Characterizing the X-Ray Emission of Intermediate-mass Pre-main-sequence Stars

Our study sample is drawn from 410 YSOs and 3657 "diskless" (no excess emission above a stellar photosphere at 4.5 μm) stars positionally matched to X-ray point sources in the CCCP catalog (Broos et al. 2011b; Povich et al. 2011, 2019). The Spitzer Space Telescope Vela–Carina Survey Point Source Archive provided mid-infrared (MIR) photometry from IRAC (at 3.6, 4.8, 5.6, and 8.0 μm; Fazio et al. 2004), as well as near-infrared (NIR) JHK_S photometry from the Two-Micron All-Sky Survey (2MASS) Point Source Catalog (Skrutskie et al. 2006). The Vela–Carina data have 2'' spatial resolution and typical sensitivity of [4.5] ≲ 15.5 mag (less sensitive in regions of bright MIR nebulosity). For YSOs, Povich et al. (2011) additionally provided Spitzer/MIPS 24 μm photometry detections or upper limits. CCCP X-ray point sources were observed with the Chandra/ACIS-I detector (Garmire et al. 2003), with positional, photometric, temporal, and spectral information obtained using ACIS Extract (Broos et al. 2010). We restrict our sample to the brightest CCCP X-ray sources, those with $\geqslant 50$ net counts (in the full ACIS 0.5–8 keV energy band) and $\geqslant 5\sigma$ significance, to ensure reliable spectral analysis. There were 1049 sources from the CCCP sample that fit our X-ray selection criteria.

Not all of the sources in our initial sample were genuine low- or intermediate-mass young stars in the Carina Nebula. Our selection criteria may include massive, OB members of the Carina Nebula and contaminating foreground stars.

To identify residual foreground stars that were not previously flagged as contaminants by Broos et al. (2011a), P19 used parallax information from Gaia DR2 (Gaia Collaboration et al. 2018) for all available sources to distinguish between members and nonmembers of Carina. There were 19 sources in our initial X-ray-bright sample with parallaxes that were consistent with being foreground sources; we excluded these.

We also cross-referenced catalogs of spectroscopically confirmed OB stars (Gagné et al. 2011; Alexander et al. 2016; Damiani et al. 2017) and removed 78 known massive stars from our sample.

Following Povich et al. (2011, 2019), we divide the MIR counterparts of X-ray sources into two broad categories: YSOs with excess 4.5 μm emission consistent with circumstellar disks (usually coupled with excess 5.8 and 8.0 μm emission), and stars with no excess emission at 4.5 μm and hence no warm dust disks. These "diskless" stars may have (1) 5.8 and/or 8.0 μm detections consistent with a Rayleigh–Jeans spectrum, (2) no photometric detection at wavelengths longer than 4.5 μm, or (3) marginal IR-excess emission at 5.8 μm or 8.0 μm. In cases (2) or (3) the stars could still possess disks with large inner holes, and in all three cases the stars could still possess debris disks that would produce excess emission at >10 μm wavelengths. These classifications were determined by fitting model spectral energy distributions (SEDs) to the 1–8 μm broadband photometry of all sources.

Diskless SEDs were fit with a set of 100,000 "naked" stellar photosphere PMS models (P19) using the Robitaille et al. (2007) SED-fitting tool. These models sample a range in stellar mass and age (M_⋆ and t_⋆), then convert these properties to the corresponding photospheric temperature and radius (T_eff and R_eff) using PMS evolutionary tracks (Bernasconi & Maeder 1996; Siess et al. 2000). For SEDs showing IR excess (the minority of our sample), we use the Robitaille et al. (2006) YSO model fit parameters published by Povich et al. (2011). For both YSOs and diskless SED models, we assumed the Indebetouw et al. (2005) extinction curve, which introduced a new free parameter, A_V , allowed to vary from 0 to 15 mag (P19). Sources for which no SED models provided satisfactory fits according to the χ² criteria of Povich et al. (2011) or P19 were excluded from our sample.

Using the methodology developed by P19, the likelihood of each model fit to a given SED is weighted individually using two distinct, mass- and age-dependent weighting functions, one based on the disk destruction timescale (see Povich et al. 2016 and references therein) and the other on the X-ray emission decay timescale for PMS stars from (Gregory et al. 2016, hereafter G16). The result is a set of probability distributions for the model stellar parameters M_⋆, t_⋆, T_eff, and L_bol.

We classify each source into one of four temperature–mass (TM) classifications: IMPS, TTS, AB stars (A- and late-B-type stars on or near the ZAMS in the same mass range as IMPS, including Herbig Ae/Be stars), or massive OB stars. We combine the weighted T_eff and M_⋆ probability distributions for each source into a two-dimensional weighted TM probability distribution (_Pi ) to determine the relative probability of each source being any particular TM class. Preliminary TM class Distributions are summed to a single value that we define as Preliminary TM class probabilities (P_TM) to compare the relative likelihood of all Preliminary TM classes to one another. We define the P_TM pairings using

$$\begin{eqnarray}{P}_{\mathrm{TM}}=\left\{\begin{array}{cl}{P}_{\mathrm{IMPS}}; & \sum {P}_{i}({T}_{\mathrm{eff}}\leqslant 7300\,{\rm{K}},\,2\,{M}_{\odot }\leqslant {M}_{\star }\lt 8\,{M}_{\odot })\\ {P}_{\mathrm{TTS}}; & \sum {P}_{i}({T}_{\mathrm{eff}}\leqslant 7300\,{\rm{K}},\,{M}_{\star }\lt 2\,{M}_{\odot })\\ {P}_{\mathrm{AB}}; & \sum {P}_{i}({T}_{\mathrm{eff}}\gt 7300\,{\rm{K}},\,2\,{M}_{\odot }\leqslant {M}_{\star }\lt 8\,{M}_{\odot })\\ {P}_{\mathrm{OB}}; & \sum {P}_{i}({M}_{\star }\geqslant 8\,{M}_{\odot }).\end{array}\right.\end{eqnarray} \tag{ 1 }$$

To make the final classifications, we compare the two most probable preliminary TM class probabilities to one another according to

$$\begin{eqnarray}\begin{array}{r}{\rm{TM}}\,{\rm{Class}}=\left\{\begin{array}{cl}{\rm{TM}}1; & {P}_{{\rm{TM}}1}\gt 2{P}_{{\rm{TM}}2}\\ U; & {\rm{otherwise}},\end{array}\right.\end{array}\end{eqnarray} \tag{ 2 }$$

where P_TM1 (and P_TM2) are the preliminary TM class probabilities defined in Equation (1) for the first- (TM1) and second-most (TM2) probable TM classes for an individual SED. "U" designations are given to sources that remain unclassified based on this criterion. Sources that were classified as OB stars, 30 in total, were removed from our sample.

To visualize these TM classes we constructed probabilistic Hertzsprung–Russell diagrams (pHRDs; see P19) by summing the probability distributions for all sources in a given TM class. The pHRDs for three TM classes plus unclassified are plotted as two-dimensional histograms in the four panels of Figure 1 (the OB class is excluded and would extend above the maximum L_bol plotted here). These pHRDs demonstrate that even the TTS sources in our sample are typically more massive than the Sun, which reflects both the relatively shallow IR photometry and our selection of the brightest CCCP X-ray sources. U sources consist primarily of stars whose SED model fits straddled the ∼2 M_⊙ mass cutoff separating IMPS from TTS; based on the IMF the majority of U sources are likely TTS.

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The numerical breakdown of sources assigned to each TM class in the cleaned initial sample is given in Table 1, which also summarizes our source counts in the two subsequent sample refinement steps.

Table 1. Sample Refinement

	Teff a	M⋆	Initial	Reclass	Final
TM Class	(K)	(M⊙)	Section 2.1–2.3	Section 2.4	Section 2.5
IMPS	$\leqslant 7300$	2–8	57	59	54
R-IMPS	$\geqslant 5600$ b	2–8	⋯	24	23
TTS	$\leqslant 7300$	$\leqslant 2$	194	196	176
AB	$\gt 7300$	2–8	52	39	35
U	⋯	⋯	102	84	82
All	⋯	⋯	405	402	370

Notes.

^a T_eff = 7300 K is the canonical value for an F0 V star. ^b R-IMPS classifications require spectroscopic T_eff,S .

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Damiani et al. (2017, hereafter D17) analyzed optical spectra of sources in the Trumpler (Tr) 14 and 16 clusters in Carina obtained as part of the Gaia–ESO survey with the FLAMES/Giraffe multifiber spectrometer at the ESO VLT/UT2 telescope. They broadly separated their sources into early-type and late-type stars, and for the latter they reported a spectroscopically measured effective temperature T_eff,S for each star. We compared our samples and found no matches to their early-type stars but found 64 matches to their late-type stars (13 AB, 12 IMPS, 25 TTS, and 14 unclassified). Three matched sources that we had classified as AB had T_eff,S  < 4800 K; these were removed from our sample as suspected foreground stars.

We refit the SEDs for the remaining 61 sources, this time constraining the model T_eff parameter using the T_eff,S and (assumed Gaussian) uncertainty values reported by D17 (see P19 for details). We were thus able to classify eight previously unclassified sources as TTS, two as IMPS, and define a new TM class of radiative IMPS (R-IMPS). R-IMPS are a transitional stage between fully convective IMPS and fully radiative AB stars in the 2–4 M_⊙ range. They have begun to traverse the Henyey tracks and have 7300 K > T_eff,S  > 5300 K, corresponding to spectral types F and early G. We hence reclassified 24 sources as R-IMPS, including 10 initially classified as AB sources, 6 as IMPS, and 8 previously unclassified. The numerical breakdown of sources after this step of sample refinement is shown in the "Reclass" column of Table 1. The vast majority (21 out of 24) of R-IMPS exhibited no MIR excess and were fit with diskless PMS models.

The two composite pHRDs plotted in Figure 2 show why the T_eff,S constraints are required to classify R-IMPS. Our age-weighting scheme for SED models seldom preferred T_eff that was close to the actual T_eff,S values for R-IMPS. This is mainly due to the low density of SED models populating this range of T_eff and L_bol in both the naked PMS and Robitaille et al. (2006) model sets. Based on photometry and our age-weighting alone, the most likely models are typically cooler and occasionally hotter (P19). There are almost certainly additional R-IMPS in our sample that lacked spectroscopic measurements, in particular those located in the wider field outside the relatively small, central region surveyed by D17. In the absence of T_eff,S constraints, about 60% of R-IMPS were misclassified as cooler, less luminous IMPS, and the remainder were predominantly misclassified as hotter, more luminous AB stars.

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We fit the 0.5–8 keV X-ray spectra of all sources in our sample with XSPEC v12.91.1 (Arnaud 1996) adopting solar abundances from Grevesse & Sauval (1998). We model each source using either one thermal plasma (apec) component (which we refer to as the 1T model) or two apec components (the 2T model; Smith et al. 2001). The plasma temperature kT in the 1T models is left as a free parameter. In the 2T models, one temperature is fixed at kT₁ = 0.9 keV (corresponding to the expected ∼10 MK base emission for coronal TTS emission observed by P05), while kT₂ is left as a free parameter.

Both the 1T and 2T models include an absorbing column N_H (tbabs; Wilms et al. 2000), which can be left as a free parameter in the fits or frozen to the equivalent absorption corresponding to the extinction (A_V ) value returned by the IR SED fits or NIR colors for the source. For sources fit with the Robitaille et al. (2006) YSO models, this extinction is the sum of the foreground A_V plus the total A_V through the circumstellar dust disk and/or infalling envelope. ⁴ A_V was converted to N_H using the relation N_H /A_V  = 1.6 × 10²¹ cm⁻² mag⁻¹ (Vuong et al. 2003). We hence further divide our X-ray spectral fitting results into "Free" or "Frozen", for which N_H was left as a free parameter or constrained using the A_V from IR SED fitting or NIR colors (when the SED fitting returned unrealistically large or poorly constrained A_V values). Table 2 summarizes the naming scheme that we use for the X-ray spectral models.

The models were fit to the unbinned X-ray spectra using the Cash statistic, C (Cash 1979). Figure 3 gives examples of both the X-ray spectrum, binned for display purposes only, and the individual pHRD of a single source from each TM class (Section 2.3). These visualizations of the X-ray spectral fits and pHRDs for our full CCCP X-ray-bright source catalog are available for download from our Zenodo repository. ⁵

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We visually reviewed all XSPEC model fits to each of our X-ray spectra using the GUI-based tool ae_spectra_viewer provided with ACIS Extract (Broos et al. 2010). In the majority of cases, the fit statistics (e.g., the Cash statistic C per degrees of freedom) between the four models were similar. We therefore chose the best-fit spectral model among the 1T Frozen, 2T Frozen, 1T Free, and 2T Free based upon the residuals and grouped spectral outputs (shown in the right column of Figure 3).

When all models showed a similar fit quality, we preferred the 1T Free model for simplicity. Typical uncertainties seen in kT, when upper and lower limits are found (∼2/3 of our sample), have a range of ±2 keV. The other one-third of the fits returned only lower limits on kT. About half of our sample fits returned doubly bounded uncertainties on N_H , typically ranging over ±0.5 × 10²² cm⁻². The other half of the sample returned only upper limits on N_H . There are some cases (∼10% of our sample) where kT or N_H do not have reported errors; in these cases the parameters were at the edge of the allowed parameter space (i.e., kT  =  10 keV or N_H  = (0.09–33) × 10²² cm⁻²). There are no sources that are missing both N_H and kT errors. There were a small number of cases (eight total) where the Free models did not fit the spectra well, and we froze N_H to the absorbing column converted from the weighted mean A_V of the IR source, which achieved good fits and reported kT uncertainties.

We removed 32 sources that could not be adequately fit with any of the models included in Table 2. ⁶ The majority of these had high X-ray background levels (≳30% of source counts), causing poor modeling of both the source and the background. The distribution of TM classes among our final sample is given in the "Final" column of Table 1.

The sky positions of all 370 sources in our final sample are overlaid on a Spitzer 3.6 μm mosaic of the Carina Nebula in Figure 4. The colored symbols denote stars in their respective TM classes, while the white contours correspond to the source density of X-ray young stellar members (Broos et al. 2011b; Feigelson et al. 2011). Every TM class is represented in all parts of the region. IMPS and TTS show more clustering compared to AB and U sources. IMPS are densely clustered in Tr 14, which contains roughly one-third of all IMPS in our sample and has the highest X-ray point-source density of the CCCP catalog (Feigelson et al. 2011). Because R-IMPS require spectroscopic confirmation for classification, all are found within the Gaia–ESO survey area (black thick box; D17). The majority of the R-IMPS (14/23) cluster around Tr 16 (Wolk et al. (2011)), which contains the famous massive binary system η Carinae (Hamaguchi et al. 2014). X-ray-bright TTS generally follow the spatial distribution of all X-ray-detected members (contours), especially in the vicinity of Tr 16 and Tr 14.

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In Table 3 we tally for each TM class the best-fit XSPEC model type (1T or 2T), the origin of the N _H parameter (free in the fit or frozen by A_V ), and the occurrence of variability in the X-ray light curve. We use the same variability criterion described in detail by Broos et al. (2010), by which the light curves of each source during a single observation are tested for uniform flux over time using a one-sided Kolmogorov–Smirnov (KS) test. P-values (Prob_KS) for the null hypothesis of uniform flux are flagged as "no variability" (0) for Prob_KS > 5 × 10⁻², "possible variability" (1) for 5 × 10⁻² < Prob_KS < 5 × 10⁻³, and "definite variability" (2) for Prob_KS < 5 × 10⁻³. Although a multiobservation KS probability is computed by ACIS Extract it is not used for determining variability in this work. The single-observation exposure times vary across the large CCCP mosaic but are generally <60 ks, a timescale well matched to the duration of individual coronal flares (Favata et al. 2005).

We found that for ∼82% (306/370 sources) of our sample, the N_H predicted from the best-fit Free models (including cases where the Frozen model was preferred) fell within the range of A_V returned by the IR SED fitting or estimated from NIR photometry. This high frequency of agreement between the absorption inferred via our independent X-ray and IR modeling analysis increases our confidence in the physical parameters output by both models. The degeneracy between absorbing column and temperature (plasma or photospheric) is the greatest challenge to our modeling in both cases.

The overwhelming majority of sources in our sample (99%; Table 3) required only a single plasma component (1T model) to achieve acceptable XSPEC fits. Even among our sample of bright CCCP X-ray sources, the majority were detected with <100 net counts. But in cases where L_X is relatively high and N_H is nonnegligible, a single (harder) component can dominate the observed spectrum; the high N_H makes it difficult to observe the soft emission because it is more readily absorbed. This leads to a lack of information about the contribution from lower coronal temperatures.

Using the best-fit model N_H to correct observed fluxes for absorption, we computed the hard-band (L_h,c ; 2–8 keV) and total-band (L_t,c ; 0.5–8 keV) X-ray luminosities assuming the Gaia DR2 parallax distance to Carina of 2.5 kpc (P19). We prefer hard-band luminosities over soft-band (0.5–2 keV) luminosities for this analysis because the hard photons are less sensitive to absorption correction. A recent distance determination based on Gaia EDR3 to a subset of massive stars in Carina reports 2.3 kpc (Shull et al. 2021). The discrepancy with our adopted distance, which is based on a much larger sample of X-ray-detected stars, implies there may be a 15% systematic uncertainty in our reported luminosities.

The best-fit X-ray and IR properties for our sample will be available as an electronic table. The columns of the electronic table are described in Table 4.

Table 4. X-Ray and IR Source Properties

Column Label	Units	Description
X-ID	⋯	IAU source; prefix is CXOGNC J(Chandra X-ray) Observatory Great Nebula in Carina
MIR-ID	⋯	Spitzer MIR Vela-Carina source name
RA	deg	R.A. (ICRS)
Dec	deg	Decl. (ICRS)
TMClass	⋯	Temperature−mass classification (Section 2.3)
YSO	⋯	(y)es or (n)o; source a YSO (See Section 2.1)
Frozen	⋯	(y)es or (n)o; NH frozen to mean IR AV (See Section 2.5)
CStat_DOF	⋯	C-statistic/degrees of freedom for X-ray spectral fit
NetCounts	count	Full-band (0.5–8 keV) net counts
Variable	⋯	(0) nonvariable, (1) possible, or (2) definite; (See Section 3.1)
SrcArea	(0492)2	Average aperture area
Theta	arcmin	Chandra off-axis angle
Mass	M⊙	Mass from SED
Mass_err	M⊙	Weighted 1σ uncertainty of log mass (Section 2.3, P19)
NHX	1022 cm−2	Hydrogen-absorbing column from XSPEC
NHX_err_lo	1022 cm−2	90% confidence interval lower bound on NH_X
NHX_err_hi	1022 cm−2	90% confidence interval upper bound on NH_X
AvSED	⋯	(y)es or (n)o; See Section 3.1
Av_mean	mag	Mean on Av; when AvSED = y, Av from SED fit displayed. Else, Av from NIR estimate is displayed
Av_min	mag	Lower bound of weighted 1σ uncertainty on Av (Section 2.3, P19)
Av_max	mag	Upper bound of weighted 1σ uncertainty on Av (Section 2.3, P19)
2T	⋯	(y)es or (n)o; Source fit with 2T plasma component
kT	keV	1T or 2T plasma temperature; when "2TModel" = y, kT2 is displayed (See Section 2.5)
kT_err_lo	keV	90% confidence interval lower bound on kT
kT_err_hi	keV	90% confidence interval upper bound on kT
Fx_hc	erg s−1 cm−2	Hard-band (2–8 keV) absorption-corrected flux
Fx_tc	erg s−1 cm−2	Total-band (0.5–8 keV) absorption-corrected flux
logLx_hc	(erg s−1)	Hard-band (2–8 keV) absorption-corrected luminosity
logLx_tc	(erg s−1)	Total-band (0.5–8 keV) absorption-corrected luminosity
logLbol	(L⊙)	Bolometric luminosity from IR SED
logLbol_err	(L⊙)	Weighted 1σ uncertainty on logLbol (Section 2.3, P19)

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We compared the distributions of N_H and kT for each TM class against one another using two-sided KS tests. We define a "significant difference" as KS probability ≲10⁻⁴, marginal as 0.01−10⁻⁴, and no difference as >0.01. These KS tests reveal no statistically significant differences in N_H distributions among the TM classes. In terms of average absorption within each TM class, the AB sources have the lowest, at (4 ± 2) × 10²¹ cm⁻², while TTS have the highest absorbing column, and largest spread, with values <40 × 10²¹ cm⁻².

Similarly we find no statistically significant differences in plasma temperatures between the TM classes. We performed the same KS tests on the kT1 of the sources that were fit with 1T models (both Free and Frozen). The average kT1 for each TM class fell within the narrow range of 2.6–3.2 keV, corresponding to coronal plasma temperatures of 30–37 MK. Because there were very few sources that preferred the 2T models (2/370; Table 3), statistical comparisons of the kT2 parameter were not performed.

The cumulative X-ray luminosity functions (XLFs) for all TM classes are shown in Figure 5. IMPS are systematically more luminous than the TTS, AB, and U classes, with a mean offset of ∼0.3 dex in both L_t,c and L_h,c . The most luminous R-IMPS (Section 2.4) have comparable L_h,c (Figure 5, right panel) to the most luminous AB sources, while the least luminous R-IMPS are comparable to the least luminous IMPS. The resultant shape of the (partially convective) R-IMPS XLF looks like a transition between that of the (fully convective) IMPS and the (radiative) AB classes. Most of the same qualitative trends among the TM classes appear in the L_t,c XLFs (Figure 5, left panel), but the curves appear noisier because the absorption correction more strongly affects the soft (<2 keV) portion of the spectrum.

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Tables 5 and 6 show the two-sided KS tests comparing L_h,c and L_t,c distributions for each class respectively. For the hard-band luminosities (Table 5) we find a statistically significant difference between IMPS and TTS. We also find marginally significant differences comparing IMPS with AB or U. The KS tests reveal no statistically significant differences among the non-IMPS TM classes. KS tests applied to the total band luminosities (Table 6) give similar results, except for the inclusion of a statistically significant difference comparing IMPS with AB stars.

The XLFs have not been corrected for survey completeness. However, in the hard-band XLF (right panel of Figure 5) the faint-end turnover for the AB/TTs/U curves occurs ∼0.5 dex fainter compared to IMPS. The faint-end cutoff for the AB/TTs/U is likely due to incompleteness, but the IMPS cutoff seems to be real as it occurs at a luminosity ∼0.5 dex higher than the likely completeness cutoff at log L_h,c  ∼ 30.4. This seems to indicate a lower bound of log L_h,c  ≈ 30.5 erg s⁻¹ for the X-ray luminosity of convective IMPS.

We have found that the X-ray spectra from our X-ray-bright sample of low- and intermediate-mass stars in the CCCP survey can generally be fit using thermal plasma models returning similar plasma temperatures, implying a similar underlying physical emission mechanism. The median hard- and total-band absorption-corrected X-ray luminosities for IMPS are ∼0.3 dex more luminous compared to TTS and AB stars, and the XLF turnover for IMPS occurs at higher luminosity (Figure 5). Because the IMPS sample is dominated by fully convective stars, this strongly suggests a coronal origin for IMPS X-ray emission. As a class, the IMPS sample is also more luminous than our TTS sample (which is itself relatively X-ray bright); thus, IMPS X-ray emission must be intrinsic, not attributable to unresolved, lower-mass companions.

R-IMPS are the second-most luminous TM class, and the XLF turnover coincides with that of IMPS in both the hard- and total-band XLFs (Figure 5). This reflects the decay in X-ray luminosity from the initially high values exhibited by IMPS, as the convective dynamo gives way to the development of an interior radiative zone (Mayne et al. 2007; Mayne 2010; Gregory et al. 2016). Once R-IMPS reach the ZAMS as fully radiative AB stars, we expect intrinsic X-ray emission to cease, hence the AB stars in our X-ray-bright sample are likely included owing to the presence of relatively bright, unresolved convective companions (themselves IMPS or, more frequently, TTS).

In Figure 6 we plot on an H-R diagram the subset of 65 sources from our X-ray-bright sample with photospheric temperatures T_eff,S measured spectroscopically as part of the Gaia–ESO survey. This subset includes 23 R-IMPS, 14 IMPS, 24 TTS, and 4 sources that remained unclassified due to poorly constrained SED model parameters. No AB stars are included because D17 did not report T_eff,S values for hot stars. For this plot we refit the SEDs of the nine IR-excess sources (boxed) using the updated sets of YSO models provided by Robitaille (2017). We then computed T_eff and L_bol using the mean parameter values for all SED models with T_eff falling within 3σ of T_eff,S reported by D17. In 12 instances (all nonexcess sources) no SED models fell within this range, most likely due to the limitations of the Castelli & Kurucz (2003) stellar atmosphere models, which do not accurately reproduce the H^– opacity minimum at 1.65 μm for PMS stars with T_eff = 4000–5000 K. In these cases we plotted T_eff,S and the mean L_bol from the 10 SED models with the nearest T_eff parameter values.

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As Figure 6 illustrates, R-IMPS (red triangles) are traversing the radiative Henyey tracks and have generally higher L_bol compared to fully convective IMPS (green asterisks). Most R-IMPS and IMPS have stellar masses of 2–4 M_⊙, but nearly all of the IMPS in this mass range lie above the 1 Myr isochrone, while nearly all the R-IMPS fall between the 1 and 3 Myr isochrones. The lower-mass TTS span the same range in isochronal ages as the R-IMPS and IMPS combined, in good agreement with the $\leqslant 3\,\mathrm{Myr}$ duration of star formation in the central regions of the Carina Nebula reported by P19. The YSOs (boxed) lie close to the intermediate-mass stellar birth line (defined by the upper-right boundary of the Haemmerlé et al. 2019 evolutionary tracks), including three with masses exceeding 4 M_⊙.

Up to this point we have focused primarily on comparing the distributions of various X-ray emission properties among our different stellar TM classes, and we have demonstrated that X-ray luminosity is by far the most distinguishing characteristic of R-IMPS compared to lower-mass TTS. To investigate trends in X-ray luminosity with the parameters of individual stars, we are limited by the source selection requirements for reliable X-ray spectral fitting. The luminosity range over which our X-ray-bright sample appears mostly complete spans ∼1.5 dex (Figure 5), which is comparable to the typical scatter observed in stellar L_X /L_bol relations (Preibisch et al. 2005; Gagné et al. 2011).

To probe more extended trends in total band X-ray luminosity (L_X ; 0.5-8 keV) and stellar mass, we add another sample of X-ray-emitting PMS stars to our analysis. The MYStIX (Massive Young Star-forming Complex Study in Infrared and X-ray) sample is a multiwavelength survey similar to CCCP that combines Chandra X-ray data and NIR/MIR data from 2MASS, UKIRT, and Spitzer/IRAC (Feigelson et al. 2013). We only used sources from the CCCP–MYStIX sample that had published X-ray luminosities and for which we could classify their IR counterparts with confidence. We made no cut to the X-ray detection significance or X-ray net counts for these sources.

In the MYStIX catalog (Broos et al. 2013), reported L_X values were computed using the XPHOT method for faint X-ray sources (Getman et al. 2010), which assumes a (luminosity-dependent) template TTS spectral shape to estimate the absorption affecting the observed spectrum. Because XPHOT was developed empirically using low-mass TTS samples, there is a danger that undiagnosed trends in X-ray spectral shape with stellar mass could bias this method toward systematically different L_X values when applied to IMPS. To check for such systematics, in Figure 7 we plot L_X derived from XPHOT (rescaled to the revised Carina distance) versus our spectral fitting (XSPEC) for the sources in common among our sample and MYStIX. We find generally good agreement, with L_X within 0.1 dex, between the two methods across our sample, with the large majority of sources falling within ∼0.1 dex of the 1:1 line between the two methods. There are no evident trends among the various TM classes. We therefore can reliably compare the L_X from either method and incorporate the larger, MYStIX sample to probe trends in L_X .

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G16 adopted previously published X-ray luminosities derived from XPHOT, and the generally good agreement we have found between XPHOT and our more careful XSPEC analysis (Figure 7) reinforces their conclusions about the decay of X-ray luminosity with time.

In Figure 8 we plot L_X against stellar mass derived from IR SED fitting. We broadly split the figure into two regions: sources powered by intrinsic coronal X-ray (CX) emission consistent with a convective interior versus sources whose IR bright primary star has a mostly or fully radiative envelope (R), meaning the X-ray emission most likely originates from a lower-mass, convective TTS (or IMPS) companion (CX companion) that is unseen in the IR. Some magnetic "peculiar" (Ap) stars have been detected in X-rays (Stelzer et al. 2003) but these would be far too faint to be detected at the Carina distance, given CCCP sensitivity limits. These dividing lines are based on the P05 L_X versus M_⋆ linear regression fit extrapolated for 2 M_⊙ to 4 M_⊙ stars. We find that the majority of IMPS and even R-IMPS fall above this extrapolation line, while the vast majority of AB X-ray sources fall below it.

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This separation in L_X between IMPS, R-IMPS, and AB stars of 2–4 M_⊙ illustrates the evolution of X-ray emission as a probe of IMPS interior structure: IMPS begin (fully) convective and X-ray luminous, then develop a radiative zone and become R-IMPS, at which point the X-ray luminosity declines. Finally, a fully radiative envelope completes the transition to an AB star, spelling the end of magnetocoronal X-ray emission. At this point an X-ray-quiet AB star would drop out of our sample, unless it has a lower-mass X-ray-bright companion. This means that the AB sources have X-ray emission characteristic of TTS, not IMPS, dropping them below the extrapolated P05 L_X –mass relation. The MYStIX sample allows us to include many more of these AB sources with lower L_X in Figure 8 (smaller symbols) than appear in our X-ray-bright sample.

In Figure 9 we plot L_X against L_bol derived from IR SED fitting. Both IMPS and R-IMPS generally follow the TTS log(L_X /L_bol) relation, with the large majority falling in the range of −4 < log(L_X /L_bol) < −3. The AB sources do not follow this relation because L_X and L_bol are decoupled in the case of unresolved binary systems where the IR and X-ray emission are dominated by different stellar components, as discussed above. No sources in Figure 9 fall below the log(L_X /L_bol) = −7 line, indicating that few to none of the AB stars exhibit intrinsic X-ray emission from shocked stellar winds (Carina OB stars have log(L_X /L_bol) = −7.26 ± 0.21; Nazé et al. 2011).

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In this section we discuss nine individual stars and YSOs drawn from the 77 IMPS and R-IMPS candidates in our sample. All of these featured objects have T_eff,S measured by D17, increasing the precision of their locations on the H-R diagram (Figure 6). Table 7 summarizes the best-fit X-ray parameters for all sources in our sample, with the nine sources discussed in this section highlighted.

Table 7. Best-fit X-Ray Parameters of Noteworthy IMPS

XName	TMClass	YSO	FrozenModel	NetCounts	Variable	NHX	kT1	log Lx _tc	log Lbol
				(Counts)		(1022 cm−2)	(keV)	(erg s−1)	(L⊙)
104454.82–594351.6	IMPS	n	n	300	2	${0.41}_{-0.24}^{+0.61}$	5.4 a	31.7	1.7
104352.31–593922.2	IMPS	y	n	139	0	${0.81}_{-0.42}^{+1.42}$	${2.7}_{-1.7}^{+5.0}$	31.4	2.0
104355.13–593330.3	IMPS	n	n	140	2	0.65 a	${1.5}_{-1.3}^{+2.1}$	31.4	1.3
104423.67–594114.6	IMPS	n	n	144	0	0.14 a	${1.9}_{-1.4}^{+2.7}$	30.9	1.0
104513.55–594404.3	RIMPS	n	n	74	0	0.17 a	3.6 a	30.8	1.2
104401.10–593535.1	RIMPS	y	n	60	0	${1.21}_{-0.51}^{+1.91}$	${0.9}_{-0.5}^{+1.4}$	31.1	2.3
104538.35–594207.5	RIMPS	y	n	105	1	${1.14}_{-0.53}^{+2.03}$	4.9 a	31.2	2.2
104432.58–593303.5	RIMPS	n	n	63	0	${0.44}_{-0.11}^{+0.91}$	${2.0}_{-1.4}^{+4.2}$	31.1	1.8
104446.53–593413.3	RIMPS	n	n	135	0	0.29 a	${2.7}_{-2.0}^{+5.4}$	31.5	2.1

Note.

^a Upper limit on N_H or lower limit on kT parameter.

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4.3.1. The Brightest X-Ray Flare from a Spectroscopically Classified, Diskless IMPS

Among the IMPS for which we have spectroscopic classifications, CXOGNC J104454.82–594351.6 is the most X-ray luminous, with log(L_X ) = 31.74 erg s⁻¹. Nearly 60% of this luminosity is emitted in the hard band (>2 keV). Without spectroscopy, this IMPS would remain unclassified by our TM scheme, because the naked PMS model fits to its SED were unconstrained (top panel of Figure 10). The H⁻ opacity bump likely caused the SED fits to miss the correct T_eff,S  = 4768 K (D17), which gives a mass of ∼2 M_⊙. This star therefore barely exceeds our mass threshold for IMPS classification, and its high X-ray luminosity appears to be due to variability produced by one or more large flares. The middle panel of Figure 10 shows the X-ray light curve of CXOGNC J104454.82–594351.6, which is dominated by a fast-rise and exponential-decay flare (Getman et al. 2008; Getman & Feigelson 2021). The blue curve is the adaptively smoothed uncertainty envelope of the observations (Broos et al. 2010), which is smoothed to produce bins with signal-to-noise ratio = 6.0 and whose thickness represents the error bars in the photon flux.

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4.3.2. Two IMPS near the Maximum Mass for Fully Convective, Nonaccreting Stars

CXOGNC J104352.31–593922.2 appears to be the least-evolved YSO among the 65 stars in our spectroscopic subsample. It has a high log(L_X ) = 31.35 erg s⁻¹ with no evident variability. We incorporated available BVI photometry from D17 into the IR SED and refit with both disk-only and disk+infalling envelope YSO models from Robitaille (2017). Example plots illustrating the multiple acceptable model fits to the photometry data are shown in Figure 11, and it is clear that the disk+envelope models provide qualitatively better fits to the MIR SED.

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The best SED models for this YSO that agree with the correct T_eff,S  = 5126 K (D17) indicate a stellar mass of 3–4 M_⊙ and a position very near the Haemmerlé et al. (2019) birth line. This interpretation is consistent with the presence of a circumstellar disk and envelope, indicating the possibility of recent or ongoing mass accretion. Even in a flare, such high X-ray luminosity is unlikely to be produced by an unresolved, lower-mass T Tauri companion, making CXOGNC J104352.31–593922.2 one of the youngest and most massive YSOs powering coronal X-ray emission that we would expect to discover, given its location at or above the maximum mass for the fully convective birth line (Haemmerlé et al. 2019). ⁷

A second IMPS (CXOGNC J104355.13–593330.3) also has a high X-ray luminosity (log L_X  = 31.41 erg s⁻¹) and a remarkably high mass. It is possibly variable (Section 3), with a light curve showing what could be post-flare exponential decay over the 60 ks observation (Figure 12). It presents a cooler X-ray spectrum than most stars in our sample, with 67% of emission at softer energies (<2 keV). Its MIR counterpart shows no excess emission out to 4.5 μm. SED modeling with stellar atmospheres indicates a mass >3 M_⊙, making CXOGNC J104355.13–593330.3 an example of the most massive, fully convective, nonaccreting IMPS theoretically allowed by Haemmerlé et al. (2019). The SED fit parameters found excellent agreement with T_eff,S  = 4994 K (D17), and the X-ray spectrum was best fit with the 1T Free models.

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This extreme star is located close to the heart of Tr 14, the densest cluster in Carina (Figure 4) with many surrounding stars within 3''. It is possible that its high IR luminosity, and hence mass, could result from the blending of two (or more) sources. This could more strongly affect the IR SED fits than the X-ray spectral fits because Chandra has a higher (on-axis) spatial resolution compared to Spitzer/IRAC or 2MASS.

4.3.3. Two Diskless IMPS at the Convective–Radiative Transition

CXOGNC J104423.67–594114.6 and J104513.55–594404.3 are both diskless IMPS with log(L_X ) ≲ 31 erg s⁻¹, on the faint end of the R-IMPS in our sample. While their SED fit parameters were too poorly constrained for TM classification without spectroscopy, they fell on either side of our (admittedly blurry) temperature dividing line between IMPS and R-IMPS, with T_eff,S  = 5218 and 5515 K (D17), respectively (Figure 13). It is possible that the X-ray emission from each of these two IMPS has begun to decay due to the development of an interior radiative zone.

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4.3.4. The Four Hottest R-IMPS