CORE–HALO AGE GRADIENTS AND STAR FORMATION IN THE ORION NEBULA AND NGC 2024 YOUNG STELLAR CLUSTERS

Ideally, it is desirable to perform analyses of cluster age gradients using spatial star samples with similar completeness limits in mass because (a) the real age distribution of a stellar cluster could be astrophysically mass-dependent; and (b) the location of data and evolutionary model isochrones on the HRD or a color–magnitude diagram (or the M_J − M diagram in case of Age_JX) could be inconsistent with each other for different mass ranges. However, the following possible incompleteness and selection biases in the MYStIX data of NGC 2024 and the ONC might complicate the construction of uniform samples complete to some mass limit.

• 1.  
  We use subsamples of MYStIX PMS stars with available Age_JX estimates (Section 2 and G14). For the Age_JX analysis, the full MYStIX PMS samples were restricted to low-mass stars with available L_X measurements with 10²⁹ < L_X < 3 × 10³⁰ erg s⁻¹ (0.2 ≲ M ≲ 1.2 M_☉) and reliable NIR photometry, and were culled of protostellar objects with extremely large K_s excesses for which there is no clear NIR dereddening procedures (G14).
• 2.  
  The sensitivity to PMS stars in the X-ray data has a spatial bias due to the decrease in the Chandra telescope sensitivity with increasing off-axis angle, and due to the MYStIX bias against highly dispersed PMS stars.
• 3.  
  The reduced sensitivity to ONC members in the Chandra-ACIS image of Orion within 1' of θ¹ Ori C due to the extended wings of its point-spread function.
• 4.  
  The limiting sensitivity to faint X-ray sources in NGC 2024 due to the shorter exposure time of its Chandra observation (Table 2 in Feigelson et al. 2013).
• 5.  
  The reduced sensitivity to NIR and X-ray NGC 2024 members in the central region due to the presence of an obscuring molecular core.
• 6.  
  The reduced sensitivity to faint NIR stars due to the presence of high background nebular emission from heated dust around the cluster center.

For the analysis of age gradients in the ONC, the six potential incompleteness and selection biases described in Section 3.2.1 were easily overcome due to the exceptionally deep Chandra-ACIS exposure of the Orion region, nicknamed the Chandra Orion Ultradeep Project (COUP; Getman et al. 2005). The "COUP unobscured" stellar sample of 839 cool ONC stars (Feigelson et al. 2005) was found to be ∼90% complete down to M ∼ 0.2 M_☉ (neglecting effects of binarity). This is shown in Figure 19 of Getman et al. (2006) that compares the initial mass function (IMF) of the "COUP unobscured" sample with the ONC IMF from Muench et al. (2002). The Age_JX ONC subsample used in our age gradient analyses is identical to the "COUP unobscured" stars with the constraint 10²⁹ < L_X < 3 × 10³⁰ erg s⁻¹ applied.

The first two potential sample bias problems are thus not present in the ONC sample. The third problem is mitigated by the L_X constraint that removes all faint X-ray sources from the sample. The fourth and fifth problems are not relevant to the ONC, while the sixth potential problem was overcome by correlating X-ray sources with a deep NIR image obtained with the Very Large Telescope/ISAAC instrument on an 8 meter telescope (Getman et al. 2005). Thus, we expect that the observed mass function of the Age_JX ONC stellar sample is representative of the IMF for ∼90% of the intrinsic ONC population within the mass range between ∼0.2 M_☉ and 1.2 M_☉, if effects of binarity are ignored.

Using the X-ray luminosity function (XLF) as a surrogate for the IMF (Getman et al. 2006), we investigate whether the X-ray luminosities have a spatial gradient that may have artificially produced an age gradient through the L_X − M (X-ray-mass) relationship central to the Age_JX estimation method (G14). Figure 2(c) shows the cumulative XLFs for the core–halo strata in the ONC. The strata have statistically indistinguishable XLFs, as confirmed with Kolmogorov–Smirnov (K-S) tests. The K-S test probabilities between the red and the remaining strata are P_K-S = 95% (green), P_K-S = 94% (blue), P_K-S = 28% (orange), and P_K-S = 95% (cyan). Since the L_X − M relation remains unvarying with time during the early evolutionary phase of PMS stars (G14) and the XLF is a surrogate for IMF, the mass functions of the Age_JX stellar subsamples within the different core–halo subregions are expected to be similar as well.

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In the case of NGC 2024, the mutual effect of the first (Age_JX sample selection), fourth (moderate X-ray exposure), and especially the fifth (high source extinction from the molecular core) and sixth (high background NIR nebula emission) biases (Section 3.2.1) is difficult to overcome, so the resulted Age_JX stellar subsamples are more heterogeneous than in the ONC.

All spatial Age_JX strata in NGC 2024 have statistically indistinguishable observed XLFs (Figure 2(a)), as confirmed with K-S tests.⁴ However, as a result of the first and fourth potential biases, the three Age_JX source subsamples for the NGC 2024 halo strata (green, blue, orange) are ∼80%–90% complete down to only log (L_X) ∼ 30 erg s⁻¹ (0.6 M_☉) when compared to the XLF of the "COUP unobscured" population. The problems are particularly acute in the cluster core where—due to the mutual effect of the first, fourth, fifth, and sixth biases—the respective Age_JX subsample is incomplete for any range of L_X or mass. A handful of Age_JX sources in the core of NGC 2024 thus might not be representative of the entire stellar population in the cluster core. We now provide additional lines of evidence for the extreme youth of the cluster core in NGC 2024.

Generally, the body of earlier work for the NGC 2024 cluster and the ONC support our findings here, though they are perhaps individually less convincing than our results (Section 3). Our work has three strengths: (1) the underlying sample arises from a multiwavelength survey that efficiently finds both disk-bearing and disk-free stars (Feigelson et al. 2013); (2) the underlying age estimator applies to both disk-bearing and disk-free stars and gives persuasive age large-scale gradients in many star-forming regions (G14); and (3) the sample studied is limited to a narrow range of stellar masses around 0.2–1.2M_☉ so there is no conflation of mass segregation and age gradient effects.

• NGC 2024 Cluster.  
  There have been no previous reports of a spatial-age gradient in the stellar cluster that ionizes the Flame Nebula. Studies have reported a very young average age for the cluster. Ali et al. (1998) perform NIR photometry and spectroscopy on 40 members and report "that the cluster is fairly young (average age 0.5 Myr) and coeval." A similar study with a larger sample of ∼70 cluster members arrives at a similar median cluster age (0.5 Myr) but with a wide age spread from ≪1 to ∼30 Myr (Levine et al. 2006). These studies cannot reveal a cluster-wide age gradient, as their NIR samples miss most of the members in the inner regions due to high obscuration (A_V ⩾ 20 mag) and high background nebular emission. Haisch et al. (2001) report a very high fraction of stars with infrared-excess disks (85% of 59 stars) and infer a very young age around ∼0.3 Myr. However, their underlying sample misses most disk-free stars that are found in X-ray studies, so their disk fraction could be overestimated (Figure 4(a)). Burgh et al. (2012) discuss how the far-ultraviolet spectrum of NGC 2024 IRS 1 has strong P Cygni wind feature characteristics of a ∼3 Myr old O8 I supergiant, rather than a younger late O main-sequence star. However, the finding is difficult to interpret and may be due to scattered light from an obscured star behind the dust lane of the nebula.
• Orion Nebula Cluster.  
  From an HR diagram constructed from Hubble Space Telescope photometry and ground-based photometry and spectroscopy, Reggiani et al. (2011) calculate ages of ∼1000 stars in the ONC based on Siess et al. (2000) evolutionary models. Their analysis is limited to masses above ∼0.4 M_☉ where the sample is >80% complete. The age distribution over most of the cluster is approximately constant with mean age around 2.2 Myr and an overall age spread of 2–3 Myr. In their spatial analysis of the age distribution, Reggiani et al. obtain a result similar to that reported here (Section 3): most of the cluster volume has a constant age distribution, but the inner core region (radius ∼0.2 pc) has an excess of younger stars with ages <1.2 Myr. However, they caution that this result could be affected by a bias in the completeness of the sample, as their optical sample may be less complete near the cluster center where the nebular background emission is brighter. They conclude with the statement, "if this "age segregation" is confirmed, this may have implications for the study of the dynamical evolution of the cluster." Unlike, the optical sample of Reggiani et al., the Age_JX sample was built to be nearly complete and uniform in L_X, and thus in mass, across the entire ONC within the Chandra field (Section 3.2).

A number of earlier studies in recent years have results relating to the age gradients presented here. We review these here.

• Serpens North, Serpens South, and Corona Australis.  
  Serpens North (Gorlova et al. 2010), Serpens South (Gutermuth et al. 2008), and Corona Australis (Peterson et al. 2011) are nearby (D < 400 pc) star formation regions with stellar clusters less rich than those studied with MYStIX (∼50 observed disk-bearing objects per cluster). Their morphologies, with primarily protostellar cores and PMS halos, are reminiscent of that of NGC 2024. By comparing the observed ratios of protostars and Class II PMS stars in these clusters to the predictions of his analytical cluster model of "constant birthrate, core-clump accretion, and equally likely stopping". Myers (2012) reports the core–halo age gradients from ∼0.3 Myr to ≳ 1 Myr. Myers speculates that the astrophysical cause of these gradients could be due to later formation of dense central parts in parental molecular filaments, similar to our scenarios (a) and (b) below (Section 4.2).
• W 3 Main.  
  The rich embedded cluster W 3 Main within the giant W 3/W 4/W 5 molecular cloud complex has a unique collection of radio H ii regions from embedded OB stars within a ∼0.3 pc radius core (Tieftrunk et al. 1998). These ionized bubbles have a range of sizes, but some are very small ultracompact and hypercompact H ii regions implying that the related massive stars are extremely young with ages ∼10⁴ yr. In an X-ray/infrared study similar to, but preceding, the MYStIX project, Feigelson & Townsley (2008) identify several hundred PMS stars tracing a large spherical cluster with radius ∼2 pc. Only a very small fraction of the PMS population have infrared-excess protoplanetary disks, implying that the extended cluster has age ⩾2 Myr, much older than the central OB stars. Bik et al. (2014) confirm this result and extend it with suggestive evidence from spatial analysis of K-band excess stars and the K luminosity function that the younger PMS stars, like the OB stars, are centrally concentrated. Altogether, it appears that W 3 Main is similar to NGC 2024 and the ONC with a spatial-age gradient in a rich young star cluster.
• IRAS 19343+2026.  
  Ojha et al. (2010) study the stars in the embedded cluster IRAS 19343+2026 at a distance around 4 kpc. Here several dozen PMS stars with estimated ages ⩾1 Myr lie in a region about 1 pc across around a core of several mid-B stars with strong infrared-excess disks. The latter have estimated ages around ∼10⁵ yr, younger than the more extended PMS cluster.
• Bright Rimmed Clouds.  
  Several cases have been found of small-scale sequential star formation in PMS stars on the periphery of rich clusters where the H ii region shocks the ambient molecular material and produces ionized bright rimmed clouds (BRCs). In these cases, the older stars lie closer to the central OB-dominated cluster and the younger stars lie embedded in the molecular cloud. This phenomenon is seen in NIR samples associated with BRC 11NE, BRC 13, BRC 14, BRC 37 among others (Ogura et al. 2007; Chauhan et al. 2009, 2011) and in X-ray samples associated with IC 1396N, Cepheus B, and IC 1396A (Getman et al. 2007, 2009, 2012). A general trend in these and other regions (e.g., the Rosette Nebula; Wang et al. 2010) is found that PMS stars on the periphery of giant H ii regions are younger than the PMS stars in the central rich cluster. These spatial-age sequences are attributed to star formation in the surrounding cloud triggered by the expansion of the H ii region over millions of years, plausibly through some combination of "radiative driven implosion" and "collect and collapse" mechanisms. The results are age gradients opposite to those discussed here with older stars at the cluster core and younger stars at the cluster periphery. These findings relating to secondary triggering processes do not provide insight into the formation process of the original rich cluster that produced the giant H ii region.

Scenario A. Although gas accretion onto stars will deplete the cloud material in both regions, gas is less dense in the periphery. There is likely a threshold below which gas is no longer unstable to gravitational collapse. André et al. (2010) find that this threshold is roughly a column density of $N_{H_2} \sim 7\times 10^{21}$ cm⁻², corresponding to A_V ≃ 8 mag extinction, in dense filaments that pervade many MSFRs. With decreasing gas surface density throughout the cloud, the less dense peripheral cloud material will drop below this threshold first and stop forming stars before the cloud center stops. Viewed later as a MYStIX star-forming region, the outer stars will appear older on average than the central stars.

Scenario B. Palla & Stahler (2000) and Stahler (2006) argue that over millions of years the combination of global gravitational contraction and star formation threshold results in acceleration of the star formation rate. Thus, most of the stars in the core would have formed at the end of the cloud lifetime and would appear younger than stars in the cluster periphery.

Scenario C. Many theoretical models of massive star formation predict that O stars form at the center of clusters (Zinnecker & Yorke 2007). Furthermore, in a few clusters observational evidence indicates that O stars may be the last stars in a cluster to form (Ojha et al. 2010; Feigelson & Townsley 2008), perhaps because the timescale needed for competitive accretion or mergers to make massive stars is longer. This would imply, that—at least for massive stars—there would be age stratification.

Scenario D. If stars are forming from a molecular core that is not gravitationally bound, then the resulting cluster may be supervirial and its stars will drift away from the cloud after they are born due to their initial velocities. This may be common for low-mass cloudlets in regions like the South Pillars of Carina (Povich et al. 2011). Unbound stars could also be produced by three-body interactions; for example, star-cluster formation simulations by Bate (2009) shows ejection of some first-generation stars. Older stars will have a longer time to drift, so they will be located farther from the cluster center. After some first-generation of stars has drifted away, infall of cloud material can lead to a new population of young stars being born at the cluster center.

Scenario E. There is growing evidence to suggest that stars are born with subvirial velocity dispersions. In hydrodynamical models, Bate et al. (2003) find that initial stellar velocities are subvirial even when the simulated gas cloud start unbound. Models of subvirial clusters match radial velocity observations of the Orion star-forming region (Proszkow et al. 2009). In this case, stars would tend to get dynamically heated with cluster relaxation. Since older stars would have more time to experience dynamical effects, they would preferentially be located at larger radii than younger, dynamically cooler stars.

Scenario F. Several phenomena can cause young cluster expansion. Most important is the loss of the gravitational potential of the molecular material that dominates the early phases (e.g., Lada et al. 1984; Moeckel et al. 2012). Stellar dynamics can cause expansion through three-body interactions with hard binaries and gravothermal core collapse associated with mass segregation (Giersz & Heggie 1996; Pfalzner & Kaczmarek 2013). MSFRs often have multiple subclusters of young stars related to the clumpy structure of the natal molecular cloud (e.g., Elmegreen 2000; Kuhn et al. 2014). Thus, the first-born subclusters may have already expanded while the later-born subclusters are still highly centrally concentrated. The expanded older subclusters may resemble a low surface-density halo of stars, while the younger, centrally concentrated subclusters may form the core of the resulting cluster.

Scenario G. Some simulations of cluster formation show star-forming filaments of gas falling into the gravitational potential minimum at the center of a MSFR, bringing along many of the young stars that formed in the filaments (e.g., Bate et al. 2003; Bate 2009). These filaments of stars and gas are more massive than unembedded stars making up a star cluster at the center of a star-forming region, so they will sink to the center due to dynamical segregation (e.g., Clarke 2010). If stars in these star-forming filaments are younger than the rest of the cluster, this can lead to the observed age stratification.

Scenario H. If subclusters expand as they age, younger subclusters are likely to be smaller and denser (Pfalzner 2009). Simulations of subcluster mergers indicate that the resulting cluster may generate a core–halo structure (Bate 2009), which may include stellar age stratification. If an older low-density subcluster merges with a younger high-density subcluster, the older stars will likely become more widely distributed.