Accepted for publication in ApJ, January 12, 2015 The Spatial Structure of Young Stellar Clusters. II. Total Young Stellar Populations 5 1 0 Michael A. Kuhn1,2,3, Konstantin V. Getman1, Eric D. Feigelson1 2 n a J ABSTRACT 1 2 We investigate the intrinsic stellar populations (estimated total numbers of ] A OB and pre–main-sequence stars down to 0.1 M ) that are present in 17 massive ⊙ G star-forming regions (MSFRs) surveyed by the MYStIX project. The study is . h based on the catalog of >31,000 MYStIX Probable Complex Members with both p disk-bearing and disk-free populations, compensating for extinction, nebulosity, - o and crowding effects. Correction for observational sensitivities is made using the r st X-ray Luminosity Function (XLF) and the near-infrared Initial Mass Function a (IMF)—a correction that is often not made by infrared surveys of young stars. [ The resulting maps of the projected structure of the young stellar populations, in 1 v units of intrinsic stellar surface density, allow direct comparison between different 0 0 regions. Several regionshave multiple dense clumps, similar insize anddensity to 3 the Orion Nebula Cluster. The highest projected density of 34,000 stars pc−2 is 5 ∼ 0 found in the core of the RCW 38 cluster. Histograms of surface density show dif- . 1 ferent ranges of values in different regions, supporting the conclusion of Bressert 0 et al. (2010, B10) that no universal surface-density threshold can distinguish 5 1 between clustered and distributed star-formation. However, a large component : v of the young stellar population of MSFRs resides in dense environments of 200– i X 10,000 stars pc−2 (including within the nearby Orion molecular clouds), and we r a find that there is no evidence for the B10 conclusion that such dense regions form an extreme “tail” of the distribution. Tables of intrinsic populations for these regions are used in our companion study of young cluster properties and evolution. 1Department of Astronomy & Astrophysics, 525 Davey Laboratory, Pennsylvania State University, Uni- versity Park, PA 16802,USA 2Instituto de Fisica y Astronom´ıa, Universidad de Valpara´ıso, Gran Bretan˜a 1111, Playa Ancha, Val- para´ıso,Chile 2 Millennium Institute of Astrophysics – 2 – 1. Introduction The Milky Way Galaxy is a critical part in the universe for studying star formation. Only here can the populations of low-mass stars—making up the vast majority of stars— be resolved and the full spatial structure of young stellar clustering and molecular clouds be analyzed, revealing detailed information about how star formation progresses within a region. Most stars, including the Sun (Gounelle & Meynet 2012; Dukes & Krumholz 2012), are born in clusters with OB-type stars, so it is important to study the massive star-forming regions (MSFRs) in the solar neighborhood. The young stellar clusters in these regions can be precursors to open clusters, but most of their stars become gravitationally unbound due to gas expulsion, so an understanding the star-formationhistories and early cluster dynamics in these regions provides clues about how bound clusters and field stars are produced (e.g., Goodwin & Bastian 2006; Pfalzner 2011; Kruijssen et al. 2012; Banerjee & Kroupa 2014). Historically, studies of massive Galactic star-forming regions have been hindered by difficulties inherent to Galactic Plane astronomy; in particular, field stars greatly outnumber members of the star-forming region in optical or infrared (IR) images (e.g., King et al. 2013; Kuhn et al. 2013b). X-ray surveys readily detect star-forming region members due to the high X-ray luminosities from strong magnetic activity of pre-main-sequence stars (L X ∼ 10−3L ; Preibisch et al. 2005a), and these surveys are not strongly effected by nebulosity, bol obscuration, or crowding. Excess IR emission fromdisk-bearing young stars has proven to be another useful method of establishing membership, but IR-only surveys will miss the large populations of members without dusty protoplanetary disks and such studies rarely account for observational sensitivities in determining intrinsic stellar populations, as we attempt to do in this paper. The combination of X-ray selected stars and IR-excess selected stars can provide better samples of stars in MSFRs than either method alone (Feigelson et al. 2013; Townsley et al. 2011). Thus, the analysis of empirical distributions of inferred stellar mass and X-ray luminosities from the combined samples can be used to estimate total populations (e.g., Getman et al. 2012, and references therein). The Massive Young Star-Forming Complex Study in Infrared and X-ray (MYStIX; Feigelson et al.2013)examines20nearbymassivestar-formingregions(MSFRs)usingacom- bination of archival Chandra X-ray imaging, 2MASS+UKIDSS near-IR (NIR), and Spitzer mid-IR (MIR) survey data. The catalogs of young stars include both high-mass and low- mass stars, and disk-bearing and disk-free stars (Broos et al. 2013). We use this sample of stars to study the intrinsic populations of young stars across 17 of the MYStIX MSFRs. The present study is closely based on the constructions of the MYStIX Probable Com- plex Members catalog (MPCM; Broos et al. 2013) and the statistical segregation of MPCMs into 140 subclusters by Kuhn et al. (2014, Paper I). Our principal objective here is to ∼ – 3 – overcome sensitivity limitations of the MPCM catalog for each MYStIX MSFR in order to normalize the observed stellar distributions to intrinsic stellar distributions. We obtain two quantities of interest: the total intrinsic stellar population and the stellar surface densities in each MYStIX subcluster. The total populations are important inputs into a multivariate analysis of young cluster properties in our forthcoming study (Kuhn et al. 2014b, Paper III). Thestellarsurfacedensitiesaddresslong-standingissuesabouttypicalenvironments inwhich stars form. 1.1. Thresholds for Clustered Star Formation The statistical relationships that traditionally underlay our understandings of star- formation processes have been scale-free relationships like the Salpeter (1955) stellar initial mass function (IMF) and the Kennicutt–Schmidt law relating global galactic star forma- tion rate to interstellar material (Schmidt 1959; Kennicutt & Evans 2012). Nevertheless, important preferred scales for star formation were later found. The power-law IMF for high stellar masses peaks around 0.2-0.3 M and declines for lower mass stars (Chabrier 2003). ⊙ And, in the Galactic neighborhood, a threshold for star formation was found at A 7 V ≈ magnitudes dust absorption ( n[H ] 3 104 cm−3) associated with Galactic disk sta- 2 ≈ ∼ × bility (Johnson et al. 2004; Lada 2010; Martin & Kennicutt 2001; Schaye 2004; Leroy et al. 2008), although this rule is not applicable within the inner 0.5 kpc of the Galaxy where star-formation is comparatively suppressed (Longmore et al. 2013). The surface density of stellar populations in star-forming regions, in units of stars per square parsec, has been a property of interest for the field of star-cluster formation (e.g., Carpenter2000;Lada & Lada2003;Allen et al.2007;Jørgensen et al.2008;Gutermuth et al. 2009). The surface densities of young stars can also have astrophysical implications, such as tidal truncation of protoplanetary disks (Pfalzner et al. 2005), binary star distributions (Bate 2009a; Moeckel & Clarke 2011), or the survival of clusters after molecular cloud dis- persal (Kruijssen 2012). Bressert et al. (2010, henceforth B10) have recently examined the shape of the distribution of stellar surface densities in star-forming regions. They use sam- ples of disk/envelope-bearing stars identified through IR excess in regions within 0.5 kpc of the Sun, including the Gould Belt (Allen et al. 2006), the Orion A and B molecular clouds (Megeath et al. 2012), the Taurus molecular cloud (Rebull et al. 2010), and the regions from the cores-to-disks (c2d; Evans et al. 2003) project—thus their sample is dominated by low- mass young-stellar-object (YSO) environments. B10 argue that if “clustered” star-formation and“distributed” star-formationweretwodistinctstar-formationprocesses, then“clustered” and “distributed” populations should appear as distinct modes in the surface-density dis- – 4 – tribution (cf. Gieles et al. 2012; Pfalzner et al. 2012), and that such a scenario could be tested by searching for a “scale” of star formation separating these two modes. Such a kink in the surface-density distribution has been used in some investigations of the structure of young stellar clusters, for example by Gutermuth et al. (2009), to separate distinct clusters of stars in star-forming regions. Given that B10 find a smooth distributions of surface den- sity from their data, which they report is adequately fit by a log-normal distribution with a peak at 22 stars pc−2, they conclude that no such “scale” exists, at least for low-mass YSO environments present in the solar neighborhood. Nevertheless, the log-normal distribution from B10 is not scale free, but instead a peak at 22 stars pc−2 and width of 0.85 dex suggests a density distribution weighted towards low-density environments. If this result is a general characteristic of most star formation in the Galaxy, rather than just the nearby regions investigated by B10, it would have impli- cations for theories of star formation as numerous researchers have discussed. For example, Parmentier & Pfalzner (2013) find that their models of local-density-driven star formation from a single molecular clump could produce the 22 stars pc−2 scale from B10. King et al. (2012) suggest that surface densities significantly greater than 22 stars pc−2 could indicate that a cluster has undergone a “cool collapse phase.” Kruijssen et al. (2012) present a model in which the low fraction of star-formation that results in bound clusters is, in part, a result of a density spectrum weighted towards low surface densities. Parker et al. (2011) notes that dynamical processing of primordial binaries by clusters depends on whether most stars form in low density regions as suggested by B10, or whether higher density clusters are more com- mon. And, de Juan Ovelar et al. (2012) investigate the threshold densities in star-forming regions where stellar interactions affect habitable planet formation—and the fraction of the stars born in environments above their 3 103 stars pc−2 threshold would depend on whether × high-density regions are just a tail of the B10 log-normal or a different mode not seen in the B10 sample. B10 support this interpretaton of the empirical results from their sample stating, “only a small fraction (<26 per cent) of stars form in dense clusters where their formation and/or evolution is expected to be influenced by their surroundings.” It is important to investigate whether these results continue to hold for more massive star-forming regions (those regions containing O-type stars). Nearly 70% of B10’s sample comes from the Orion Giant Molecular Clouds, which do contain O-type stars, but they note that the IR-excess methods used are ineffective at identifying young stars in the presence of nebulosity and crowding in this complex. Their other star-forming regions are lower mass. Given that studies of the mass function for star-forming regions favor the birth of stars in more massive complexes, investigation of these complexes in a way that is more effective at probing the densest regions could be helpful for determining the validity of B10’s suggestion that clustered stars (Σ > 200 stars pc−2) exist in the tail of the surface-density – 5 – distribution, rather than being a dominant component. Nevertheless, a definitive study of surface-density distributions forstar formationwouldrequire theconstruction ofanunbiased survey of all star-forming environments. MYStIX neither includes the most massive star- forming environments in the Galaxy (such as W 43, Wd 1, NGC 3603, or the Arches Cluster) nor includes large angular area studies of diffuse molecular clouds necessary to capture the lowest surface density environments. 1.2. MYStIX The MYStIX survey (Feigelson et al. 2013) differs from many previous studies in that it focuses on relatively massive star-forming regions lying in nearby Galactic spiral arms, and supplements samples of IR-excess young stars with X-ray selected young stars and spectroscopically identified OB stars. MYStIX is a survey of 20 of the nearest (d < 3.6 kpc) MSFRs that have been ob- served with NASA’s Chandra X-ray Observatory, the Spitzer Space Telescope, and the United Kingdom Infra-Red Telescope (UKIRT) or the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006). The MYStIX regions include the Orion Nebula, the Flame Nebula, W 40, RCW 36, NGC 2264, the Rosette Nebula, the Lagoon Nebula, NGC 2362, DR 21, RCW 38, NGC 6334, NGC 6357, the Eagle Nebula, M 17, W 3, W 4, the Carina Nebula, the Trifid Nebula, NGC 3576, and NGC 1893, from which a sample of 31,784 MYStIX Prob- able Complex Members (MPCMs; Broos et al. 2013) is obtained. The MPCM catalog thus consists ofyoung starsthatareX-rayselected, IRexcess selected, orOBstarsfromthelitera- ture. MYStIX provides the cleanest and largest lists of young stars for most of the 20 regions included in the study, so these catalogs should be scientifically useful for different purposes. One of the requirements of the MYStIX project was to use sensitive and homogeneous data analysis procedures for all 20 regions to facilitate inter-comparisons between regions. Spe- cial procedures had to be developed to deal with challenges working in the Galactic Plane, as described in the MYStIX technical-catalog papers: Kuhn et al. (2013a), Townsley et al. (2014), King et al. (2013), Kuhn et al. (2013b), Naylor et al. (2013), Povich et al. (2013), and Broos et al. (2013). The spatial distributions of MPCMs in 17 of the MYStIX MSFRs are investigated in Kuhn et al. (2014, henceforth Paper I) and in this work. Three regions are omitted, NGC 3576, W 3, and W 4, because they lack JHK UKIRT photometry and have a low match rate between X-ray sources and sources from the 2MASS catalog. We use a subset of the MPCM sources ( 17,000 stars) produced after X-ray selected MPCMs are pruned to ∼ a uniform X-ray sensitivity within each region (Paper I). This eliminates artificial surface – 6 – density gradients associated with differing X-ray exposure times in Chandra mosaics and the sensitivity variations within each Chandra field due to telescope coma and vignetting, the “egg-crate effect” (Townsley et al. 2011). To prune a region, we remove sources with X-ray photon fluxes (log PhotonFlux t; Broos et al. 2013) that are lower than the completeness limits provided in Table 1 of Paper I. Nevertheless the resulting observed surface densities, used by the analysis in Paper I, do not contain theentire intrinsic population, differ insensitivity fromMSFR to MSFR, andare affected by spatially variable N absorption and mid-IR sensitivity. As pre–main-sequence H (PMS) X-rayluminosities strongly scale withstellar mass (Telleschi et al. 2007), inconsistent X-ray sensitivities due to differing Chandra exposure times and MSFR distances lead to different samplings of the cluster IMFs. We overcome these selection effects calibrating the observedX-rayluminosityfunction(XLF)andIMFdistributionstotheOrionNebulaCluster (ONC) that serves as a template for young cluster populations, rather than attempting to model instrumental and observational effects. The organization of this paper (Paper II) is as follows. We analyze the IMF and X-ray luminosity function (XLF) to infer intrinsic populations from observed young stellar popu- lations (Section 2). We derive intrinsic stellar surface density maps from these populations (Section 3), and investigate surface density distributions (Sections 4 and 5). The MYStIX sample of star-forming regions are typically richer than those in the sample studied by B10. The MYStIX MSFRs exhibit a large diversity in their surface density distributions (ranging from 10 to 30,000 stars pc−2), neither showing a tendency to follow a universal surface ∼ ∼ density distribution nor showing a convincing peak at some characteristic surface density. These results are discussed in Sections 4 and5 andsummarized in the conclusion (Section 6). 2. Stellar Populations The completeness limits and detection fractions1 of the MPCM samples vary from re- gion to region, due to differences in distance, obscuration, and X-ray and IR observation exposures. Extrapolations of the total numbers of stars in a region, which we infer empiri- cally from observed MPCM samples based on comparisons with the ONC, are necessary for comparison of intrinsic properties of stellar populations in different star-forming regions. 1The completeness limit of a sample is defined to be the minimum luminosity (or mass) such that nearly 100% of objects with greater luminosity (or mass) are included in the sample. The detection fraction is the number of observed sources Nobs divided by the intrinsic number of sources Ntot. – 7 – 2.1. X-ray Luminosity Functions Young stars in the Chandra Orion Ultradeep Project (COUP; Getman et al. 2005b) had large numbers of X-ray counts, allowing X-ray luminosities (L ; total 0.5–8.0 keV band and t,c absorptioncorrected)tobeobtainedbyparametricmodelingoftheX-rayspectrumusingthe XSPEC code (Arnaud 1996). As the MYStIX stars are mostly too faint for this procedure, X-ray luminosities for other MPCMs were computed using non-parametric calibrations for PMS stars (XPHOT; Getman et al. 2010) by Kuhn et al. (2013a), Townsley et al. (2014), Broos et al. (2011), and Kuhn et al. (2010). The probability distribution of L , called the XLF, is associated with the IMF due t,c to the statistical link between X-ray luminosity and stellar mass M (e.g., Feigelson et al. 1993; Preibisch et al. 2005a; Telleschi et al. 2007). The assumption of a “universal XLF” (Feigelson & Getman 2005) has been used to estimate total populations in young stel- lar clusters, including Cep B (Getman et al. 2006), M 17 (Broos et al. 2007), NGC 6357 (Wang et al. 2007), Rosette (Wang et al. 2008, 2009, 2010), W 40 (Kuhn et al. 2010), Trum- pler 15 (Wang et al. 2011), Trumpler 16 (Wolk et al. 2011), Sh 2-254/255/256/257/258 (Mucciarelli et al. 2011), NGC 1893 (Caramazza et al. 2012), and IC 1396 (Getman et al. 2012). During PMS stellar evolution, there is a weak relation between X-ray luminosity and age (e.g., Preibisch & Feigelson 2005; Pandey et al. 2014); however, L does not rapidly t,c decline during the first 5 Myr, unlike the rapid decrease in bolometric luminosity L during bol PMS evolution along the Hayashi track. Instead, L M appears to be the fundamental t,c ∼ relationshiprather thanL L (Getman et al.2014b). Thus, X-rayluminosity evolution t,c bol ∼ appears to have little effect on the shape of the PMS XLF (e.g., Bhatt et al. 2013). Following these previous studies, we use a sample of stars from COUP to approximate the probability distribution of the universal XLF. The COUP study contains a sample of 839 lightly absorbed stars (Feigelson et al. 2005), which are identified as the members of the ONC, while the more highly absorbed stars are identified as being embedded in the Orion Molecular Cloud (OMC) behind the ONC. These lightly obscured COUP stars are complete down to a mass of 0.1–0.2 M (with partial coverage into the proto–brown-dwarf regime; ⊙ Preibisch et al. 2005b) and show an XLF shape characterized by a falling distribution at high luminosities with a break to an approximately flat distribution at luminosities below L 1030.4 erg s−1. Henceforth, we label this distribution the COUP XLF. The tail with X- t,c ≈ ray luminosities greater than this turnover can be fit with a power-law (Pareto) distribution of slope α, with a minimum variance unbiased estimator α∗ and variance Var(α∗) given by the equations 2 n α∗2 α∗ = 1 and Var(α∗) = , (1) −(cid:18) − n(cid:19) n (lnx lnx ) n 3 i=1 i − m − P – 8 – where x is the X-ray luminosity of the turnover point and x is the X-ray luminosity of m i the ith source in a sample of n sources in the distribution tail (Johnson et al. 1994). Thus, α∗ = 0.9 0.1 with n = 61, while the distribution is roughly flat in logarithmic bins below − ± the turnover point. Mucciarelli et al. (2011) have also found similar L Pareto distributions t,c for the ONC and the Sh 2-254–258 regions. The L distributions for the MYStIX regions can be compared to the empirical dis- t,c tribution function (EDF) of 839 lightly absorbed COUP sources to further investigate the universality of the XLF shape. For example, Wang et al. (2008, their Figure 9b) shows that the XLF cumulative distributions in the Rosette star-forming region agree with the COUP XLF above the X-ray luminosity completeness limit for the Rosette sample. For this analysis it is necessary to be cautious about how completeness limits are treated because differen- tial absorption can change the apparent shape of the XLF if the sample of highly absorbed sources is incomplete. For example, a sample of sources that are more deeply embedded will have a higher mean luminosity than a sample of sources from the same observation that are unabsorbed, which could lead to a flattening of the power-law of the combined distribution. In Figure 1, we show the COUP EDF running from unity at very low luminosities (L 1027 erg s−1) to zero for the most luminous PMS star in the Orion Nebula field. Note t,c ∼ that spectroscopically identified OB stars have been removed from both the COUP XLF and from MYStIX samples considered here because MYStIX regions can differ widely in their massive stellar subpopulations. The L EDFs for the other regions are shown below, with t,c arbitrary vertical spacings. Only the portion of the XLF where the sample is complete is shown. (The completeness limit for the full sample is set to the completeness limit for the most heavily obscured subpopulation in the region.) In general there is excellent agreement between the shapes of the different lines. Some curvature can be seen in the COUP XLF between 1030.5 erg s−1 and 1032.5 erg s−1, which is also reflected in the shapes of the XLFs for other regions. The nearest regions tend to probe a lower-luminosity section of the XLF, while the more distant regions tend to probe a higher-luminosity section of the XLF. Due to the XLF curvature, the XLF shape appears less steep for nearer regions and steeper for more distant regions. Table 1 (Column 2) gives the power-law indices2 (for the full sample) calculated over the regions shown in Figure 1. This confirms the trend in which more distant regions have steeper slopes—not because of differences in intrinsic XLF shape, but due to differences in the available portion of the XLF. 2 The power-lawfits are often poor and we do not recommend that these values be used for astrophysical interpretation. – 9 – 0 COUP Flame W 40 2 − RCW 36 NGC 2264 Rosette Lagoon NGC 2362 4 − nst. DR 21 o C + F D E g RCW 38 lo NGC 6334 −6 NGC 6357 Eagle M 17 Trifid Carina 8 − NGC 1893 0 1 − 29.5 30.0 30.5 31.0 31.5 32.0 32.5 33.0 log Ltc [erg s-1] Fig. 1.— The EDF of X-ray luminosities, L , for the 839 lightly obscured, low-mass stars tc from COUP (complete down to 0.1-0.2 M ) is shown by the thick gray line. The black lines, ⊙ from top to bottom, are the X-ray luminosity EDFs for the other MYStIX regions. Vertical shifts of 0.3 units are used to separate the different lines for visual clarity. Lines end at the completeness limit for the full sample (i.e. the completeness limit for the most heavily obscured subpopulation in the region). – 10 – Table 1. XLF properties of MSFRs Region α∗ N N N N tot ME<1.5 1.5<ME<2.5 ME>2.5 (stars) (stars) (stars) (stars) (1) (2) (3) (4) (5) (6) Orion -0.9 2600 700 1200 720 Flame -1.0 800 55 250 500 W 40 -1.1 520 0 250 270 RCW 36 -0.8 550 0 230 320 NGC 2264 -1.0 1900 1100 230 570 Rosette -1.3 2500 840 1000 610 Lagoon -1.1 3800 2000 870 930 NGC 2362 -1.1 600 570 30 0 DR 21 -1.0 2900 50 550 2253 RCW 38 -1.3 9900 70 1900 8000 NGC 6334 -1.2 9400 180 2900 6200 NGC 6357 -1.2 12000 440 7400 3700 Eagle -1.3 8100 1300 4300 2500 M 17 -1.3 16000 170 5400 11000 Carina -1.5 34000 9500 17000 7000 Trifid -1.0 3100 1500 1100 470 NGC 1893 -1.5 4600 1700 2400 590 Note. —Column 1: Nameof MYStIX MSFR. Column2: Power- law index (dlogN/dlogL ) for the portion of the XLF tail shown t,c in Figure 2 (uncertainties are 0.1). Column 3: Inferred intrinsic ± total population. Columns 4–6: Inferred intrinsic numbers of stars with ME < 1.5 keV, 1.5 < ME < 2.5 keV, and ME > 2.5 keV, respectively. (Due to rounding, the sum of Columns 4, 5, and 6 is not always equal to Column 3.)