Survey, which is a joint project of the Universityof Massachusetts and the Infrared Processing and Analysis Cen-ter/California Institute of Technology, funded by the NationalAeronautics and Space Administration and the National ScienceFoundation. c (cid:13) , 000–000
GC 7538 : IRS 1-3 and IRS 9 California Institute of Technology (CIT) system (Oasa etal. 2006), and hence the 2MASS magnitudes too were con-verted to CIT system (using Carpenter 2001) for calibra-tion purpose. On comparison of our photometry with thatof Ojha et al. (2004a), we find that the average dispersion(in the entire K magnitude range) was ∼ JHK bands. Our higher spatial resolution permits bet-ter source separation and sky determination. Sources whichwere bright and saturated in Subaru images, but had goodquality (‘phqual=A or B’ for J , H , and K s bands each)2MASS photometry had their magnitudes taken from the2MASS catalog after conversion to CIT system. Similar pho-tometric procedure was also carried out for the off-targetsky region. However, the western edge of the sky region wasfound to be slightly contaminated by a nearby nebula, andhence the sky frame was trimmed to remove the nebulouswestern portion before doing the photometry. The final skyframe size on which photometry (and completeness calcu-lation below) was carried out is ∼ (cid:48) × (cid:48) . Since theseobservations were carried out in service mode, it was foundthat during the later observations, of IRS 9 region in K band,source profiles at the north-east part of the images were elon-gated, due to some likely optics problem. Since this part(north-east of IRS 9 region) of the image is not crowded ornebulous, aperture photometry was carried out to estimatethe source magnitudes of the sources with elongated profiles.Even then, due to limitations, we use IRS 9 photomtery forqualitative assessments only in this work.The completeness limits of the images were evaluatedthrough artificial star experiments using addstar in iraf .Since the IRS 1-3 and IRS 9 regions have varying nebulosity,the images were divided into separate regions as shown inFigure 1, followed by completeness determination for eachsub-region. A fixed number of stars were added in every 0.5magnitude interval, followed by photometry to see how manyof these added stars were recovered. This cycle was carriedout repeatedly. We thus obtained the detection rate - whichis just the ratio of the number of recovered artificial stars tothe number of added stars - as a function of magnitude foreach of the sub-regions in IRS 1-3 and IRS 9 regions, as wellas the sky region. Table 1 summarizes the 90% completenesslimits for all three bands in each of the sub-regions. The 10 σ limiting magnitudes for our observations are estimated to be ∼
22, 21 and 20 in the J , H , and K bands, respectively. Ascan be seen, the sky frame 90% completeness limits are equalto these 10 σ limiting magnitudes for the H and K bands,and slightly lower for the J band. Radio continuum observations were carried out using the Gi-ant Metrewave Radio Telescope (GMRT) for the frequencybands 325 MHz (2004 July 03), 610 MHz (2004 Septem-ber 18), and 1280 MHz (2004 January 25). The GMRTarray, consisting of 30 antennae, is in an approximate Y-shaped configuration. Each of these antennae has a diam-eter of 45 m, and thus a primary beam size of ∼ (cid:48) , 43 (cid:48) , and 26.2 (cid:48) for 325, 610, and 1280 MHz, respectively . Thereis a central region ( ∼ × ∼
14 km each. The minimum and maximum baselinesare 100 m and 25 km, respectively. Further details about theGMRT array can be looked up in Swarup et al. (1991).The total observation time ranged from ∼ aips software. Successive rounds of flaggingand calibration were carried out to improve the calibration.Flagging involved removal of bad data (including bad an-tennae, baselines, channels, time-ranges resulting from ter-restrial radio frequency interference, etc), and was doneusing the ‘ vplot-uvflg ’ and ‘ tvflg ’ tasks. The respec-tive flux and phase calibrators were used in the standard‘ calib-getjy-clcal ’ procedure for amplitude and phasecalibration. After satisfactory calibration, the source data(NGC 7538) was ‘ split ’ from the whole file (which containsflux and phase calibrator data in addition). Facet imagingwas done using the aips task ‘ imagr ’ to generate the req-uisite images. To remove the ionospheric phase distortioneffects, a few rounds of (phase) self-calibration - with de-creasing ‘solint’ - were carried out using the task ‘ calib ’ .Table 2 gives the details of the GMRT observations andthe parameters of the generated images. In addition, VLAarchival image for 4860 MHz, for the observation date 2000September 22 (Project ID BP0068), was also used in theanalysis . Chandra
X-ray Observations
Publicly available archival X-ray data for NGC 7538 regionwas retrieved from the
Chandra site (Obs. ID 5373). TheX-ray observations of this H ii region were carried out usingthe Advanced CCD Imaging Spectrometer (ACIS; Garmireet al. 2003) onboard the Chandra X-ray Observatory (CXO;Weisskopf et al. 2002). For our purpose, we use only theimaging array of ACIS (ACIS-I). ACIS-I consists of a 2 × × ∼ (cid:48) × (cid:48) . The net exposure time was 30 ks.Initial steps in the data reduction were carried out usingthe Chandra
Interactive Analysis of Observations ( ciao ; Fr-uscione et al. 2006) tool version 4.5 and
Chandra
CalibrationDatabase ( caldb ) version 4.5.8. The data was reprocessedusing the ‘ chandra repro ’ tool to apply the latest calibra-tion to it. Light curve of source-free background regions wereconstructed to verify that the data was not affected by so-lar flare activity. Subsequently, with the help of the waveletbased source detection tool - ‘ wavdetect ’ (Freeman et al.2002) - source detection was carried out at a threshold levelof 2 × − . Data image and exposure map with the defaultpixel scale of ∼ (cid:48)(cid:48) were used for this purpose. Once we GMRT manual fromhttp://gmrt.ncra.tifr.res.in/gmrt hpage/Users/doc/manual/Manual 2013/manual 20Sep2013.pdf This paper uses data produced as a part of the NRAO VLAArchive Survey (NVAS). The NVAS can be accessed throughhttp://archive.nrao.edu/nvas/. http://cda.harvard.edu/chaser/c (cid:13)000
CalibrationDatabase ( caldb ) version 4.5.8. The data was reprocessedusing the ‘ chandra repro ’ tool to apply the latest calibra-tion to it. Light curve of source-free background regions wereconstructed to verify that the data was not affected by so-lar flare activity. Subsequently, with the help of the waveletbased source detection tool - ‘ wavdetect ’ (Freeman et al.2002) - source detection was carried out at a threshold levelof 2 × − . Data image and exposure map with the defaultpixel scale of ∼ (cid:48)(cid:48) were used for this purpose. Once we GMRT manual fromhttp://gmrt.ncra.tifr.res.in/gmrt hpage/Users/doc/manual/Manual 2013/manual 20Sep2013.pdf This paper uses data produced as a part of the NRAO VLAArchive Survey (NVAS). The NVAS can be accessed throughhttp://archive.nrao.edu/nvas/. http://cda.harvard.edu/chaser/c (cid:13)000 , 000–000 K. K. Mallick et al. have a final list of positions of detected sources from ‘ wavde-tect ’ , we used the IDL based
ACIS Extract ( ae ) softwarepackage (Broos et al. 2010, 2012) version ‘March 6, 2013’to extract the relevant source properties. The algorithm de-tailed in the ae user’s guide was followed. The source countsare extracted within ∼ ae , the X-ray spec-tra are compiled and fitted with an optically-thin thermalplasma model attenuated by an interstellar absorption us-ing the ‘ xspec ’ fitting package. A total of 182 sources wereobtained in the FoV, all of which were verified to have P B (cid:54) B gives the probability that the extracted counts in thetotal band are solely a result of background fluctuations.The intrinsic hard band luminosity for all the sources wasfound to range from ∼ × to 3.5 × erg s − , whilethe intrinsic total luminosity was in the range ∼ × to 6 × erg s − . The hard band luminosity function peakwas at about 5 × erg s − . For sources with spectral fit-ting results, the column density peaks at ∼ cm − andthe plasma temperature at ∼ xphot program of Getman et al. (2010)to estimate the intrinsic fluxes and X-ray column densities.Among the total number of sources obtained, there willalso be extragalactic contaminants like Active Galactic Nu-clei (AGN), and foreground stellar sources. Though we usea small subset of sources for our study (see Sections 3.1and 3.2), and thus have not carried out a detailed contam-inantion analysis here, we can obtain an estimate using thevalues for the Cepheus B region (Getman et al. 2006) whichis close to NGC 7538 and had the same exposure time as wellas FoV. Getman et al. (2006) find that the extragalactic con-tamination in Cepheus B is (cid:54) (cid:54) ∼
16 contaminants (out of 182 total) in the NGC 7538 ACIS-I FoV. Table 3 gives the properties of 27 X-ray sources withNIR counterparts in the NIR FoV which have been selectedin this paper for further analysis. CO + ( J =1 - 0) Observations The H CO + ( J =1–0) (formylium) molecular line (86.754GHz) observations were carried out on 2004 May 02 withthe Nobeyama 45 m radio telescope. At 87 GHz, the half-power beam width and main beam efficiency, η , of the tele-scope were 18 (cid:48)(cid:48) and 0.51, respectively. We used the 25-BEamArray Receiver System (BEARS) (Sunada et al. 2000). Tocorrect for the beam-to-beam gain variation, we calibratedthe intensity scale of each beam using a 100 GHz SIS re-ceiver (S100) with an SSB filter. Furthermore, we observedthe same grid point in mapping with 9 different beams tosmooth the beam-to-beam gain variation. At the back end,we used 25 arrays of 1024 channel Auto-Correlators (ACs),which have a 32 MHz band width and a 37.8 kHz resolution, The
ACIS Extract corresponding to 0.13 km s − (Sorai et al. 2000). All the ob-servations were carried out in position-switching mode. Thestandard chopper wheel method was used to convert thereceived intensity into the antenna temperature, T ∗ A . Ourmapping observations covered the same region of the NIRimage. The mapping grid has 21 (cid:48)(cid:48) spacing, corresponding tohalf of the beam separation of the BEARS, i.e., nearly full-beam sampling. During the observations, the system noisetemperatures were in the range of 200 to 400 K, resultingin a noise level of 0.35 K in T ∗ A . The telescope pointing waschecked every 1.5 hours by observing the SiO maser sourceR Cas. The pointing accuracy was better than 3 (cid:48)(cid:48) . The photometric catalogs containing the J , H , and K bandmagnitudes for the IRS 1-3 region (see Section 2.1) and thesky field region were used to construct the NIR J-H vs H-K colour-colour diagrams (CC-Ds) shown in Figure 2. In thisfigure, the red curve denotes the dwarf locus from Bessell& Brett (1988) (converted to CIT system), blue solid linedenotes the locus of Classical T Tauri Stars (CTTS) fromMeyer et al. (1997), and the three parallel dashed green linesdenote the reddening vectors drawn using the reddening lawsof Cohen et al. (1981) ( A J /A V = 0 . , A H /A V = 0 . , and A K /A V = 0 . J-H colour is larger than that of the CTTS locus ex-tended into this region. There may also be an overlap in theNIR colours of the upper end band of Herbig Ae-Be starsand in the lower end band of CTTS in the ‘T’ region (Hil-lenbrand et al. 1992).The sky field CC-D shown in Figure 2(b) is used toexamine the extent upto which IRS 1-3 CC-D is affected byfield star contamination. As can clearly be seen in Figure2(b), almost all field star contamination is present in the ‘F’region. Therefore, while the sources falling in the ‘T’ and ‘P’regions of Figure 2(a) are most probably YSOs, the Class III-type sources from the ‘F’ region will be contaminated byfield stars.To further separate the most-likely YSOs from the ‘F’region, since pre-main sequence (PMS) stars display muchstronger X-ray emission than the field main sequence (MS)stars (Feigelson & Montmerle 1999; Montmerle 1996), we usethe X-ray source identifications from Section 2.3. For this,we cross-matched our NIR catalog with the X-ray catalogwithin 0.5 (cid:48)(cid:48) radius. X-ray detected sources, however, in gen-eral, suffer from extragalactic contamination (mostly AGN)and foreground stellar contamination. But since we are us-ing only those X-ray sources which have NIR counterparts,it is unlikely - similar to the work of Getman et al. (2006, for c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Cepheus B) and Kuhn et al. (2010, for W40) - that there willbe any extragalactic contamination. Also since the resolu-tion of
Chandra images ( ∼ (cid:48)(cid:48) ) is similar to our NIR imag-ing ( ∼ (cid:48)(cid:48) , see Section 2.1), mismatching should not be aconcern. From the matching radius and the source numberdensity, the number of X-ray sources to have an NIR coun-terpart by chance was calculated to be one at most. Aproposforeground contamination, the X-ray sources lie beyond thelow-density gap at about H − K ∼ . H − K colour space. Hence, these X-ray matched sourcesare unlikely to be foreground contaminants too.Finally - using the CC-D for IRS 1-3 region - 251Class III-type sources including probable contaminants (14have X-ray counterparts), 144 Class II-type sources (2 haveX-ray counterparts), and 24 Class I-type YSO candidateswere identified from the ‘F’ , ‘T’ , and ‘P’ regions, respec-tively. Table 4 lists these YSO candidates along with theirrespective NIR magnitudes, and IAU designation from Ta-ble 3 where applicable. Similar NIR CC-D could not be con-structed for the IRS 9 region as we only have H and K mag-nitudes available for it. Many embedded and young sources can only be seen in H and K bands due to high extinction at J band wavelengths.Therefore we use the K/H-K colour-magnitude diagram(CM-D) for the identification of additional YSOs. Figure 3shows the
K/H-K
CM-D for IRS 1-3, IRS 9, and the sky fieldregions. The almost vertical solid lines represent the zero-age-main-sequence (ZAMS) locus at a distance of 2.65 kpcreddened by A V = 0, 15, 30, 45, and 60 mag. Slanting linesindicate the reddening vectors for the marked spectral types.A low density gap in H − K colour ∼ . H − K (cid:54)
1. This H − K (=1) limit also correspondsto the average extinction of A V = 15 mag found towards theNGC 7538 region by Ojha et al. (2004a). Thus, in general,a background contaminant field source suffering extinctiondue to the cloud should also be confined to H − K (cid:54)
1. Also,on the same lines as Ojha et al. (2004a), if we were to assumethat sources had large IR colours (say, H − K >
2) purelydue to interstellar extinction, then that would imply thatthe reddening due to molecular cloud is A V >
30 mag. But,with such a large A V , diffuse emission will hardly be seenin NIR, which is definitely not the case here. Sources withcolour over and above this limit (i.e. H − K >
1) are there-fore most likely to have large H − K colour due to intrinsicinfrared (IR) excess associated with YSOs. Hence, we usethis colour cut-off of H − K > H and K counterparts + 1 X-ray sourcewith only K counterpart) in the IRS 9 region. The catalogs of these red sources for the IRS 1-3 and IRS 9 regions areincluded in Tables 4 and 5, respectively. The K band image of the IRS 1–3 region is shown in Fig-ure 4 with the overlaid YSOs and H CO + ( J =1–0) con-tours. Green squares mark the Class I sources, blue plus sym-bols the Class II-type or CTTS, and red circles the sourceswith H − K >
1. IRS 1, 2, and 3 are saturated and havebeen marked. Dense cloud is seen around these marked IRSsources. There appears to be relatively higher nebulositytowards the northern as opposed to the southern region.Almost all stellar sources are present in the northern re-gion. While the Class II-type sources (blue plus symbols)seem distributed throughout the northern part, sources with H − K > ii region andthe molecular cloud, which might have formed due to trig-gered star formation. The large diffuse emission extendingto the north-west of IRS sources is probably due to a combi-nation of free-free and bound-free emissions, correspondingto what is seen optically, and coincides well with the radiobrightness from the GMRT observations, while the brightand compact infrared nebula embedded within IRS 1, 2, and3 is coincident with the peak of radio continuum (see Section4.3).The H CO + ( J =1–0) contours show a peak to thesouth-east of the IRS 1–3 nebula, where YSO density is muchlower, and most of the sources around and near this peakare the red H − K > CO + ( J =1–0) contours, with contours closely spaced as one moves fromthe northern hump towards the southern peak. Preliminarycalculations were carried out to get an idea of the columndensities, local thermodynamic equilibrium (LTE) mass, andvirial mass of the clump associated with the peak. Assum-ing LTE, we tried to estimate the molecular column densityusing the formula from Troitsky et al. (2005), with an excita-tion temperature of 10 K, and a dipole moment of 3.9 debye(Botschwina et al. 1993). Fitting a 2D Gaussian to the clumpresults in a peak integrated line intensity of 2.0 K km s − anda source size at half intensity level of 1 pc. This gives us theLTE column density n(H CO + ) as ∼ . × cm − af-ter applying the main beam efficiency correction. Since theabundance - X(H CO + ) - estimates are variable from re-gion to region and we do not have a measure of it here, we c (cid:13) , 000–000 K. K. Mallick et al. use the range seen for other massive star-forming regions -0.5–3.0 × − from Zinchenko et al. (2009). Using these val-ues, n(H ) range is obtained to be ∼ × cm − , andthe LTE mass range of the clump to be ∼ M (cid:12) . Thespectrum for the IRS 1–3 region clump is shown in Figure5 (upper) . Applying a 1D fit to the spectrum of the clump,we obtain a linewidth of ∼ − . The source size iscorrected for the beam width to get the ‘deconvolved sourcesize’ (Zinchenko 1995). Using these values along with theexpression from Zinchenko et al. (1994), the virial mass isapproximated to be of the order of 1000 M (cid:12) . Alternatively,under the reasonable assumption of gravitational equilib-rium, the LTE mass and virial mass can be equated, whichwill imply an abundance X(H CO + ) of ∼ × − -which is within the range derived by Zinchenko et al. (2009).The gas-to-dust ratio for a cluster can be estimated bythe relation obtained between the X-ray column density andthe visual extinction for each source (Kuhn et al. 2010).Using the value of this column density ( logN H ) from Table3 and A V from IR analysis (discussed in Section 5.1.2), wefind log( N H /A V ) ∼ . ± .
20. The relation is shown inFigure 6. It is slightly higher than that for the interstellarmedium, ∼ A stellar surface density analysis of this region was carriedout using the nearest-neighbour (NN) method (Casertano &Hut 1985; Schmeja et al. 2008). We use the catalog of can-didate YSOs identified in Section 3, and a procedure similarto Schmeja et al. (2008) with 20 NN. The resultant sur-face density map is shown in Figure 7 (left) , also overplottedwith contours. Figure 7 (right) shows the histogram of NNdistances, with the peak NN distance in 0.12-0.14 (cid:48) range. InFigure 7 (left) three major clusterings can be made out. Oneis towards the south, associated with the IRS 1 and IRS 3sources, while the other two are to the north and north-westof the IRS 3 source. Each of these clusterings display multi-ple peaks of their own. The maximum surface density valuesrange from 860 to 1050 pc − , with the maximum exhibitedby the clustering to the north of the IRS 3. These values arehigher than the peak calculated for the overall NGC 7538region by Chavarr´ıa et al. (2014), which could be a result ofdeeper data used here. These high peak values, though, aresimilar to that for Serpens Core(A) (1045 pc − ; Schmeja etal. 2008). Figure 8 shows the K band image of the IRS 9 region withthe overlaid YSOs and H CO + ( J =1–0) contours. Red cir-cles denote YSO candidate sources. The main IRS sources- 9, 9N1, 9N2, 9N3, and 9N4 - from Ojha et al. (2004a) -have been marked on the image. As can be seen in Figure 8,sources are distributed throughout the image in no partic-ular orientation, but with significantly more sources in thenorthern portion as opposed to the nebular southern portion - possibly an indication of the high extinction in this nebularregion. This suggests that the region is extremely young, alsoaffirmed by the fact that there is no free-free radio emissionseen in the nebulous part (see Section 4.3). There appearsto be clustered star formation going on around the IRS 9 re-gion. The IRS 9N4 source from Ojha et al. (2004a) is resolvedinto two distinct sources in this image. The H CO + ( J =1 -0) molecular line emission peak lies to the eastern portion ofthe IRS 9 sources, a region deficient in YSOs. This indicatesthe presence of dense gas in this region. A 450 µ m clumpfrom Reid & Wilson (2005) is close to this peak. Using thesame procedure as for the IRS 1–3 region (see Section 4.1), apeak integrated line intensity of 1.5 K km s − , and a sourcesize at half intensity level of ∼ CO + ) is calculated to be ∼ . × cm − . Thisleads to n(H ) range of ∼ × cm − , and an LTEclump mass range of ∼ M (cid:12) . The spectrum for theclump is shown in Figure 5 (lower) . The virial mass - follow-ing same steps as for IRS 1–3 region - is approximately ofthe order of 500 M (cid:12) . Alternatively, as Section 4.1, assuminggravitational equilibrium gives X(H CO + ) ∼ × − . The maximum resolution radio continuum images of the en-tire NGC 7538 region which could be constructed are shownfor 325 MHz (resolution ∼ (cid:48)(cid:48) × (cid:48)(cid:48) ), 610 MHz (resolu-tion ∼ (cid:48)(cid:48) × (cid:48)(cid:48) ), and 1280 MHz (resolution ∼ (cid:48)(cid:48) × (cid:48)(cid:48) )(Figures 9 and 10). The positions of the IRS sources in theregion have been indicated by numbers in Figure 9. Theradio contours in Figure 9 show a definite champagne flowmorphology (Tenorio-Tagle 1979; Whitworth 1979). Whilethe contours are closely packed in the south-west corner,they become spread as one moves from the south-west tothe north-east direction. The south-west corner is densitybounded, while the north-east side is ionization bounded.In the relatively lower resolution 325 and 610 MHz maps(Figure 9), there are definite peaks associated with IRS 1-3,as well as with the other IRS sources 4 and 5 (note thatthese IRS 4 and 5 sources are outside our NIR FoV). Thepeak around the IRS 1-3 region is resolved into three sepa-rate peaks - to the North, East, and West - in the higherresolution 1280 MHz image (Figure 10 (left) ). Out of these,the IRS 1-3-East peak coincides with the IRS 2 source. Ascan be seen in this high-resolution image, the correspondingradio source for IRS 2 has a cometary appearence, as hasalso been observed at higher radio frequencies (Bloomer etal. 1998; Campbell & Persson 1988). The IRS 1-3-North andWest peaks do not have any NIR sources associated withthem, though the IRS 1-3-West peak (keeping in mind thatthe beam size is ∼ (cid:48)(cid:48) × (cid:48)(cid:48) here) is very close to the IRS 2Cpeak from the 6 cm radio map of Campbell & Persson (1988).The IRS 1-3-East and West cores are approximately of thesize of the synthesized beam ( ∼ (cid:48)(cid:48) × (cid:48)(cid:48) ), with a flux of ∼
50 mJy and 30 mJy, respectively. The IRS 1-3-North core is ∼ (cid:48)(cid:48) × (cid:48)(cid:48) in size, with a total flux of ∼ ii region (size from0.1 to 0.5 pc), while the North, East, and West cores can beclassified as ultracompact H ii regions (size (cid:46) c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Figure 9; outside our NIR FoV) also shows multiple cores(Figure 10 (right) ).The nature of a free-free emission region can be stud-ied by calculating its spectral index α , given by S ν ∝ ν α ,where ν is the frequency and S ν is the integrated flux den-sity of the region at ν . We can calculate the spectral indexusing d log S ν /d log ν . As free-free emission changes from op-tically thick to optically thin, α varies from 2 to -0.1 (Pana-gia & Felli 1975; Olnon 1975). First of all, we obtainedall the GMRT images at the same uniform resolution ofabout ∼ (cid:48)(cid:48) × (cid:48)(cid:48) (as this is the maximum resolution mapwe could make for 325 MHz). Next, we calculated the inte-grated flux density within the IRS 1-3 compact H ii regionfor all three frequencies. In addition to the GMRT frequen-cies, VLA archival image at the frequency of 4860 MHz (at avery similar resolution of ∼ (cid:48)(cid:48) × (cid:48)(cid:48) ) was also obtainedand integrated flux density calculated for the compact H ii region. The values obtained are given in Table 2. Figure11 shows the radio SED fit using these data points. Thesolid grey line shows the SED fit using all four data points( α = 0 . ± . α = 1 . ± .
02) using only the GMRT points.These values of α suggest that the region is optically thickat these low frequencies, in consistency with earlier radiostudies (Akabane et al. 1992).If we assume that this compact H ii region is homoge-neous and spherically symmetric, then we can calculate theLyman continuum photon luminosity (photon s − ) using thefollowing formula from Moran (1983, see their Equation 5) : S ∗ = 8 × (cid:18) S ν mJy (cid:19) (cid:18) T e K (cid:19) − . (cid:18) Dkpc (cid:19) (cid:16) νGHz (cid:17) . (1)where S ν is the integrated flux density in mJy from the con-tour map, D is the distance in kiloparsec, T e is the electrontemperature, and ν is the frequency in GHz for which theluminosity is to be calculated. Now choosing the VLA datapoint of 4.860 GHz (as it will lie in the most optically thinregime of the free-free emission SED), and T e a typical valueof 10000 K (Panagia & Felli 1975; Olnon 1975), S ∗ was cal-culated to be ∼ × (i.e. log S ∗ ∼ . S ∗ = 48 . (left) .Additionally, this caveat of dust absorption of radiation sug- gests that O9 ZAMS spectral type should be the lower limitand the actual spectral type could be earlier than this. We use the YSO catalogs from Section 3 to generate the K -band luminosity function (KLF) of the IRS 1-3 and IRS 9stellar clusters. K band, as opposed to H or J band, isused as : the effects of extinction are minimum, it probessources upto much fainter luminosities, and the results canbe compared to the existing literature. K − band luminosity function KLFs for the IRS 1-3 region were generated using 2 sets ofYSOs taken from Table 4 : the first set containing a com-bination of ‘F+T+P+red-sources’ (basically the entire Ta-ble 4), and a second set containing only ‘T+P+Any sourcewith X-ray detection’ (see Section 3 and Figures 2 and 3).This was done as the first set may contain YSO candidateswith field star contamination and will need to be correctedfor it, while the second set is most likely YSOs with muchlower field contamination. To derive the KLF of a region,one needs to apply corrections for the following : star countincompleteness (which is a function of magnitude), and thefield star contamination towards the cluster.Star count incompleteness was corrected for by usingthe completeness calculations from Section 2.1. The com-pleteness fraction had been obtained for each 0.5 magnitudebin. The counts in each magnitude bin were scaled up bydividing the counts by the completeness fraction in the re-spective bins. This gives us the completeness-corrected KLF.The field star contamination was assessed using the skyfield source catalog (from Section 2.1) in conjunction withthe Galactic model of Robin et al. (2003), similar to Ojhaet al. (2004a,b). Two sets of catalogs were generated usingthe Besan¸con model of stellar population synthesis (Robinet al. 2003) in the direction of the sky field region. The firstset contains the sources generated by setting A V = 4 . A V of sources in thesky field CM-D (between H − K = 0 and the low densitygap at H − K = 0 . < .
65 kpc. In addition tothe total and foreground sources towards this region, weneed to assess the background field star contamination too.However, the background field star contaminants will sufferan extra extinction due to the intervening molecular cloud,which needs to be taken into account. Now, the average ex-tinction towards the NGC 7538 region has been found to be A V = 15 mag (Ojha et al. 2004a). If we assume a spheri-cal geometry of the molecular cloud medium, then it followsthat the sources behind the molecular cloud should sufferan extinction of A V = 15 + 15 = 30 mag. Therefore, we gen-erated a second model catalog set by setting A V = 30 mag.In this second set, all the sources with distances > .
65 kpc c (cid:13) , 000–000 K. K. Mallick et al. will give us the background contaminants. After having ob-tained the total, foreground, and the background sources,the K band histogram (with binwidth=0.5) was plotted andthe contamination fraction (foreground+background/total)was obtained for each bin. Finally, to obtain the absolutenumber of contaminating sources in each magnitude bin, weuse the sky field K band histogram. Each magnitude bin ofthe sky field K magnitude histogram is scaled by the ratio( ∼ .
75) of the areas of sky field to IRS 1-3 region, as wellas by its contamination fraction calculated above. Fig. 12shows the contamination fraction, along with the numberof field contaminants in the IRS 1-3 region, as a function ofmagnitude. The obtained contaminant number in each binwas subtracted from the completeness-corrected KLF (bin-wise) to obtain the field- and completeness-corrected KLF.The KLFs for the first YSO set (‘F+T+P+red-sources’ ), and second YSO set (‘T+P+Any source with X-ray detection’ ) are shown in Figure 13. A binsize of 0.5 hasbeen chosen as it is much larger than the errors in sourcemagnitudes. To compare with the literature, we calculatethe ( d log N/dm K ) slope for the rising part of the KLFs tobe 0 . ± .
03 (in the magnitude range 12.5–16.5) for the firstYSO set, and 0 . ± .
03 (in the magnitude range 12.5–16.5)for the second YSO set. While the KLF slope for the firstYSO set is higher than that for the completeness- and field-corrected KLF for the whole NGC 7538 region (0 . ± . ∼ . ± .
07) from Sharma et al. (2007), Tr 14( ∼ . ± .
01) from Sanchawala et al. (2007), andIRAS 06055+2039 ( ∼ . ± .
09) (Tej et al. 2006).The slope for the second set is consistent with that calcu-lated earlier in Ojha et al. (2004a) for the completeness-corrected whole NGC 7538 region (0 . ± .
02) as well asthat for the younger regions in NGC 7538 (0 . ± . ∼ . ± .
01) (Ojha et al. 2004b) and Sh2-255 IRregion ( ∼ . ± .
03) from Ojha et al. (2011). Aturnoff is seen in both the KLFs after 16-16.5 magnitude bin,similar to the Tr 14 region from Sanchawala et al. (2007).
The mass function (MF) is usually described by the follow-ing differential form : ξ (log M ∗ ) = dN/d log M ∗ (2)where N is the number of stars and M ∗ is mass of stars(Bastian et al. 2010; D’Antona 1998; Chabrier 2003; Kroupaet al. 2013). Since magnitude ( m K ), and not mass ( M ∗ ), isan observable quantity, ξ has to be re-written as : ξ (log M ∗ ) = dN/d log M ∗ = ( dN/dm K ) ÷ ( d log M ∗ /dm K )(3)where ( dN/dm K ) is nothing but the KLF slope, and( d log M ∗ /dm K ) represents the derivative of the so-calledmass-luminosity relation (MLR). If we have the form of theKLF and the MLR derivative, then ξ can be evaluated.The MLR depends on the age of the cluster, and inour case we use the age estimate of 1 Myr for the NGC 7538region from Ojha et al. (2004a). The theoretical isochrones(for 1 Myr) from Baraffe et al. (2003) (for the mass range0 . − . (cid:12) ), Baraffe et al. (1998) (0 . − .
50 M (cid:12) ), and Palla & Stahler (1999) (2 . − . (cid:12) ) are used for the MLR.The absolute magnitudes were converted to apparent magni-tudes using the distance modulus (at a distance of 2.65 kpc).The complete MLR is shown in Figure 14, along with thecurve fit to it. To calculate ξ , we need the derivative of thisMLR. We limit our analysis to sources with m K (cid:62)
12 mag,as it the lower limit of the MLR.In addition to the MLR, a form of the intrinsic KLF isalso needed. To derive the intrinsic KLF, the sources werecorrected for extinction by dereddening them along the red-dening vectors to the respective loci as per the followingorder of steps. First, the sources which were present in the‘F’ region of the NIR CC-D (Figure 2(a)) were dereddenedto the dwarf locus (whose low-mass regime - from the turn-over onwards - was approximated by a straight line; similarto Tej et al. 2006; Samal et al. 2007), while those in the ‘T’and ‘P’ regions were dereddened to the CTTS locus. Therest of the sources (those not dereddened using the NIR CC-D) were dereddened using the H and K magnitudes to theZAMS locus (approximated by a straight line) in the NIRCM-D (Figure 3(a)) to estimate their extinctions, thoughthis is only an approximation as the YSOs are most-likelynot on ZAMS yet. The major source of uncertainty in usingthe CM-D is the correction of the locus for distance, whichneed not be well-determined. The individual visual extinc-tion of the sources was found to range upto 60 mag. Thisis much deeper, as expected, than upto 40 mag which wasestimated by Ojha et al. (2004a) for their detected YSOs.The histogram (not shown here) of these visual extinctionswas found to peak in the range 7.5-10 mag. The mean ex-tinction value was ∼
15 mag, consistent with that used formodel simulations in Section 5.1.1 and Ojha et al. (2004a).The sources with A V >
40 mag were mostly found to bedistributed along the southern boundary between the nebu-lous and non-nebulous region (also see Figs. 1 (left) and 4). Afew such sources were also associated with the small nebularpatch at the south-east corner of the IRS 1-3 region.Using this catalog of reddening-corrected sources, field-,completeness-, and reddening-corrected KLFs were obtainedfor the two YSO sets (‘F+T+P+red-sources’ being the firstset and ‘T+P+Any source with X-ray detection’ being thesecond set; see Section 5.1.1). To preserve the informationabout the form of the KLF, different magnitude intervals(each interval containing three or more bins) were fit withequations of straight line using simple linear regression. Thisgives us the KLF slope for each magnitude bin.After we obtain the KLF slope ( dN/dm K ) in eachmagnitude bin and the form of the MLR derivative( d log M ∗ /dm K at discrete points), value of ξ is calculatedusing Equation 3 for each magntiude bin - which is furthermapped onto the log M ∗ space using the MLR. The result-ing form of ξ is shown in Figures 15 and 16 along with theKLFs. Poissonian error of ±√ N is marked for each bin. Itshould be kept in mind that equal magnitude intervals donot map onto equal log M ∗ intervals. The shape of the ξ isclosest to that derived by Scalo (1986) for field stars, witha peak at the low mass end, and another peak at the inter-mediate mass (Meyer et al. 2000). The low mass peak is atlog M ∗ bin of − .
09 to − .
00, i.e 0 . − . M (cid:12) (for Figures15 and 16). This rise in the MF till the BD limit has beenseen for other regions like W3 Main (Ojha et al. 2009) andS106 (Oasa et al. 2006) too, as well as mentioned likely by c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Kroupa (2007). The curve does not extend enough in theintermediate mass range to clearly discern the peak.Another way to test the MF form is to use the MLR toassign a mass to each star in the catalog, and then bin thosemasses to obtain the N (log M ∗ ), rather than the differentialform ξ (log M ∗ ) (Chabrier 2003, see its Section 1.3). Usingthis, we obtain the MFs shown in Figure 17. The field starsubtraction for the first catalog here was carried out statis-tically using the NIR CM-D as follows. Similar to Sharmaet al. (2007), we divided the CM-Ds of the IRS 1-3 regionand the sky field region into grids with ∆ K =0.5 mag and∆( H − K )=0.1 mag. The number of stars was compared ona grid-by-grid basis, and from the IRS 1-3 CM-D, a fixednumber of stars (equal to the number in the correspondingsky field grid) was removed based on their distances to thesky field stars in the colour-magnitude space. Each grid wascorrected for incompleteness.As can be seen, the MFs are similar in shape to thosein Figures 15 and 16, with a peak in the log M ∗ = -0.75 –-1.0 bin (i.e. 0.1–0.18 M (cid:12) ), and another at log M ∗ = 0–0.25bin (i.e. 1–1.78 M (cid:12) ). However, the peak at the lower massregime, though consistent with the other method, is on theslightly higher side here. The mass range of the turn-off pointin the lower mass regime is consistent with those for otherprominent clusters in the literature (Bastian et al. 2010), like σ Orionis (Pe˜na Ram´ırez et al. 2012), ρ Ophiuchi (Alves deOliveira et al. 2012), IC 348 (Alves de Oliveira et al. 2013),and Orion Nebula Cluster (Hillenbrand & Carpenter 2000).A secondary peak seen here is also observed in the IMF ofthe ρ Ophiuchi cluster from Alves de Oliveira et al. (2012)and Orion Nebula Cluster from Hillenbrand & Carpenter(2000). If we assume a power law form of the MF (similarto Salpeter 1955), then : dN/d (log M ∗ ) ∝ M − Γ ∗ (4) ⇒ dN/dM ∗ ∝ M − (Γ+1) ∗ . (5)Now, if we additionally assume that the star formation isstrictly coeval, then it can be mathematically shown that − Γ = d (log N ) /d (log M ∗ ) , (6)and that the present day mass function will have the sameslope as the IMF (Massey 1998, see its Section 2.1). Also,since the age of this region is ∼ (cid:12) ) using Equation6, we get the value of Γ for the first and second YSO setsas 0 . ± .
05 (say, Γ ) and 0 . ± .
18 (say, Γ ), respec-tively. Both the slopes are lower than the Salpeter slopeof 1.35. While Γ seems consistent with that from Kroupa(2002) (also see Figure 2 of review by Bastian et al. 2010),Γ is slightly steeper. This steepness, though, might be ex-plained by the fact that Figure 17 (right) includes mostly theyoungest sources with fainter magnitudes - thus making thisMF ‘bottom-heavy’ , i.e. more sources at lower mass ranges.On the other hand, Figure 17 (left) includes Class III sourcesand thus more sources in relatively higher mass ranges. Ingeneral, more complicated/realistic forms of the IMF canemerge due to accretion processes, leading to a tail towardsthe high mass end (Dib et al. 2010), which will become no-ticeable only in high-mass star-forming regions where the intermediate to high-mass bins are well populated. Finally,we should keep in mind the caveat that any derivation of anIMF suffers from multiple unavoidable and systematic bi-ases, e.g. those arising due to - among others - choice of thestellar MLR, PMS evolution, effect of unresolved sources,binning, etc. Kroupa et al. (2013, see their Section 2.1) havedealt with these biases in a succinct manner. Different treat-ment of these biases might accordingly alter a derived IMF.The ratio of stars to BDs in a region is often used asanother quantitative indicator for the mass function. Weconsider the following two definitions of this ratio : R = N (0 . < M/M (cid:12) (cid:54) /N (0 . (cid:54) M/M (cid:12) (cid:54) . , and (7) R = N (0 . < M/M (cid:12) (cid:54) /N (0 . (cid:54) M/M (cid:12) (cid:54) . , (8)similar to Scholz et al. (2012). However, since our observa-tions are complete only upto 0.06 M (cid:12) , the R and R valuesobtained will be the upper limit. Taking this caveat into ac-count and using the above equations, we get the value of R < / ∼
8, and R < / ∼ .
2. The compi-lation by Scholz et al. (2012) shows that the values of R and R for other star-forming regions lie in the range 2–8,while Luhman et al. (2007) state that R ranges from 5–8 instar-forming regions. On the other hand, Alves de Oliveiraet al. (2012) find higher value of R (upto 11 depending ontheir analysis parameters) in the ρ Ophiuchi cluster. How-ever, given the fact that the values of R and R calculatedhere are upper limits, they are consistent with those of otherstar-forming regions. We obtained the KLF for the IRS 9 region using the catalogof sources identified in at least K band, as well as the catalogof candidate YSOs (red sources with H − K > (left) shows the raw KLF(grey line) along with the field- and completeness-correctedKLF (black line). Since the statistics are low for this re-gion, we only make a few qualitative comparisons here. The( d log N/dm K ) slope was calculated to be 0 . ± .
04 (in13–19 K mag range), and is lower than that calculated foryounger regions in Ojha et al. (2004a) and some other star-forming regions (see Section 5.1.1), though similar to Sh2-255 IR region (Ojha et al. 2011). The KLF of red sources( H − K >
1) is shown in Figure 18 (right) . There appearto be two peaks in Figure 18 (right) - one near 15–15.5 magand another at about the completeness limit (marked by adotted vertical line). The KLF seems to be plateauing nearthe completeness limit. The brighter peak is most likely tobe due to field contamination, which has not been correctedfor due to a lack of statistics here. If we consider the 16–17.7mag interval of this YSOs’ KLF, we see that it first has asteeper slope in the 16–16.5 mag interval, and then plateausoff in the 16.5–17.7 mag interval. This steep slope followedby plateauing is seen in other regions like NGC 1624 (Joseet al. 2011) and Sh2-255 IR region (Ojha et al. 2011) too, al-beit for different magnitude limits. In this range (16–17.5),the slope comes out to be 0 . ± .
11, which is very simi-lar to that from Ojha et al. (2004a) for younger regions ofNGC 7538, and is consistent within errors with that obtainedfor the Sh2-255 IR region (Ojha et al. 2011). c (cid:13) , 000–000 K. K. Mallick et al.
Analysis of star-forming regions in different stages is es-sential in understanding how star formation proceeds andthe effect of manifold physical processes on various diag-nostic tools (like LF, MF, etc). In general, however, phys-ical conditions (like density, temperature, chemical compo-sition) could differ from one region to another. The studyof NGC 7538 cluster regions (IRS 4-6, IRS 1-3, and IRS 9,which follow an age sequence in descending order; Ojha etal. 2004a), being part of the same complex, should mitigatethis problem. Here, using the deepest NIR data, we have ob-tained the KLF and the MF of the IRS 1-3 region, while onlythe KLF of the IRS 9 region has been discussed. The MFfor the IRS 1-3 region shows that it rises till the BD limitbefore turning over, which indicates lower temperature ordenser gas distribution than for Orion nebula cluster (Hil-lenbrand & Carpenter 2000; Muench et al. 2002), thoughcomparison of LF and MF of different regions from litera-ture always follow the caveat that the method used for theirconstruction might be slightly different. Presence of densemolecular material has been attested by surveys in submil-limetre ranges too (Sandell & Sievers 2004; Reid & Wil-son 2005). Our molecular line analysis also reveals massiveclumps which could fragment and lead to future stellar clus-ter formation. The 850 µ m emission (Chavarr´ıa et al. 2014)shows the IRS 1-3 region to be located on a junction of fila-ments, which could partially explain the active star forma-tion going on. Confinement of most IR clusters at filamentjunctions has also been observed by Schneider et al. (2012)and obtained in the simulations of Dale, Ercolano, & Bonnell(2012). The entire morphology of NGC 7538 seems similar tothe hub-filament structure proposed by Myers (2009), wherethe IRS 1-3 cluster region forms the ‘hub’ to which variousfilaments merge. The molecular hydrogen column density(which is > cm − ; Fallscheer et al. 2013) satisfies thecondition which Myers (2009) proposes for a ‘hub’ .The IRS 9 region, however, appears to be distinct and atone end of the filament which connects it with IRS 1-3 (thisfilament goes on to connect IRS 4 too; see Sandell & Siev-ers 2004). IRS 9 region has been found to be much youngerthan IRS 1-3, owing to a lack of free-free radio emission aswell as a low number of YSOs associated with the nebula.The Herschel temperature maps (Fallscheer et al. 2013) alsoshow that IRS 9 is much colder than IRS 1-3 region. Thedecreasing age-sequence along the filament connecting thethree cluster regions of IRS 4-6, IRS 1-3, and IRS 9 alludesto the possibility that star formation could have been trig-gered along this filamentary structure.To gain a firm understanding of the NGC 7538 regionstellar population, as well as the evolution of the KLF andMF as one moves from relatively older to relatively youngerregions in a star-forming region, we need to obtain the de-tailed LFs and MFs for the IRS 4-6 region as well as IRS 9region. The advantage will be that all the sub-regions be-long to the same region NGC 7538, and should thereforedifferences arising due to the differences in physical condi-tions (leading to different temperature and density distribu-tions, which leads to different Jeans masses and thus differ-ent LFs/MFs) need not be a concern. Future analysis of theBDs detected in the region, construction of MF from a spec-troscopic sample, an analysis of core mass function of this region, and examination of spectral energy distributions ofindividual sources are also required for a better idea of thestar formation going on.
We have carried out the deep NIR imaging survey of IRS 1–3 (
J, H , and K ) and IRS 9 ( H and K ) sub-regions in theNGC 7538 star-forming region with the highest spatial res-olution so far. In addition, GMRT observations at 325, 610,and 1280 MHz are used to examine the radio emission andphysical characteristics. H CO + ( J =1–0) molecular lineemission from Nobeyama radio telescope is used to under-stand the morphology. Our main results are summarized asfollows.(i) Based on the NIR CC-D ( J − H/H − K ), 144 Class II-type, and 24 Class I-type YSOs were identified in the IRS 1–3region. Using the NIR CM-D ( K/H − K ), 145 sources wereidentified in the IRS 1-3 region, and 96 in IRS 9 region. 27sources were found to have X-ray counterparts.(ii) In the IRS 1–3 region, the red sources and the Class Isources are concentrated around the compact nebula associ-ated with luminous IRS sources, and the H CO + ( J =1–0) contours show a peak (column density n(H CO + ) ∼ . × cm − ) to the south of these sources. Stellar sur-face density analysis reveals three clusterings in this region.The IRS 9 region does not have any particular distributionof the YSOs, with the nebula hardly containing any sources.An H CO + ( J =1–0) peak (n(H CO + ) ∼ . × cm − )lies to the east of the cluster around IRS 9 source. The virialmasses are approximately of the order of 1000 M (cid:12) and500 M (cid:12) for the clumps in IRS 1–3 and IRS 9 regions, re-spectively.(iii) Radio emission shows a champagne flow morphologyin the NGC 7538 region. In low-resolution 325 and 610 MHzmaps, a compact H ii region is seen associated with IRS 1–3 sources, with its spectral index calculated to be 0 . ± .
11, suggesting optically thickness. In very high resolution1280 MHz maps, the IRS 1–3 compact H ii region is resolvedinto three separate peaks, one of which coincides with theknown IRS 2 source.(iv) KLFs were constructed for IRS 1–3 region for two setsof sources : ‘F+T+P+red-sources’ and ‘T+P+Any sourcewith X-ray detection’ . The rising part of the KLF has a( d log N/dm K ) slope of 0 . ± .
03 for the first set, and 0 . ± .
03 for the second set ( K magnitude range 12.5–16.5). TheKLF slopes for the IRS 9 region using sources with K bandonly detections was calculated to be 0 . ± .
04 (13–19 mag).(v) Theoretical mass-luminosity relation is used to obtain ξ (log M ∗ ) (differential form of MF) and N (log M ∗ ) for theIRS 1–3 cluster region. Both ξ (log M ∗ ) and N (log M ∗ ) showa peak in the low mass regime as well as a peak in theintermediate mass regime. In low-mass regime, ξ (log M ∗ )extends upto BD limit before turn-off (0.08–0.1 M (cid:12) ),while N (log M ∗ ) peak is in 0.1–0.18 M (cid:12) range. The slope d log N/d log M ∗ (from N (log M ∗ ) distribution) for the firstand second YSO sets in the range 0.1–1 M (cid:12) are 0 . ± . . ± .
18, respectively - much lower than the Salpetervalue of 1.35. The MFs most closely resemble that of Scalo(1986). The star to BD ratio upper limit was calculated tobe 10.2. c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 ACKNOWLEDGMENTS
We thank the anonymous referee for a critical reading of themanuscript and several useful comments and suggestions,which greatly improved the scientific content of the paper.This research made use of data collected at Subaru Tele-scope, which is operated by the National Astronomical Ob-servatory of Japan. We are grateful to the Subaru Telescopestaff for their support. We thank the staff of GMRT managedby National Center for Radio Astrophysics of the Tata In-stitute of Fundamental Research (TIFR) for their assistanceand support during observations. D.K.O. was supported bythe National Astronomical Observatory of Japan (NAOJ),Mitaka, through a fellowship, during which part of this workwas done. This research was partly supported by Grants-in-Aid for Scientific Research on Priority Areas, “Developmentof Extra-Solar Planetary Science”, and is partly supportedby Grants-in-Aid for Specially Promoted Research, fromthe Ministry of Education, Culture, Sports, Science andTechnology of Japan (16077101, 16077204), and by JSPS(16340061). K.K.M., D.K.O., I.Z., and L.P. acknowledgesupport from DST-RFBR Project (P-142; 13-02-92697) un-der the auspices of which some part of this work was carriedout. S.D. is supported by a Marie-Curie Intra European Fel-lowship under the European Community’s Seventh Frame-work Program FP7/2007-2013 grant agreement no 627008.I.Z. and L.P. are also partly supported by the grant withinthe agreement of August 27, 2013 No. 02.B.49.21.0003 be-tween The Ministry of education and science of the RussianFederation and Lobachevsky State University of Nizhni Nov-gorod.
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90% Completeness Limits for NIR bands
K H J (mag) (mag) (mag)IRS 1-3 regionOverall 18 19 20.21 17 18.4 19.22 18.5 19.4 20.23 18 20 19.7IRS 9 regionOverall 17.7 16.61 19.2 16.62 17.7 16.6Sky regionWhole 20 21 21.2
Table 2.
Details of Radio Continuum Observations1280 MHz 610 MHz 325 MHz VLA 4860 MHz Archival ImageDate of Obs. 2004 January 25 2004 September 18 2004 July 03 2000 September 22 (BP0068)Phase Center α = 23 h m s α = 23 h m s α = 23 h m s δ = 61 o (cid:48) (cid:48)(cid:48) δ = 61 o (cid:48) (cid:48)(cid:48) δ = 61 o (cid:48) (cid:48)(cid:48) Flux Calibrator 3C48 3C48 3C48, 3C147Phase Calibrator 2355+498 2350+646 2350+646Cont. Bandwidth 16 MHz 16 MHz 16 MHzPrimary Beam 26.2 (cid:48) (cid:48) (cid:48) Resolution of mapsused for fitting 11.5 (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) rms noise 1.93 mJy beam − − − − Integrated flux densityfor IRS 1-3 region 0.69 Jy 0.30 Jy 0.14 Jy 1.53 Jyc (cid:13)000
Details of Radio Continuum Observations1280 MHz 610 MHz 325 MHz VLA 4860 MHz Archival ImageDate of Obs. 2004 January 25 2004 September 18 2004 July 03 2000 September 22 (BP0068)Phase Center α = 23 h m s α = 23 h m s α = 23 h m s δ = 61 o (cid:48) (cid:48)(cid:48) δ = 61 o (cid:48) (cid:48)(cid:48) δ = 61 o (cid:48) (cid:48)(cid:48) Flux Calibrator 3C48 3C48 3C48, 3C147Phase Calibrator 2355+498 2350+646 2350+646Cont. Bandwidth 16 MHz 16 MHz 16 MHzPrimary Beam 26.2 (cid:48) (cid:48) (cid:48) Resolution of mapsused for fitting 11.5 (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) × (cid:48)(cid:48) rms noise 1.93 mJy beam − − − − Integrated flux densityfor IRS 1-3 region 0.69 Jy 0.30 Jy 0.14 Jy 1.53 Jyc (cid:13)000 , 000–000 K. K. Mallick et al. T a b l e . X - r a y S o u r ce s w i t h N I R c o un t e r p a r t s i n t h e N I R F o V S o u r ce X s p ec ( U s i n g A C I S E x t r a c t ) X ph o t I AU D e s i g n a t i o n R A D ec C t , n e t E m e d i a n l og N H k T l og L h l og L t l og L h c l og L t c l og L h c l og L t c l og N H ( d e g )( d e g )( c o un t s )( k e V )( c m − )( k e V )( e r g s − )( e r g s − )( e r g s − )( e r g s − )( e r g s − )( e r g s − )( c m − ) ( )( )( )( )( )( )( )( )( )( )( )( )( )( ) . + . . . . . . . . . . . . . .
176 231338 . + . . . . . . . . . . .
519 231338 . + . . . . . . . . . . . . . .
301 231339 . + . . . . . . . . . . . . . .
342 231339 . + . . . . . . . . . . . . . .
041 231340 . + . . . . . . . . . . .
826 231340 . + . . . . . . . . . . . . . .
23 231340 . + . . . . . . . . . . . . . .
398 231341 . + . . . . . . . . . . . . . .
708 231342 . + . . . . . . . . . . . . . .
716 231342 . + . . . . . . . . . . .
574 231343 . + . . . . . . . . . . . . . .
079 231344 . + . . . . . . . . . . . . . .
875 231345 . + . . . . . . . . . . .
782 231345 . + . . . . . . . . . . . . . .
886 231345 . + . . . . . . . . . . . . . .
924 231345 . + . . . . . . . . . . . . . .
947 231346 . + . . . . . . . . . . .
48 231347 . + . . . . . . . . . . .
286 231348 . + . . . . . . . . . . . . . .
778 231352 . + . . . . . . . . . . .
634 231357 . + . . . . . . . . . . . . . .
477 231358 . + . . . . . . . . . . . . . .
785 231400 . + . . . . . . . . . . . . . .
301 231401 . + . . . . . . . . . . . . . .
255 231401 . + . . . . . . . . . . . . . .
591 231402 . + . . . . . . . . . . . . . . C o l. ( ) : I AU d e s i g n a t i o n , R A a nd D ec . C o l. ( ) : N e t c o un t s e x t r a c t e d i n t h e t o t a l e n e r g y b a nd ( . k e V ) ; B a c k g r o und - c o rr ec t e d m e d i a nph o t o n e n e r g y (t o t a l b a nd ) . C o l. ( ) : C o l u m nd e n s i t y a ndp l a s m a t e m p e r a t u r ec a l c u l a t e du s i n g X s p ec . C o l. ( ) : A pp a r e n t h a r d a nd t o t a l b a nd l u m i n o s i t y C o l. ( ) : I n t r i n s i c h a r d a nd t o t a l b a nd l u m i n o s i t y C o l. ( ) : I n t r i n s i c h a r db a nd l u m i n o s i t y , t o t a l b a nd l u m i n o s i t y , a nd t h ec o l u m nd e n s i t y c a l c u l a t e du s i n g X ph o t . c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Table 4.
YSOs in IRS 1-3 NIR FoVRA Dec.
J H K
YSO Classification,(J2000) (J2000) (mag) (mag) (mag) X-ray IAU Designation348.438812 61.461308 21.014 ± ± ± ± ± ± ± ± H − K > ± ± ± ± ± ± Table 5.
YSOs in IRS 9 NIR FoVRA Dec.
H K
X-ray IAU Designation(J2000) (J2000) (mag) (mag)348.46637 61.466164 16.278 ± ± ± ± ± ± ± ± ± ± : : . . : . RA (2000) D ec ( ) IRS 1-3 : . . : : . RA (2000) D ec ( ) IRS 9 Figure 1. (left)
Colour composite image of the IRS 1-3 region using J (blue), H (green), and K (red) bands. Three sub-regions aremarked on the image using cyan rectangles. (right) Colour composite image of the IRS 9 region using H (green), and K (red) bands,with two sub-regions marked. Each sub-region of the respective region has been labelled by a number. Completeness limit was calculatedfor each sub-region.c (cid:13)000
Colour composite image of the IRS 1-3 region using J (blue), H (green), and K (red) bands. Three sub-regions aremarked on the image using cyan rectangles. (right) Colour composite image of the IRS 9 region using H (green), and K (red) bands,with two sub-regions marked. Each sub-region of the respective region has been labelled by a number. Completeness limit was calculatedfor each sub-region.c (cid:13)000 , 000–000 K. K. Mallick et al.
Figure 2. (a) J − H/H − K NIR CC-D for the IRS 1-3 region. The red curve shows the dwarf locus from Bessell & Brett (1988). TheCTTS locus (Meyer et al. 1997) is shown by the blue solid line, and its extension into the ‘P’ region by grey dot-dashed line. The threeparallel and slanted dashed lines are the reddening vectors using the reddening laws of Cohen et al. (1981). Blue crosses mark the sourceswith X-ray counterparts. All points are in CIT system. (b) The CC-D for the sky field. c (cid:13) , 000–000
GC 7538 : IRS 1-3 and IRS 9 Figure 3.
K/H − K NIR CM-D for (a) IRS 1-3 region, (b) IRS 9 region, and (c) the sky region. Nearly vertical solid lines are the lociof ZAMS stars reddened by A V =0, 15, 30, 45, and 60 mag. Parallel, slanting lines indicate the reddening vectors for respective spectraltypes. Blue crosses mark the sources with X-ray counterparts.c (cid:13)000
K/H − K NIR CM-D for (a) IRS 1-3 region, (b) IRS 9 region, and (c) the sky region. Nearly vertical solid lines are the lociof ZAMS stars reddened by A V =0, 15, 30, 45, and 60 mag. Parallel, slanting lines indicate the reddening vectors for respective spectraltypes. Blue crosses mark the sources with X-ray counterparts.c (cid:13)000 , 000–000 K. K. Mallick et al. : : . . : . RA (2000) D ec ( ) Figure 4. K band image of the IRS 1-3 region overlaid with YSOs and H CO + ( J =1–0) contours (black lines). The contours are drawnin the range 0.5–2.2 K km s − , with step size of 0.1 K km s − . Class I sources are shown with green square symbols, Class II with blueplus symbols, and sources with H − K > (cid:13) , 000–000
GC 7538 : IRS 1-3 and IRS 9 Figure 5.
The H CO + ( J =1–0) molecular line spectra towards (upper) the peak in IRS 1–3 region, and (lower) the peak in IRS 9region.c (cid:13)000
The H CO + ( J =1–0) molecular line spectra towards (upper) the peak in IRS 1–3 region, and (lower) the peak in IRS 9region.c (cid:13)000 , 000–000 K. K. Mallick et al.
Figure 6.
X-ray column density (log N H ) vs visual extinction ( A V ) plot for the sources in the IRS 1–3 region. The solid grey line marksthe Ryter (1996) gas-to-dust relation of N H = 2 . × A V , while the dash-dotted grey line marks the relation from our analysis. : : . . : . RA (2000) D ec ( ) IRS 3IRS 2IRS 1
Figure 7. (left)
20 NN surface density map of the IRS 1-3 region with overplotted contours. The IRS sources have been marked bysmall green circles and labelled. The contour levels are at 250, 350, 500, 600, 700, 800, 900, 950, and 1000 YSOs pc − . Three distinctclusterings (indicated by white dashed circles) can be seen on the image - one close to the IRS 1 and IRS 3 sources, while the other twoto the north and north-west of the IRS 3 source. All display multiple peaks. (right) The histogram of the NN distances of the sources.c (cid:13) , 000–000
GC 7538 : IRS 1-3 and IRS 9 : . . : : . : . RA (2000) D ec ( ) N N N N Figure 8. K band image of the IRS 9 region overlaid with YSOs and H CO + ( J =1–0) contours (black lines). The contours are drawnin the range 0.5–1.6 K km s − , with step size of 0.1 K km s − . Candidate YSOs have been shown with red circles. IRS 9, 9N1, 9N2, 9N3,and 9N4 sources from Ojha et al. (2004a) have been marked.c (cid:13)000
GC 7538 : IRS 1-3 and IRS 9 : . . : : . : . RA (2000) D ec ( ) N N N N Figure 8. K band image of the IRS 9 region overlaid with YSOs and H CO + ( J =1–0) contours (black lines). The contours are drawnin the range 0.5–1.6 K km s − , with step size of 0.1 K km s − . Candidate YSOs have been shown with red circles. IRS 9, 9N1, 9N2, 9N3,and 9N4 sources from Ojha et al. (2004a) have been marked.c (cid:13)000 , 000–000 K. K. Mallick et al. : . : : . : . RA (2000) D ec ( )
87 6 54321
Figure 9.
The maximum resolution radio continuum images for 325 MHz (cyan contours; 12.3 (cid:48)(cid:48) × (cid:48)(cid:48) ) and 610 MHz (green contours;9.0 (cid:48)(cid:48) × (cid:48)(cid:48) ) obtained using GMRT for the entire NGC 7538 region. The contours for 325 MHz image are drawn at 12, 17, 25, 30, 35, 37,40, and 42 σ ( σ ∼ σ ( σ ∼ (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 BOTH: NGC7538 IPOL 1288.000 MHZ NGC7538 I.FLATN.4Grey scale flux range= -7.67 47.79 MilliJY/BEAMCont peak flux = 4.7792E-02 JY/BEAM Levs = 5.286E-04 * (15, 20, 25, 30, 40, 50, 70,80, 83, 85, 87, 90)0 10 20 30 40 D E C L I NA T I O N ( J2000 ) RIGHT ASCENSION (J2000)23 13 47 46 45 44 43 4261 28 50454035302520151005 BOTH: NGC7538 IPOL 1288.000 MHZ NGC7538 I.FLATN.4Grey scale flux range= -7.67 47.79 MilliJY/BEAMCont peak flux = 4.7792E-02 JY/BEAM Levs = 5.286E-04 * (12, 15, 20, 22, 25, 27, 30)0 10 20 30 40 D E C L I NA T I O N ( J2000 ) RIGHT ASCENSION (J2000)23 13 36 34 32 30 28 2661 30 4530150029 4530
Figure 10.
The maximum resolution radio continuum images for 1280 MHz (3 (cid:48)(cid:48) × (cid:48)(cid:48) ). (left) IRS 1-3 region. Three separate cores areresolved here - to the North, East, and West. The contours are at 15, 20, 25, 30, 40, 50, 70, 80, 83, 85, 87, and 90 σ ( σ ∼ (right) High resolution image of the north-west part of the NGC 7538 region, around the source marked ‘5’ in Figure 9. The contoursare drawn at 12, 15, 20, 22, 25, 27, and 30 σ ( σ ∼ Figure 11.
SED fitting for the IRS 1-3 compact H ii region. The circular markers show the data points from the GMRT at 325, 610,and 1280 MHz, while the square marker shows the VLA data point at 4860 MHz. The solid grey line is the fitting using all four datapoints (with spectral index α =0.87 ± α =1.16 ± (cid:13) , 000–000 K. K. Mallick et al.
12 16 200.10.30.50.7 C o n t a m i n a t i o n F r a c t i o n
12 16 20K magnitude26101418 N u m b e r o f c o n t a m i n a n t s Figure 12. (upper)
The contamination fraction (per magnitude bin) calculated using the Galactic model of Robin et al. (2003). (lower)
The number of contaminants (per magnitude bin) for the IRS 1-3 cluster region. The error bars show the error due to counting statistics.A similar exercise was carried out for the IRS 9 region.
Figure 13.
KLFs for the IRS 1-3 region. (a) For ‘F+T+P+red-sources’ sources. Grey line histogram represents the raw KLF. Solidblack line histogram shows the final field- and completeness-corrected KLF. (b) For ‘T+P+Any source with X-ray detection’ sources.Grey line is for the raw KLF, while the black line shows the final completeness-corrected KLF. The vertical dotted line in both figuresmarks the K band 90% completeness limit at 18 mag. The error in each bin is the Poissonian ±√ N error. The black curve shows thepower law fit to the KLF. c (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Figure 14. (upper)
MLR from literature (see text). The grey crosses mark the data points from literature and the black line shows thefitted curve to it. We confine our analysis to m K (cid:62)
12, i.e. lower limit of MLR.
Figure 15.
KLF fits and ξ (differential form) for ‘F+T+P+red-sources’ YSO catalog in the IRS 1-3 region. (upper) The field-,completeness-, and reddening-corrected KLF and the straight line fits to its different portions. (lower) ξ calculated using equation3. Each 0.5 mag bin from the KLF has been mapped to a corresponding bin in log M ∗ space here. The vertical dashed-dotted lineindicates the 90% completeness limit. Poissonian errors are marked for each bin.c (cid:13)000
KLF fits and ξ (differential form) for ‘F+T+P+red-sources’ YSO catalog in the IRS 1-3 region. (upper) The field-,completeness-, and reddening-corrected KLF and the straight line fits to its different portions. (lower) ξ calculated using equation3. Each 0.5 mag bin from the KLF has been mapped to a corresponding bin in log M ∗ space here. The vertical dashed-dotted lineindicates the 90% completeness limit. Poissonian errors are marked for each bin.c (cid:13)000 , 000–000 K. K. Mallick et al.
Figure 16.
KLF fits and ξ for ‘T+P+Any source with X-ray detection’ YSO catalog in the IRS 1-3 region. Rest is same as for Figure15. Figure 17.
IRS 1-3 region : N (log M ∗ ) for (left) ‘F+T+P+red-sources’ YSO catalog, and (right) ‘T+P+Any source with X-ray detection’YSO catalog obtained by assigning mass to each source individually and binning. Error bars in each bin show Poissonian error. Thegrey curve shows the fit to the MF in 0.1–1 M (cid:12) mass range. The vertical dashed line indicates the mass corresponding to the K (cid:13) , 000–000 GC 7538 : IRS 1-3 and IRS 9 Figure 18.
KLFs for the IRS 9 region. (left)
The grey line histogram shows the raw KLF of all sources detected in K -band, while theblack line shows the KLF after field- and completeness-correction. (right) KLF of sources which had H − K >
1, or were detected inX-ray. Error bars are Poissonian. The vertical dotted line marks the K band 90% completeness limit at 17.7 mag.c (cid:13)000