A CHANDRA OBSERVATION OF THE OBSCURED STAR-FORMING COMPLEX W40

The distance to W40 has been controversial. Radial velocity based distance measurements (Reifenstein et al. 1970; Downes 1970; Radhakrishnan et al. 1972) using the Schmidt (1965) model of the galaxy collectively suggest a distance of 600 ±  300 pc (Vallée 1987). Shaver & Goss (1970) also find a distance of 700 pc using galactic kinematics. Other distance measurements fall into this range too. Crutcher & Chu (1982) find a distance of 400 pc assuming a spectral type for the brightest star of B0V. Smith et al. (1985) find a distance of 700 pc using measurements of W40's stellar component in radio/infrared continuum. Kolesnik & Iurevich (1983) use OH absorption-line measurements of the cloud and calculate a distance of 600 pc. These estimates range from 400 pc to 700 pc, and we adopt a distance of ∼600 pc in line with Rodney & Reipurth (2008) and investigate the validity of this distance in the analysis of the Chandra data. W40 has Galactic coordinates l = 288, b = 35. The fairly high Galactic latitude would place the cluster more than 50 pc above the Galactic plane if the distance were greater than 800 pc.

The Aquila Rift, which contains the young-star cluster Serpens South (Gutermuth et al. 2008), is projected near W40 in the sky (Serpens South is 05 to the west; see Figure 1(a)) and is only 260 ± 37 pc distant (Straižys et al. 1996), which is much closer than typical distance estimates for W40. However, W40 and Serpens South are usually regarded as separate objects due to their different distances (Straižys et al. 2003; Gutermuth et al. 2008), and 600−700 pc is the most commonly cited distance for W40 (cf. Zhu et al. 2006; Zinnecker & Yorke 2007; Rodríguez et al. 2010). The nearby Serpens Main cluster is 3° north of W40 and is at a third distance of 415 ± 15 pc (Dzib et al. 2010), established through parallax measurements of its brightest star. Dzib et al. (2010) note that the superposition of the three distinct star-forming regions is not unexpected since the line of sight passes just above the Galactic plane. Alternatively, Bontemps et al. (2010) assume that W40, the Aquila Rift, and Serpens Main are parts of the same star-forming region and are therefore at the distance of 260 pc for the Aquila Rift. This paper will comment on implications of this lower distance for W40.

The core of the W40 molecular cloud was mapped by Zeilik & Lada (1978) in ¹²CO and ¹³CO emissions. The mass of the core is estimated to be ∼200–300 M_☉ by Zhu et al. (2006), and Rodney & Reipurth (2008) report a probable mass for the entire cloud of ∼10⁴ M_☉. The center of the star cluster is located at the east edge of the molecular core. Three probable OB stars are identified by Smith et al. (1985) as important ionizing sources for the cluster. There is evidence for circumstellar material around two of these stars detected by Smith et al. (1985) and Vallée & MacLeod (1994). An observation of W40 by the Midcourse Space Experiment (MSX) reveals the H ii region to have an hourglass shape, oriented with one lobe to the southeast and another to the northwest, 17' × 30' in extent (see Figure 6 in Rodney & Reipurth 2008). The cluster core is located just to the northwest of the waist of the hourglass. Bontemps et al. (2010), who assume that W40 and Serpens South are part of the same star-forming complex at a distance of 260 pc, report ∼200 protostellar candidates in Herschel observations. A weak outflow is detected in CO lines by Zhu et al. (2006) centered on the molecular core, although the driving source is unseen.

The Chandra X-ray Observatory (CXO) observed W40 for ∼38 ks during 2007 August using the ACIS camera (Garmire et al. 2003). The observation has a nominal pointing of R.A. = 18^h31^m238 and decl. = −2°05'59'' (J2000), the approximate center of the W40 cluster, and a roll angle of 251°. Data from the imaging array (ACIS-I) are analyzed. The ACIS-S3 chip was also operational, but these data are omitted since the point-spread function (PSF) is degraded due to the large off-axis angle. The data were taken in very faint telemetry mode to improve sensitivity to faint sources. No variations in background levels are detected. Properties of the telescope and detector are available via the Proposers' Observatory Guide (CXC 2009).

A data reduction protocol that has been used for Chandra ACIS-I observations of other young-star clusters is followed (see Appendix B of Townsley et al. (2003) for more details on the steps used for data reduction). Briefly, using the tool acis_process_events from the CIAO3.4 software package (Fruscione et al. 2006), the latest calibration information on time-dependent gain and a Penn State bad pixel mask are applied, background event candidates are identified in the very faint mode, and the data are corrected for CCD charge transfer inefficiency. Using the acis_detect_afterglow tool, additional afterglow events not detected with the standard Chandra X-ray Center (CXC) pipeline are flagged. The event list is cleaned with the "grade" (only ASCA grades 0, 2, 3, 4, 6 are accepted), "status"⁵, "good-time interval," and energy filters. A small astrometric correction is applied based on matches between the eight brightest Chandra sources with small off-axis angles and optical/infrared sources from the Naval Observatory Merged Astrometric Dataset (NOMAD; Zacharias et al. 2004a). The slight PSF broadening from the CXC software position randomizations was removed.

Figures 2(c) and (d) show the ACIS-I field in which more than 200 X-ray sources are seen. Candidate X-ray sources in the Chandra data are detected using an aggressive method that minimizes missed sources but allows spurious sources. Data images and exposure maps with spatial resolutions 05 and 1'' pixel⁻¹ are used for source detection on the center of ACIS-I and the full ACIS-I, respectively. A wavelet-based source detection procedure ($\it wavdetect$; Freeman et al. 2002) is run with a threshold of P = 10⁻⁵. Sources are detected on a soft (0.5–2.0 keV), a hard (2.0–8.0 keV), and the total (0.5–8.0 keV) band images. The images are examined visually to locate other candidate sources, mainly close doubles and sources near the detection threshold. A total-band image reconstruction is generated using the maximum likelihood method to search for additional weak sources in the center region (Broos et al. 2010).

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Refined source positions and the final source list are established using the ACIS Extract software package⁶ (Broos et al. 2002, 2010). Photons are extracted within polygonal contours of ∼90% (∼70% for crowded sources) encircled energy using position-dependent models of the PSF. Background extraction is performed locally and takes into account spatial variations due to PSF wings of nearby point sources (Broos et al. 2010). Production of the final source list follows the simple procedure of Getman et al. (2006, 2007, 2008a): the list of candidate sources is trimmed to omit sources with fewer than ∼4 estimated source background-subtracted counts (NC_t/PSFfrac ≲ 4; Columns 7 and 11 in Table 1). The final catalog has 225 sources.

The ACIS Extract package is also used to construct source and background spectra, compute redistribution matrix files (RMFs) and auxiliary response files (ARFs), construct light curves and time–energy diagrams, perform a Kolmogorov–Smirnov (K-S) variability test, compute photometric properties, and perform automated spectral grouping and fitting. The following inferred source photometric properties are presented in Table 1: source coordinates, off-axis angle, net and background counts within the extraction region, source significance assuming Poisson statistics, effective exposure (correcting for telescope vignetting, satellite dithering, and bad CCD pixels), median energy after background subtraction, a variability indicator extracted from the one-sided K-S statistic, and occasional anomalies related to positions on chip gaps or field edges. Net counts has a range 4–1000 and typical values of ∼20. Median energy has a range of 1–5 keV and typical values around 2.4 keV.

Chandra source positions were compared with source positions from the Two Micron All Sky Survey (2MASS) NIR catalog (Figure 2(a)). Chandra sources were considered to have stellar counterparts when the positional coincidences were better than 1'' within ∼35 of ACIS-I field center and 2'' in the outer regions of each ACIS-I field where Chandra's PSF deteriorates. Out of 225 X-ray sources, 190 have 2MASS matches. We have also acquired JHK images of the central part of the cluster from the United Kingdom Infra-Red Telescope (UKIRT), which have better spatial resolution and sensitivity than the 2MASS images (Figure 2(b)). Using UKIRT images 12 additional matches are identified, 10 of which are blended in 2MASS.

Two of the three OB stars identified in Smith et al. (1985) were matched to X-ray sources⁷. The third OB star was located on a chip gap and was not detected as an X-ray source.

Rodríguez et al. (2010) detect 20 Very Large Array (VLA) radio sources in the W40 complex near the center of the cluster, and 15 of them have X-ray counterparts. All sources with VLA counterparts also have infrared counterparts. The reported VLA source coordinates are rounded (Rodney & Reipurth 2008), so Chandra–VLA positional offsets may be greater than 1'' (source 141). Individual radio and NIR counterparts for Chandra sources are listed in Table 2 along with their JHK_s photometry.

All X-ray sources with infrared counterparts are likely to be stars since YSOs have high apparent NIR fluxes compared to extragalactic contaminants. X-ray sources with NIR counterparts are classified as either W40 cluster stars or foreground stars (Column 9 in Table 2).

Most of the 23 X-ray detections without NIR counterparts are likely to be active galactic nuclei (AGNs; Getman et al. 2006). However, some of these are classified as W40 members. Sources 56, 140, 142, and 155 have strong variability, which is a characteristic of T-Tauri X-ray emission, and source 56 is located near the molecular core and is likely to be a highly embedded star. With their median energies >3.5 keV, sources 56 and 155 are the most likely protostellar candidates, judging from the evolutionary class versus X-ray median energy relation shown in Figure 8 of Getman et al. (2007).

Figure 3 presents NIR properties for most of the Chandra sources with NIR counterparts based on the photometric data in Table 2. The nature of sources with known NIR photometry can be estimated from these diagrams. Our analysis uses models of intrinsic JHK_s photometric properties for stars with ages of 1 Myr assuming a distance of 600 pc (see Section 6). PMS evolutionary models of Baraffe et al. (1998) and Siess et al. (1997) are considered for the mass ranges of 0.02 M_☉ ⩽ M ⩽ 1.4 M_☉ and 1.4 M_☉ ⩽ M ⩽ 7M_☉, respectively, and stellar photometric properties of stars with masses >7 M_☉ are taken from Cox (2000). Sources used in the analysis have errors on their NIR colors <0.2 mag.

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The cluster stars are shifted to the upper right by A_V⩾ 5 mag on the color–color diagram (Figure 3(a)), so the foreground stars are easily identified due to the lack of significant absorption. Ten foreground stars are detected.

The mass sensitivity limit of the X-ray detected PMS sample is ∼0.2 M_☉; ∼90% of stars have masses <2 M_☉; and seven stars have masses ≳10 M_☉ (Figure 3(b)). The 55 X-ray stars located >1.5σ to the right of the reddening vector originating at 0.2 M_☉ (Figure 3(a)) are classified here as K_s-band excess stars⁸, leaving 109 X-ray stars as non-K_s-band excess stars. No stars with K_s-band excess are classified as protostellar objects; the X-ray observation is not sensitive to a protostellar population that might exist in W40 (Bontemps et al. 2010). The disk fraction, taking into account the differences in X-ray sensitivity to stars with and without K_s-band excess, is estimated in Section 6.

Photometric mass and V-band absorption derived from the color–magnitude diagram (Figure 3) are tabulated in Table 2. Uncertainties in the photometric mass estimates are discussed in the Appendix. Typical uncertainties are around 0.2 M_☉ for lower mass stars and 0.8 M_☉ for higher mass stars. There is a degeneracy in JHK_s photometry that leads to uncertain masses between 2 M_☉ and 10 M_☉ for the 1 Myr isochrone. We report the lower mass solution (2–4 M_☉) as masses in this range are more likely due to the shape of the IMF.

Extragalactic sources, mostly AGNs at moderate redshifts, dominate X-ray source counts at high Galactic latitudes and some will be detected in fields near the Galactic plane despite the heavy obscuration (Broos et al. 2007). Even the low X-ray detection rate of main-sequence stars will lead to contaminants in the X-ray image due to the huge number of foreground field stars. The field stars detected by X-ray observations will tend to be younger members of the disk population, since stellar X-ray emission declines rapidly after ∼1 Gyr (Feigelson et al. 2004; Preibisch & Feigelson 2005). However, background field stars are a less important source of contaminating X-rays for W40, due to the high obscuration from the cloud.

Out of 225 X-ray sources detected by our observation 19 are classified as extragalactic sources (Section 3.1) and 10 are classified as foreground stars (Section 3.2). The remaining 194 stars are likely W40 cluster members, although 30 do not have accurate IR colors for classification on the color–color diagram. Cluster membership is indicated in Table 2.

The foreground and extragalactic contamination of the W40 sources may be compared with the analysis of contamination in a Chandra ACIS-I observation of the young-star cluster Cep B. The galactic latitudes of Cep B and W40 are somewhat similar (∼35 for W40 and ∼27 for Cep B), and the distances (600 pc for W40 and 700 pc for Cep B) and the Chandra exposures (38 ks for W40 and 30 ks for Cep B) are similar, but the galactic longitudes (288 for W40 and 110° for Cep B) are different. Confirmed by simulations, the numbers of extragalactic and foreground objects in Cep B of 24 and 13, respectively (Getman et al. 2006), are similar to those of W40.

YSC members are typically identified by IR excess, and K_s-band excess is used to detect PMS stars within the ACIS-I field of view missed by Chandra. The 38 additional 2MASS cluster members with K_s-band excess and the massive star OS 3a (no K_s-band excess) are shown in Table 3. The K_s-band excess is identified in a similar way as for X-ray sources, but a reddening vector originating from 0.09 M_☉ instead of 0.2 M_☉ is used since the 2MASS point-source catalog is deeper than the Chandra observation and use of a reddening vector from 0.2 M_☉ would likely find foreground diskless stars. None of these 39 sources have a VLA counterpart.

In Figure 5, the COUP XLF is compared to the W40 XLF with three different trial distances: 600 pc, the most commonly reported distance; 260 pc, the distance to the nearby on the sky Serpens South cluster; and 900 pc, the largest reported distance (Section 1). Distances of 600 and 900 pc provide good fits, with a less complete 900 pc observed XLF. A distance of 500 pc provides a qualitatively worse fit, with a slight excess of stars above the COUP XLF at a log L_hc ∼ 30 erg s⁻¹ (graph not shown). With the assumption of a universal XLF, the W40 XLF analysis favors the distance of 600–900 pc; throughout the paper we adopt the most often reported distance of 600 pc.

Further on we carry out the analysis assuming d = 600 pc. However, as mentioned in Section 1.1, some studies favor the distance of 260 pc. Therefore, below we comment on possible modifications of the results if a distance of 260 pc is considered instead.

If the distance to W40 is 260 pc, then the excess of stars with 28.5 erg s^-1 < L_hc < 30 erg s⁻¹ is inconsistent with a universal XLF. This may indicate the absence of the expected higher mass stars in the cluster (see Section 7 for a discussion of the IMF for 260 pc), or may be due to L_X evolution if the cluster is much older than 1 Myr. The excess would be comparable to the excess of stars at L_hc = 29.3 erg s⁻¹ in Cep B (Getman et al. 2006).

The X-ray completeness limits, i.e., where the W40 XLF diverges from the scaled COUP model, are log L_hc = 30.2 and log L_tc = 30.6 corresponding to 50% completeness at 1.4 M_☉.

The vertical shift between the COUP and the W40 XLFs for the total as well as the K_s-band excess stratified star samples gives the same estimate of the total W40 stellar population down to 0.1 M_☉ of 70% the COUP sample, i.e., 600 PMS stars (Table 5).

The same inferred vertical scaling of 35% to fit the COUP XLF model to both the W40 XLFs of stars with and without K_s-band excess gives a W40 K_s-band excess fraction of ∼50%. The K_s-band excess fraction found for the W40 cluster is likely to be a lower limit on the disk fraction, since JHK is not the most sensitive tracer of disks. For example, L-band photometry in addition to JHK gives a more robust estimate on the fraction of stars with circumstellar disks. Clusters such as IC 348 (Haisch et al. 2001a; age ∼3 Myr), NGC 2024 (Haisch et al. 2001b; age <1 Myr), and the ONC (Lada et al. 2000; age 1–2 Myr) have the following reported JHK (JHKL) disk fractions: 20%–25% (65%) in IC348, 60% (85%) in NGC 2024, and 55%–90% (85%) in the ONC. The JHK_s disk fraction of 50% thus suggests that the W40 cluster is young with an age of likely ⩽1 Myr. W40's likely astrophysical disk fraction of ∼80% gives an age of 0.5 Myr using the regression line in Mamajek (2009) for age versus disk fraction of 22 star clusters.

However, there is a somewhat controversial situation, since six out of the eight high-mass star candidates (M ≳ 10 M_☉) have K_s-band excess, suggesting a K_s-band excess fraction of 75⁺⁹₋₁₉%⁹. Theoretical disk depletion timescales for early-type stars, due mostly to photoevaporation with some contribution from material removal by winds, are roughly 0.2 Myr and 0.7 Myr for O7V and B1V stars, respectively (Hollenbach et al. 1994, 2000). The observed disk fractions and the theoretical depletion timescales might suggest that most of W40 X-ray star high-mass candidates formed somewhat later than low-mass stars, for example the latter phenomenon is reported for stars in W3 (Feigelson & Townsley 2008), M17 SWex (Povich & Whitney 2010), and IRAS 19343+2026 (Ojha et al. 2010).

If W40 were at 900 pc the XLF would indicate completeness limits at log L_hc = 30.4 erg s⁻¹ and log L_tc = 30.8 erg s⁻¹ and a total population of at least 1000 stars down to 0.1 M_☉, but the disk fraction would not change. However, if the distance is 260 pc then these values cannot be derived from the XLF since the shape of the XLF would differ from the shape of the COUP XLF.

For the analysis of W40's structure, we choose to define the center of the cluster as the median position of all Chandra-detected members, which has coordinates R.A. = 18^h31^m 2514, decl.=−2°05'357 (J2000). An alternative strategy is to use the OB stars as the center of the cluster, but in W40 the median position of the high-mass stars is offset from the median positions of other stellar populations as shown in Table 7, so we judge that the median position of all the stars is a better estimate. For discussion of projected radial distances in the cluster d = (D/600 pc) accounts for uncertainty in the distance D to W40.

Fifty percent of the Chandra-detected cluster members are within 0.50 d pc of the cluster center and 75% are within 0.90 d pc. The edge of the ACIS-I array is 75 (1.3 d pc) from the center of the cluster, so our analysis of structure is restricted to the region within this radius. The most distant detected star is 1.8 d pc from the center. The core radius is ∼0.15−0.2 d pc (Section 9.2). In the core there is a small clump of 8 stars, including OS 1a, within a radius of 10''. A smoothed stellar surface density plot of the cluster is shown in Figure 8.

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The structure of YSCs may be affected by both the locations where stars form and by cluster dynamical evolution. The velocity dispersion of stars in W40 is likely to be similar to other YSCs; Fűrész et al. (2008) find a radial velocity distribution of σ = 3.1 km s⁻¹ in the ONC, and simulations of small and large clusters find one-dimensional stellar velocity dispersions of 1.2 km s⁻¹ and 4 km s⁻¹ (Bate et al. 2003; Bate 2009). Assuming the stellar velocity dispersion in W40 of ∼2–4 km s⁻¹ and a cluster size of 2d pc, the cluster crossing time is t_cross ∼ 0.5d–1d Myr, on the order of the age of the cluster. The two-body relaxation time for a cluster is

$$\begin{equation} t_{{\rm relax}} = \frac{N}{8\ln N}\times t_{{\rm cross}}, \end{equation} \tag{ 1 }$$

where N is the number of stars (Binney & Tremaine 1987). In W40, N ∼ 600 so the two-body relaxation time is ∼5–10 Myr, longer than the age of the cluster. However, violent relaxation may proceed more quickly (Lynden-Bell 1967).

If the distance of 260 pc is considered instead of 600 pc, the relaxation time would decrease to ∼1–2 Myr.

9.2.1. Radial Profile

Figure 9 shows the radial surface density profile of W40. All cluster members detected by Chandra are included to improve counting statistics. The radial profile of stars from COUP (Feigelson et al. 2005) is provided for comparison, and a scaled version of the COUP radial profile closely resembles the radial profile of W40. Various functional profile models are evaluated using the cumulative distribution function (CDF) of the radial distances of cluster members and the K-S statistic. No single power law provides a good fit. However, the inner 0.2 d pc part of the profile is flatter and can be fit with a power-law index of −0.2, and the outer part of the cluster is fit with a power-law index of −1.6. The 90% confidence interval on the indices is ±0.3. YSC surface-density profiles are often fit by shallower power laws that typically have an exponent of −1. Examples include IC 348 (σ ∝ r⁻¹) and NGC 2282 (σ ∝ r^−1.1) (Lada & Lada 1995; Horner et al. 1997).

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Assuming spherical symmetry, a surface density distribution with a power law σ ∝ r^α and α < 0 will correspond to a three-dimensional density distribution with a power law ρ ∝ r^α−1, so the three-dimensional power-law index for the inner part of the cluster will be approximately −1.2 and the power-law index for the outer part of the cluster will be −2.6 (similar to the three-dimensional power-law index derived from the Q parameter analysis described in Section 9.2.2).

We define the core of W40 as the region within 0.2 d pc, since this region has a noticeably less steep profile than the outside of the cluster. Within the core there are 48 Chandra-detected stars, the three ionizing sources OS1a, OS2a, OS3a, and three other high-mass star candidates. This core radius is similar to the core radius of the ONC which was found to be r_c ≃ 0.15 pc (Hillenbrand & Hartmann 1998).

The ONC stellar density profile is well fit by the King profile (Hillenbrand & Hartmann 1998) for an isothermal sphere (King 1962) that is applicable to gravitationally relaxed clusters and is described by the equation

$$\begin{equation} \sigma (r)\approx \sigma _c(r) = \frac{\sigma _0}{1+(r/r_c)^2}. \end{equation} \tag{ 2 }$$

Nevertheless, Hillenbrand & Hartmann (1998), Feigelson et al. (2005), and Fűrész et al. (2008) argue that the Orion cluster is not truly dynamically relaxed. The W40 cluster can also be fit by an isothermal sphere with a core radius of 0.15 d pc (K-S probability of 92%), but W40 might also not be dynamically relaxed due to its young age (Section 9.1).

9.2.2. Profile Fitting and Detection of Subclustering with the Q-Statistic

A statistic Q indicates the existence of subclustering and measures the central concentration of clusters without subclustering (Cartwright & Whitworth 2004). This parameter combines a measure of the separation between stars and a measure of the edge lengths of the Euclidean minimal spanning tree (EMST). The EMST is the unique graph with minimum total edge length that connects all vertices. Figure 10 shows the EMST for all W40 cluster members detected by Chandra, where the stars are the vertices of the graph. The parameter s is the mean separation between stars and m is the mean edge length on the graph. Cartwright & Whitworth (2004) define

$$\begin{equation} \bar{s} = s/r_{{\rm max}} \end{equation} \tag{ 3 }$$

and

$$\begin{equation} \bar{m} = \frac{m(N_{{\rm max}}-1)}{N_{{\rm max}}\pi r_{{\rm max}}^2}, \end{equation} \tag{ 4 }$$

where r_max is the maximum radius, which is 75 for W40 (stars outside of this radius are excluded), and N_max is the number of sources within the radius. The parameter Q is defined by

$$\begin{equation} Q = \frac{\bar{m}}{\bar{s}}. \end{equation} \tag{ 5 }$$

Figure 5 in Cartwright & Whitworth (2004) gives fractal dimension or central concentration as a function of Q generated from simulated clusters. A YSC with subclustering will have a value of Q < 0.8. For W40 Q = 1.47, indicating that W40 does not have subclustering (within 75) and that the cluster has a three-dimensional density profile ρ ∝ r^α, where α = −2.7. In addition, a visual examination of the EMST in Figure 10 reveals no unusually long segments, which suggests that no subclustering is present. The analysis also agrees closely with the results of the power-law fits to the outer part of the cluster (Section 9.2.1). For comparison, the shallower three-dimensional radial profile exponents of −1.2, −2.2, and −1.7 are found for ρ Ophiuchus, IC348, and σ Ori (Cartwright & Whitworth 2004; Caballero 2008), respectively.

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9.2.3. Cluster Elongation and Asymmetry

There is no evidence of that the W40 cluster of all Chandra-detected PMS stars is elongated; no correlation is found between right ascension and declination of cluster members (Person correlation coefficient = −0.1), and the standard deviations of right ascensions and declinations are similar (173'' and 180'', respectively).

To further investigate whether the exterior of W40 (r>0.2 d pc) has radial symmetry, the distribution of azimuthal angles of stars is compared to an isotropic distribution, and the median distances of sources from the center are examined as a function of azimuthal angle (Figure 11). For the former test the CDF of the angles was found to be consistent with a uniform distribution using Kuiper's statistic (Kuiper 1962), providing additional evidence that subclustering does not exist in W40. For the latter test, sources are binned by azimuthal angle with bin sizes of 60°, and median distances are determined with error on the median calculated using 1000 bootstrap values. The median distances are consistent with a single value (reduced χ² is 0.4 when fit with a constant). However, with bin sizes of 180° the reduced χ² is 3.4 due to larger radial distances in the south half of the cluster, indicating that these stars are less centrally concentrated.

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Most YSCs including both the ONC (Hillenbrand & Hartmann 1998) and σ Orionis (Caballero 2008) have asymmetric morphologies. These asymmetric morphologies have been taken as another sign of incomplete dynamical relaxation (Hillenbrand & Hartmann 1998) and may be an effect of the elongation of the star-forming molecular clouds (Allen et al. 2007). If W40 is not dynamically relaxed, the near radial symmetry could be a result of spherically symmetric star formation or a projection effect if we are looking down the asymmetric axis of the cluster. Fűrész et al. (2008) caution about the interpretation of radial profiles that average over all angles, since asymmetry may cause steeper power laws, but this is not a great concern for W40 because of the near radial symmetry.

Finally, if considering only sources with K_s-band excess the azimuthal distribution is not uniform (0.5% K-S probability). We further study this in Section 9.4.

The dependence of cluster structure on stellar mass in YSCs provides clues about cluster formation and dynamical evolution. It is observed that massive stars are preferentially detected near the centers of open clusters and YSCs. Mass segregation is an expected result of dynamical relaxation, but must be explained by different astrophysics for its appearance in clusters that are not dynamically relaxed. Mass segregation is seen in clusters that are not dynamically relaxed, such as NGC 2071, the Trapezium, and NGC 2074 (Lada et al. 1991; Hillenbrand & Hartmann 1998; Bonnell & Davies 1998). This mass segregation would be caused if higher mass stars tend to be formed nearer the center of clusters (Proszkow & Adams 2009) or it could be an effect of dynamics during the formation of a not-yet dynamically relaxed star cluster as described by Maschberger et al. (2010) and Allison et al. (2009). This phenomenon is also seen in W40.

We stratify W40 cluster members by three mass ranges at 1.5 M_☉ and 10 M_☉ and by K_s-band excess (we will refer to the mass ranges as low mass, intermediate mass, and high mass). Both the intermediate-mass and high-mass populations should be approximately complete (based on the results of the XLF/IMF analysis). The spatial positions of stars in these strata are plotted in Figure 12 and the centers and median radii are given in Table 7. Low-mass stars are clearly less centrally concentrated than medium-mass stars and high-mass stars. The high-mass stars are the tightest group, except for star 46 which is several arcminutes away from the rest of the group. We do not have proper motions to evaluate whether this star is a runaway.

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The CDFs of radial distances of low-mass stars, intermediate-mass stars, and high-mass stars show these mass segregation trends, and the K-S probabilities that the three mass distributions come from the same population are negligible¹². Moeckel & Bonnell (2009) describe a method that uses the area of the convex hull for n stars to search for mass segregation. The convex hull is defined as the minimal convex polygon which covers a set of points, and the area may be used to determine stellar density. For W40, the probabilities that n randomly selected low-mass stars could have a convex hull with an area less than the area of the convex hull of the n high- or intermediate-mass stars are 7 × 10⁻⁴ and 5 × 10⁻², respectively. For the 25 stars with M = 1.5 ± 0.1 M_☉ the probability is 2 × 10⁻².

This result is unusual since mass stratification typically is seen starting at higher masses than 1.5 M_☉, for example Allison et al. (2009) find no mass segregation in the ONC at masses less than 5 M_☉. However, mass segregation beginning at 1 M_☉ in 1 Myr old simulated clusters is found by Moeckel & Bate (2010) in an N-body simulation.

The distance to W40 does not affect the existence of mass segregation, since radial distances scale similarly and the masses derived for 260 pc are an increasing function of the masses derived for 600 pc. However, mass segregation would starts at 0.3 M_☉ for 260 pc rather than 1.5 M_☉.

In Figure 12(a), the low-mass stars with K_s-band excess are concentrated on the east side of the cluster, while the stars without K_s-band excess are evenly spread over the entire cluster. This effect is not as strong among the intermediate-mass stars, many of which reside in the core from both populations. In Table 7, the median position for low-mass stars with K_s-band excess are 0.27 d pc to the east of the cluster center, which is farther away from the center than for any of the other populations listed.

Figure 13 shows the spatial distribution of K_s-excess stars and the molecular core. Almost no stars with K_s-band excess are located west of the cluster core, and 20% of the stars without K_s-band excess are located west of the westernmost K_s-excess star. The K-S probability that the spatial distributions are the same is P = 2 × 10⁻⁶.

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To the west of right ascension 18^h31^m15^s (27781), 23 Chandra-detected stars have no K_s-band excess and 0 Chandra-detected stars have K_s-band excess, so the 1σ upper limit on the observed JHK_s disk fraction in this region is 5% (Equation (21) in Gehrels 1986). East of 18^h31^m24^s (27785), 45 Chandra-detected stars have no K_s-band excess and 35 Chandra-detected stars have K_s-band excess, so the observed JHK_s disk fraction in this region is ∼44⁺⁵₋₇%. Since only 20% of T-Tauri stars with K_s-band excess are detected, compared to 45% of T-Tauri stars without K_s-band excess, the astrophysical JHK_s disk fraction in these two regions is <10% and 63% for west and east regions, respectively.

The extremely different disk fractions must have been caused recently, since this phenomenon will be erased due to mixing on the order of the cluster crossing time, which is <1 Myr. This provides further evidence that the age of the population of stars with K_s-band excess is <1 Myr.

Different K_s-band excess fractions may be attributed to environments hostile to disks or to different stellar ages. In the second case, our assumption of a coeval cluster is violated. This may be due to two different epochs of star formation or progressive star formation moving from west to east. Alternatively, the spatial distribution could be explained if the youngest stars moved to the east side of the cluster due to a similar initial velocity. Subclustering is also a possibility, although Section 9.2 gives evidence that the stars are from only one cluster.

A depleted disk fraction due to a harsh environment in the western part of the cluster seems unlikely, since the K_s-band excess disk fraction is high in the cluster core where the UV radiation and stellar winds would be strongest, and even some of the most massive stars have K_s-band excess. The disky stars in the core could have moved there recently, so they would not have been exposed to the environment for long enough to lose their disks. However, many of the disky stars in the core are high- or intermediate-mass stars, which are concentrated toward the center of the cluster (Section 9.3).

The MSX data show that W40 is a bipolar nebula with an hourglass shape (Figure 6 in Rodney & Reipurth 2008). This type of structure is fairly common for H ii regions; for example W40's shape closely resembles Sharpless 106 (S106) (Oasa et al. 2006), IRAS 19343+2026 (Ojha et al. 2010), and the Lagoon Nebula (Tothill et al. 2008). In W40, the waist of the hourglass is the location of a dust lane which bifurcates the H ii region and shows up in the optical image (Figure 14(b)). Larger column densities of dust and gas are also measured for stars in the dark lane from the JHK_s data and the X-ray data. The arrangement of the J − H> 2.2 sources (corresponding roughly to A_V ≳ 10–13 mag) is shown in Figure 14(a) in comparison to the rest of the cluster and to the molecular core. We draw a region which encloses most of the J − H> 2.2 sources, but few of the less absorbed sources, and plot this on a map of the smoothed extinction¹³ (shown in Figure 15). The mean XPHOT hydrogen column density is (3.2 ±  0.4) × 10²² cm⁻² in the dark filament and (1.8 ±  0.1) × 10²² cm⁻² outside this region, considering only sources without K_s-band excess. These correspond to visual extinctions of 15 mag and 9 mag, respectively. The filament appears to have a normal gas-to-dust ratio: log(N_H/A_V) = 21.33 ±  0.03 for stars in the filament and log(N_H/A_V) = 21.34 ±  0.02 for stars outside the filament.

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The dust lane passes through the eastern half of the cluster core and lies several arcminutes to the east of the CO core. The filament has dimensions 3' by 12', and an approximate angular area of 36 arcmin² or 1.1×10³⁷ cm² at a distance of 600 pc. The filament's mass is estimated by multiplying its angular area by the difference in mean column density inside and outside the lane giving a total mass of ∼200 M_☉. This is comparable to the mass of the molecular core found by Zhu et al. (2006). If we assume that the filament's extent along the line of sight is similar to its width of 3 arcmin, then the hydrogen density of the filament is 10⁴ atoms cm⁻³.

If the distance of 260 pc were considered instead, the masses of both the molecular core and dust lane would be scaled down by a factor of ∼5, but the density would be the same.

The presence of a large number of sources with K_s excess near the dust lane suggests that the lane may be a region of active star formation. This is further supported by the high concentration of Herschel protostar candidates from Figure 3 of Bontemps et al. (2010) that lie in this region. In contrast, few deeply embedded X-ray sources are found in the CO core, suggesting that the molecular core is not the location of present star formation.

The geometry of the dust lane and the molecular core suggests that they form a ring, similar to the rings described by Beaumont & Williams (2010). However, YSOs projected on the molecular core do not have very high A_V, and CO is not detected strongly in the dust lane. The former problem may be explained if the ring is oriented from our point of view so that the dust lane passes in front of the cluster and the molecular core is behind the cluster. The molecular core probably has a normal gas-to-dust ratio and we would see both CO emission and a visual dust lane if we were observing the cluster along a line of sight that passes through the cloud.

The lack of CO detection in the dust lane might mean that the molecular material has been destroyed in this region, or it might be an effect of the lack of sensitivity of the CO observations. CO may become frozen out onto dust grains in a molecular cloud (van Dishoeck & Blake 1998). Mitchell et al. (2001) find evidence of this effect in two parts of the Orion B molecular cloud with bright dust continuum but almost absent CO emission. Alternatively, CO may be destroyed by UV radiation or expanding H ii regions produced by OB stars.

Out of 225 X-ray sources, only 24 sources have more than 100 net counts, and almost a third of the sources have fewer than 10 net counts. Composite spectra are useful for gaining insight into the sources which lack sufficient counts to be fit parametrically (e.g., Feigelson et al. 2005). They are created for the W40 point sources by merging individual source spectra, backgrounds, RMFs, and ARFs using the ACIS Extract software. Separate composite spectra are generated for cluster stars with more than 100 counts, cluster stars with fewer than 100 counts, and the extragalactic sources; these spectra are plotted in Figure 16(b).

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The spectra are fit in XSPEC using the thermal-plasma model apec and the interstellar photoelectric-absorption model wabs. A two-temperature model with fixed parameters Z = 0.3 Z_☉ (see Section 4) and kT₁ = 0.8 keV (typical cool component in T-Tauri stars from Preibisch et al. 2005) best fits the composite spectra of >100 count (<100 count) sources with N_H = 1.7 × 10²² cm⁻² and kT₂ = 5.4 keV (N_H = 2.2 × 10²² cm⁻² and kT₂ = 5.2 keV). For >100 count (<100 count) sources, model fitting with metal abundance Z as a free parameter gives a value of Z= 0.43^+0.09_−0.08 (Z=0.44^+0.14_−0.11), indicating that Z = 0.3 Z_☉ is a good approximation for the cluster. The stacked spectrum of extragalactic sources is well fit by an absorbed power law with a photon index of 1, within the typical range of 1–2 for AGNs (Alexander et al. 2003).

For the composite spectrum of >100 count (<100 count) sources XSPEC calculates observed (not corrected for absorption) hard-band fluxes of (2.9 ±  0.1)×10⁻¹² erg s⁻¹ cm⁻² ((1.7 ± 0.1) ×10⁻¹² erg s⁻¹ cm⁻²) and soft-band fluxes of (3.5 ± 0.2) × 10⁻¹³ erg s⁻¹ cm⁻² ((2.6 ± 0.1) ×10⁻¹³ erg s⁻¹ cm⁻²), implying observed hard-to-soft flux ratios of 8.3 ± 0.6 (6.5 ± 0.5).

In a number of star-forming regions the soft (kT < 1 keV) diffuse thermal emission has been detected from a gas shocked in wind–wind or wind–surrounding medium interactions (Townsley et al. 2003; Güdel et al. 2008). The uncommon hard diffuse synchrotron emission has also been reported (e.g., Wolk et al. 2002). In some cases the observed X-ray diffuse emission can be completely explained by the unresolved stellar population (e.g., Getman et al. 2006).

The Chandra observation W40 has detected diffuse X-ray emission near the core of the cluster that is unassociated with the resolved point sources and can be seen in the smoothed image in Figure 2. To isolate the diffuse emission, a "Swiss-cheese" mask is created (Broos et al. 2010). Despite the Swiss-cheese masking, there is some light remaining from the wings of very bright X-ray sources concentrated in the core. To avoid any of this contamination a generously sized polygon surrounding the central stars is excluded (Figure 16(a)). Three background regions are used; backgrounds 1 and 2 are on the Chandra ACIS-I3 chip, while background 3 is on the Chandra ACIS-I2 chip. Background 2 is adjacent to the extraction region, while backgrounds 1 and 3 are further away¹⁴.

A moderate-resolution spectrum is extracted with ACIS Extract from the source region and the three background regions. Fits with different backgrounds give similar results; reported results are given for background 3. A degeneracy in spectral model fit exists due to the high absorption which makes it difficult to constrain the soft component (kT < 1 keV) due to the small number of counts. A one-temperature model produces a good fit (reduced χ²= 0.94) with N_H = (1.2 ±  0.2) × 10²² cm⁻², kT =2.9 ±  1.0, and Z = 0.3 Z_☉. A variety of two-temperature models work as well, including N_H = 2.2 × 10²² cm⁻², kT₁ = 0.66, kT₂>15, and Z = 0.3 Z_☉ and N_H = 3.3 × 10²² cm⁻², kT₁ = 0.27, kT₂ = 4.3, and Z = 0.3 Z_☉, both with a reduced χ² of ∼0.8.

The observed (uncorrected for absorption) hard-band and soft-band fluxes of the diffuse emission are (2.0 ±  0.2) × 10⁻¹³ erg s⁻¹ and (4.8 ±  0.1) × 10⁻¹⁴ erg s⁻¹, respectively, so the hard-to-soft flux ratio is 4.2 ±  0.4. This is smaller than that of the stacked stellar X-ray sources at a statistically significant level (P < 0.001), which demonstrates that the spectra have a different shape. This can be seen visually in Figure 16(b), where the bump at low energies is relatively larger in the diffuse spectrum than in the stacked stellar spectra. This result is an indication that the diffuse spectrum may not be entirely stellar. However, the unresolved stellar population, being composed of lower mass sources, is also expected to have spectra that are softer than the resolved population (Figure 11 in Preibisch et al. 2005).

In the hard band only X-ray emission from stellar sources should contribute to the diffuse emission. The measured hard-band luminosity of the diffuse emission is compared with the expected hard-band luminosity of undetected stellar sources within the extraction region. Eleven percent of the Chandra-detected stars lie within the extraction region, so we assume a similar percentage of the unresolved stars lie in this region. The sum of the hard-band luminosity of all the missing sources from the XLF below the completeness limits is 6.8 ×10³¹ erg s⁻¹, and thus the hard-band emission expected within the extraction region is 7.5×10³⁰ erg s⁻¹. The hard-band luminosity of the diffuse emission is calculated using the one-temperature and two-temperature models discussed above, and uncertainty is estimated by varying parameters within their 1σ errors. The result is L_hc = (8.2 ±  3.4) × 10³⁰ erg s⁻¹, which is consistent with that of the unresolved stellar component.

The estimated total-band luminosity of undetected T-Tauri stars in the extraction region is 2.0 × 10³¹ erg s⁻¹, which is calculated in the same way as the estimated hard-band luminosity. The total-band luminosity of the diffuse emission is L_tc = (1.9 ±  0.7) × 10³¹ erg s⁻¹ for the one-temperature model fit, consistent with that of the undetected T-Tauri stars. However, it may be more than five times greater for the two-temperature model fits. Although, the total-band diffuse emission may be consistent with only the emission expected from unresolved stars, it is unclear if a real nonstellar X-ray component is present due to the degeneracy in spectral model fits.

If the distance to W40 is 260 pc, then diffuse emission luminosities decrease by a factor of five. However, the IMF analysis indicates that the observation would be complete down to 0.1 M_☉ so the X-ray emission from unresolved stars would be an order of magnitude lower in both the hard and total bands.

Long and powerful flares from YSOs are sometimes detected in Chandra observations of YSCs; for example, in the COUP project ∼200 flares are detected indicating a flare rate of approximately one per star per week (Getman et al. 2008b). During the 38 ks observation of W40, the decay phase of a powerful flare is detected in the light curve of source 138, an intermediate mass (4 M_☉) YSO near the center of the cluster. This flare has a peak luminosity ⩾40 times its non-flaring luminosity and an e-folding decay timescale of 7.6 ks. The flare is strongly affected by pileup on the ACIS-I chip, so we do not present flare cooling analysis.

At least two alternative explanations for powerful flare activity from a 4 M_☉ YSO exist. The object can be an F-type T-Tauri star with a partially developed radiative core. Big super-hot flares are typically seen from two types of T-Tauri stars: (1) low-mass stars (M < 2 M_☉) with active disks (2) and more massive (M>2 M_☉) disk-free stars (Section 5 in Getman et al. 2008c). It is possible that the formation of a radiative core in the latter case is associated with the change in the magnetic field dynamo, for example from turbulent to alpha–omega, which in turn strengthens their magnetic fields and allows production of super-hot flares.

Alternatively, the object can be a fully radiative A or late B-type star. Although X-ray activity in late B and early A stars is generally weak, X-ray flares associated with these stars have been seen in several cases such as HD 161084 (Miura et al. 2008), HD 261902, and HD 47777 (Yanagida et al. 2007). One of the possibilities for the X-ray emission is the presence of an X-ray active T-Tauri companion to an IR-bright, A/B-type star.