Calibrating X-Ray Binary Luminosity Functions via Optical Reconnaissance. I. The Case of M83

In the absence of a bright active galactic nucleus (AGN), X-ray binaries (XRBs) dominate the point-source X-ray emission of a galaxy, with only minor contributions from coronally active binaries, cataclysmic variables, unresolved sources, and supernova remnants (Fabbiano 2006; Boroson et al. 2011, and references therein). Owing to their different formation and evolutionary timescales, XRBs with low- and high-mass donors (hereafter referred to as LMXBs and HMXBs, where the former refers to donor masses below ≲3M_⊙, whereas latter refers to donors in excess of ≳8M_⊙) can be expected to trace the integrated stellar content and recent star formation output of their host galaxy, respectively. Indeed, seminal work by Grimm et al. (2003), based on ASCA and early Chandra X-ray Observatory data for the Milky Way (MW) and the Magellanic Clouds (see also Ranalli et al. 2003) first established a quantitative scaling between the integrated X-ray luminosity of HMXBs with the host galaxy star formation rate (SFR). In a follow-up study, Gilfanov et al. (2004) crystallized the notion of a “universal” HMXB X-ray luminosity function (XLF) for star-forming galaxies, the normalization of which is proportional to the host galaxy SFR. Along the same lines, using Chandra data for 11 nearby galaxies, Gilfanov (2004) demonstrated that the total number of LMXBs and their integrated X-ray luminosity are proportional to the stellar mass (M_⋆) budget of the host galaxy, thereby establishing a “universal” XLF for LMXBs (see also Kim & Fabbiano 2004).

Since these pioneering works, quantitative investigations of the scaling relations between the HMXB and LMXB XLFs and host galaxy properties have progressively sharpened, largely thanks to several megaseconds of subarcsecond resolution X-ray imaging data accumulated by Chandra for tens of nearby galaxies. Updated XRB XLFs and their scaling relations are routinely employed for a variety of purposes. For example, the total X-ray luminosity is taken as a reliable SFR proxy in distant, star-forming galaxies (Mineo et al. 2014), and the expected total X-ray luminosity in XRBs (Lehmer et al. 2010) can be used to argue in favor or against a low-luminosity AGN on a statistical basis. Nevertheless, perhaps not surprisingly, a larger degree of complexity has also emerged from this wealth of data.

There is reason to question the supposed universality of the XRB XLFs and their scaling relations. From a theoretical standpoint, large variations in the LMXB XLFs are to be expected with stellar age, whereas metallicity effects are expected to drive variations in the HMXB XLF (Fragos et al. 2013). The notion that both may have sizable effects on the XRB XLFs is consistent with the claimed redshift evolution of L_X/M_⋆ and L_X/SFR, whereby the cosmic decline in mean stellar age and metallicity would be responsible for the inferred increase of both ratios with z (Lehmer et al. 2016; Aird et al. 2017, and references therein). However, a quantitative assessment of the role of age and metallicity in shaping the XRB XLF’s functional form is inevitably challenging, as deep, high-statistics XLFs have only been assembled for nearby galaxies spanning a relatively limited range in both (see, e.g., Irwin et al. 2004; Colbert et al. 2004; Kaaret et al. 2011; Prestwich et al. 2013; Plotkin et al. 2014; Basu-Zych et al. 2016; Tzanavaris et al. 2016; Wang et al. 2016).

There may also be issues with the overall approach to characterizing XRB XLFs. In an effort to isolate the LMXB population, even the most comprehensive studies select massive elliptical galaxy samples, with large numbers of sources and negligible SFR levels, so as to ensure virtually zero HMXB contamination. Conversely, HMXB XLF studies focus on high specific SFR (sSFR, defined as the ratio SFR/M_⋆) galaxies so as to minimize the contribution from LMXBs. Although practical, these selection strategies may affect the robustness of the inferred XLFs, or, at a minimum, pose a challenge to their claimed universality. For one, late-type galaxies with moderate sSFRs are excluded targets, as they are guaranteed to have a mixed LMXB/HMXB population. This, however, also means that we have no reliable knowledge of the LMXB XLF in star-forming galaxies (to this end, it is perhaps indicative that, when Mineo et al. 2012 attempted to correct their inferred HMXB XLF for possible LMXB contamination using the XLF derived from elliptical galaxies, they obtained negative counts). Since the LMXB contribution theoretically depends on mean stellar age, it is reasonable to expect that early- and late-type galaxies may exhibit different correlations with stellar mass, as well as different spatial distributions.

Lastly, there are indications that globular cluster (GC) specific frequency may also affect the shape and normalization of the LMXB XLF (Sivakoff et al. 2004; Humphrey & Buote 2008; Kim et al. 2009; Zhang et al. 2011; Peacock & Zepf 2016); this is not surprising, since field versus GC LMXBs likely have different origins and evolutionary paths. If so, then the higher specific frequency of GCs in massive ellipticals could yield higher XLF normalizations than for LMXBs in late-type galaxies. Additionally, metallicity can affect the XLF of GC XRBs, as red GCs may be more often associated with bright LMXBs (Jordán et al. 2004; Kim et al. 2006; Sivakoff et al. 2007; Kim et al. 2013; Peacock et al. 2017; Luan et al. 2018).

In a recent endeavor to properly characterize the XLFs of both HMXBs and LMXBs in late-type galaxies, Lehmer et al. (2019, hereafter L19) fit the XLFs of 38 nearby galaxies spanning a broad range of SFR and M_⋆ with a global model that fits simultaneously for the contributions from HMXBs, LMXBs, and background sources using sub-galactic SFR and stellar-mass maps (see also Lehmer et al. 2017, and references therein, for other examples of sub-galactic modeling studies). This novel and powerful approach reveals a smooth, progressive decline in the XLF normalization per unit SFR, accompanied by a decrease in normalization at the bright end with increasing sSFR, i.e., as the dominant contribution to the XRB population shifts from LMXBs to HMXBs. The study also unveils further interesting subtleties, such as an intriguing flattening of the HMXB XLF between 10³⁸ − 10⁴⁰ erg s⁻¹ and a possible disagreement in the LMXB XLF slopes below 10³⁸ and above 10³⁹ erg s⁻¹ compared to the results obtained for elliptical galaxies only (Zhang et al. 2012). This further emphasizes the need to move beyond a one-size-fits-all XLF modeling concept.

Motivated by the same kinds of considerations, this paper follows a very different approach to disentangling the LMXB and HMXB XLFs: by leveraging Hubble Space Telescope (HST) multiband imaging data, we directly classify the optical counterparts to Chandra-detected pointlike X-ray sources in the field of view of the target galaxy. This technique, which was developed for and tested on the nearby spiral galaxy M101 by Chandar et al. (2020, hereafter C20), hinges on the notion that, on average, HST imaging enables the direct detection of XRB donor stars down to a given distance-dependent mass limit (e.g., down to ∼3 M_⊙ at the distance of M101). By construction, this procedure does not rely on underlying assumptions about the relationship between a galaxy’s XRB populations and their local environments; it also enables us, for the first time, to elucidate the role of intermediate-mass XRBs, i.e., XRBs with donors in the ∼3–8 M_⊙ range.

Here, we introduce a number of improvements upon C20 and apply our revised methodology to M83 (NGC 5236). M83 is a face-on (i = 24°; Talbot et al. 1979) spiral galaxy with M_⋆ ∼ 2 × 10¹⁰ M_⊙, a moderate SFR of ≈2.5M_⊙ yr⁻¹ (L19), and no significant AGN contribution in the nuclear region. At a distance of 4.66 Mpc (Saha et al. 2006), yielding a distance modulus of 28.32 and a physical scale of 1″ ≈ 22 pc, it is closer than M101 (6.4 ± 0.2 Mpc, with 1″ ≈31 pc). Furthermore, the Galactic absorption is low along the line of sight to M83 (N_H = 4 × 10²⁰cm⁻²; Kalberla et al. 2005), making it ideal for an optical photometric study of X-ray source populations.

In this work, we present a fully classified catalog of X-ray sources in M83 that builds upon that published in L19. Each source is classified on a rigorous, source-by-source basis as either a low-, intermediate-, or high-mass XRB, a background galaxy, or a supernova remnant (SNR). We use these classifications to construct “uncontaminated” XLFs for each XRB population. Our main goal is to assess the shape of the XLFs and establish whether or not there is evidence for a statistically significant cutoff at the bright end, the presence of which has been widely debated (e.g., Zhang et al. 2012; Mineo et al. 2012; C20). We are also interested in the normalization of each XLF, and how well it matches predictions from the global model presented by L19 and other studies. The rest of this work is organized as follows: In Section 2, we identify the optical counterparts to X-ray sources in M83, separating out contamination (AGNs, quasars, and SNRs; Section 2.4) from the XRBs, and we estimate the masses of XRBs, which may appear as either an individual donor star or existing within a parent cluster. In Section 3, we investigate the spatial distribution of the classified XRBs. In Section 4, we present Schechter and power-law function fits to the XRB XLFs and assess the presence of a downturn or cutoff. Finally in Section 5, we compare the normalizations of our optical data-based XLFs with the literature (namely, L19).

2.1. X-Ray Source Catalog

As our primary X-ray point-source list, we adopt the M83 catalog constructed from deep Chandra ACIS imaging data by L19, which examines a total of 38 galaxies. The L19 study includes a thorough estimate of the completeness of the detected X-ray point sources, which is crucial to our purposes. The Chandra data were reduced following the methods detailed in Lehmer et al. (2017): for each galaxy, the analysis was restricted to data sets with aim points within 5′ of the nominal center position, ensuring a sharp point-spread function (PSF) for the nuclear regions, which tend to be the most crowded. The source detection and parameter extraction were performed within 0.5–7 keV, where ACIS is best calibrated.

Out of a total of 456 pointlike sources ⁶ brighter than 10³⁵ erg s⁻¹, we restrict our analysis to the 325 objects that fall within the M83 HST footprint, shown in Figure 1. For comparison, L19 restricts its XLF fitting to those 363 sources that are located within an ellipse that traces the K_s ≈ 20 mag arcsec⁻² galactic surface brightness, outlined in white. Long et al. (2014) also published a catalog of X-ray point sources in M83 based on a partial set of the data used in L19. The main focus of their work was to detect a sample of SNRs using multiwavelength observations. In Section 2.4, we use classification information provided in the Long catalog to eliminate SNRs and some background AGNs from our initial X-ray point-source catalog.

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2.2. Combining X-Ray and Optical Data

2.3. Candidate Optical Counterparts

2.4. Non-X-Ray Binary Sources

Contributions from stellar sources such as coronally active binaries and cataclysmic variables are completely negligible above L_X ≃ 10³⁶ erg s⁻¹ (Boroson et al. 2011), the completeness limit of our sample (L19). Hence, the main sources of contamination are background AGNs and quasars, and bright SNRs within the host galaxy. We address them in turn below. Our approach differs substantially from all other XLF investigations in that we aim to directly identify and reject all contaminants, whereas published works almost exclusively correct for AGN contamination statistically, using the known cosmic X-ray background .

In an extended, multiwavelength spectral and temporal analysis of M83's X-ray point-source population, Long et al. (2014) classified a significant fraction of the point-source population as SNRs. These were classified based on variability, spectral hardness, [S ii]:Hα line ratios or strong [O iii] emission, and cross-referencing with earlier SNR catalogs using Chandra, XMM-Newton, Magellan, the Australia Telescope Compact Array, and the sites of historical supernovae (Wood & Andrews 1974; Soria & Wu 2003; Maddox et al. 2006; Dopita et al. 2010; Blair et al. 2012; Ducci et al. 2013).

Long’s investigation provides us with the rare opportunity to construct a set of X-ray-based diagnostic criteria that can be used to reject contaminants that have not been previously classified, and that are typically ignored in other studies. Out of the 87 X-ray sources identified by Long et al. (2014) as SNRs or SNR candidates, 76 are included in the HST footprint. Of these, 55 have available X-ray soft and hard counts (S and H, corresponding to the 0.5–1.2 keV and 2–7 keV bands, respectively) in the CSC R2. We obtain a hardness ratio, defined as the difference between H and S over the total counts in both, for each source where available. We plot the measured X-ray luminosity, L_X against the hardness ratio in Figure 2. The value of L_X for each source is taken from L19, in which luminosities are obtained from 0.5 to 8 keV X-ray fluxes. This energy range allows for a straightforward comparison with (most of) the literature (see L19 for details). The Long et al. (2014) SNR (red +'s), AGN (orange circles), and XRB (green X’s) classifications are indicated where given.

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We find that the majority of SNRs belong to a distinct parameter space that is well separated from other X-ray sources. Based on this phenomenological approach, we adopt minimum L_X and HR cuts to automatically select out candidate SNRs in our catalog. Our L_X cut is set to the highest L_X of the Long SNRs in our sample, or ℓ ≤ 37.5, where (hereafter) ℓ represents logarithmic X-ray luminosities in units of erg per second. The minimum HR is chosen such that 60% of all sources softer than this limit are Long-classified SNRs, which corresponds to HR ≤ −0.75. Excluding (76) X-ray sources classified by Long et al. (2014) as candidate SNRs, an additional 27 sources meet our criteria. All 27 X-ray sources with these properties are rejected from our catalog. We assess the impact of this on the XLFs in Section 5.2 and the Appendix.

After removing SNRs, the remaining population of contaminants consist of background AGNs and quasars. The rest may be identified through catalog cross-referencing and an analysis of optical properties. Long et al. (2014) classify several foreground and background contaminants based on X-ray hardness, X-ray-to-optical flux ratios, color, and prior catalogs. We classify additional contaminants on the basis of their morphology. Background galaxies can typically be identified by their distinct morphologies, including features such as nuclei, spiral arms, and/or disks, with the exception of distant quasars, which appear in optical images as primarily red sources with extended radial profiles. In total, we remove from our sample three visually identifiable background AGNs and two sources identified as AGNs in Long et al. (2014). We also remove two candidate quasars.

2.5. Classification of XRBs Based on Parent Cluster Age

We expect to find some XRBs in our sample still occupying their parent star clusters. In early-type galaxies, between 25% and 70% of LMXBs are found in ancient globular clusters (Angelini et al. 2001; Kundu et al. 2002; Jordán et al. 2004; Kundu et al. 2007; Humphrey & Buote 2008; Peacock & Zepf 2016). In spiral and star-forming galaxies, however, the fraction of LMXBs found in globular clusters remains quite uncertain, albeit significantly lower: the dwarf starburst NGC 4449 and the spiral galaxy M101 each have only a single LMXB in a globular cluster (Rangelov et al. 2011; C20). The fraction of HMXBs in spirals that still reside in their parent clusters is also poorly known but higher, with ≈ 15% of XRBs in M101 (C20) and ≈25% in the Antennae (Rangelov et al. 2012) found in clusters younger than a few 100 Myr.

Because of their high stellar density, the donor stars feeding XRBs that reside within compact stellar clusters cannot be identified individually at the distance of M83. However, the ages of parent clusters can be used as a proxy for estimating the masses of the donor stars in XRBs, since the most massive surviving stars within a cluster are the most dynamically active, and hence the most likely to form tight binaries. High-mass stars (≥8 M_⊙) have hydrogen burning lifetimes of only ∼10 Myr, and intermediate-mass (≳3 M_⊙) stars have lifetimes of ∼400 Myr. This means that clusters older than ∼400 Myr only contain stars less massive than 3 M_⊙ and may only host LMXBs, while clusters younger than ∼10 Myr are likely to host HMXBs. We assume that clusters with ages between 10 and 400 Myr host IMXBs since the most massive stars remaining in clusters in this age range (3–8 M_⊙) have intermediate mass.

To identify possible clusters among our candidates, we compare our optical matches for each XRB to a catalog of M83 clusters previously published by Chandar et al. (2014). This catalog selected clusters to be broader than the PSF based on the FWHM of the radial profile, as well as the concentration index, defined as the difference in magnitudes measured for a 1 and 3 pixel aperture radius (see Chandar et al. 2014 for details about selection). We find that a total of 12 (∼5% of the total) XRBs in M83 are found within a compact stellar cluster. We compare the colors measured for the XRB-cluster hosts with those predicted by the Bruzual & Charlot (2003) stellar evolution models at solar metallicity in Figure 3. These models start at 1 Myr (upper left) and go through 13 Gyr (lower-right), with key ages marked along the model track. The arrow indicates the direction the colors of clusters would move due to reddening by dust. XRB-cluster hosts have a range of colors and, hence, ages.

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While the color–color diagram provides a good visual comparison of cluster colors with model predictions, the age of each cluster is estimated using a spectral energy distribution fitting method, where we fit for the best combination of age and reddening, as described in Chandar et al. (2014). Magnitudes measured in the UBVI and Hα filters for each cluster are fit to predictions from Bruzual & Charlot (2003) using a standard χ² minimization; see Chandar et al. (2014) for details. The best-fit age for each cluster is recorded in Table A2 and used to classify each XRB: HMXBs have parent clusters <10 Myr, IMXBs have parent clusters with best-fit ages between 10 and 400 Myr, and LMXBs have parent cluster ages >400 Myr.

2.6. Classification of XRBs Based on Donor Star Mass

The majority of X-ray sources contain at least one optical point source within their 2σ radius, with several coincident with multiple candidates. The most likely XRB donor is chosen on a case-by-case basis. In general, priority is given to brighter sources that fall within or closest to the 1σ radius. In most cases, it is not necessary to identify the exact donor of an XRB with several bright candidates, so long as the candidates fall within the same mass regime. For cases in which multiple sources are detected over a range of possible donor masses, intermediate-mass sources are deprioritized, since few IMXBs have been identified in the MW compared to high- and low-mass counterparts. When given the option between high-mass and low-mass potential counterparts, high-mass stars are prioritized as the most likely donor, given the relative rarity of both high-mass stars and XRBs within galaxies (see Section 2.7).

We directly estimate the masses of bright donor candidates by comparing them to the theoretical evolutionary mass tracks for solar metallicity stars from the Padova models on a color–magnitude diagram (CMD; Figure 4), using the mass limits defined in Section 1 (LMXB ≤ 3 M_⊙, HMXB ≥ 8 M_⊙). C20 find that archival HST images of M101 are deep enough to see stars down to 3 M_⊙ at a distance of 6.4 ± 0.2 Mpc. Consistent with this, we find that the majority of the M83 XRB donors lie above the 3 M_⊙ line, with a few sources falling below. This suggests that, indeed, we are able to detect sources down to the minimum threshold required to identify the donor stars of HMXBs within M83. On the other hand, X-ray sources that lack an optical counterpart likely have stellar components that fall beneath the observable magnitude threshold, suggesting the system is an LMXB.

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The left and right panels of Figure 4 compare the V–I colors and B–V colors of the XRBs. We note that we are unable to extract B-band magnitudes from all of the point sources in our sample since the observations are not as deep in the B band as they are in the V band. Nevertheless, it is the absolute V-band luminosity that is most important for estimating the masses of the donor stars.

In order to investigate the potential effects of extinction of the donor stars in our X-ray binaries, we can compare the measured U − B versus V − I colors of donor stars with predicted stellar tracks, following the procedure in Kim et al. (2017). Reddening will move the observed colors off the model tracks and allow for an estimate of E(B − V). This method requires photometric errors to be less than ≈0.1 mag in each band, so it is only applicable to a subsection of donor stars. The colors of the donor stars that satisfy this requirement indicate low typical E(B − V) values of ∼0.1 to 0.2 mag, which is reasonable given that M83 is oriented nearly face-on. This level of extinction would only affect the classification of a few IMXBs, in the sense that they would just exceed the 8 M_⊙ threshold of the model tracks, but otherwise does not have much impact on our classifications.

In total, 214 of the 325 X-ray sources that fall within the HST footprint are classified as XRBs using the methods described, 12 of which exist within compact stellar clusters. We present these sources, their positions, X-ray luminosity, optical colors, and source classification in Table A2 and Figure A2. For these X-ray sources, we find that 30 are LMXBs, 120 are HMXBs, and 64 fall in the intermediate-mass range between the two limits. For each of the panels in Figure A2, the 1σ and 2σ positional uncertainties are shown as yellow concentric circles, each detected optical source within the 2σ radius is highlighted by dashed yellow circles, and the chosen donor is indicated with bold red circles. In both Table A2 and Figure A2, italicized SNRs are those classified using our HR-L_X criterion described in Section 2.4 (as opposed to those identified directly in Long et al. 2014), italicized XRBs are those associated with clusters, and classifications in parentheses are objects with uncertain “candidate” classifications, as reported in Long et al. (2014) or as determined by our methods.

2.7. Assessing Misclassifications

In general, owing to the short lifetimes of the donors, HMXBs trace regions of recent star formation, whereas LMXBs trace the integrated stellar-mass content. Almost all previous works have taken a statistical approach to classifying and studying populations of HMXBs and LMXBs, typically based on their location relative to different galactic structures (e.g., bulge, disk, or outer region, as identified by, e.g., Mineo et al. 2012) or based on the SFR or stellar mass at their location (L19). However, there are dynamical processes that can impart high space motions to XRBs, and thereby move them away from their sites of formation, and we would not expect a perfect spatial correlation, in any case. This means that statistical and spatially-based classifications are likely to have at least a few erroneous classifications of individual sources. In this Section, we study the locations of HMXBs, IMXBs, and LMXBs based on our source-by-source classification method.

Figure 5 shows the spatial distribution of each class of XRB: HMXBs (blue squares), IMXBs (green crosses), and LMXBs (red points). We also find seven AGNs/quasars (orange “x” symbols). The classifications are over-plotted on three different maps of M83 constructed by L19 in Figure 6: stellar mass (M_⋆; top), SFR (middle), and sSFR (bottom). These maps show both a high stellar mass and a high SFR in the central region, higher SFRs in the spiral arms, and significantly higher sSFR in the arms compared to the inter-arm regions.

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In the central 066 or 894 pc of M83, there are a total of 46 XRBs; of these, 36 are HMXBs and seven are LMXBs. This high fraction of HMXBs is perhaps not surprising, since M83 has a central starburst. However, it is different than the central region of M101, which is strongly dominated by LMXBs, even though it is a later-type galaxy with a smaller bulge.

Most HMXBs outside of the central region are found in regions of high sSFR. We find a few in “dark” regions in the middle and bottom panels of Figure 6; these may be sources with high space motions that have moved from their birth sites. HMXBs also tend to be preferentially found in the spiral arms, with a fairly “clumpy,” rather than even, distribution.

LMXBs appear fairly centrally concentrated as expected from an old spheroidal (bulge/halo) population. There are, however, sources distributed fairly evenly throughout M83, which may come from an old disk population. There are also a few LMXBs farther away from the center and located in regions of high sSFR, i.e., where the SFR strongly dominates over the stellar mass. We checked the local background in these regions; extinction appears to be lower than closer to the center of M83, and the background level is sufficiently low that we would easily be able to detect donor stars down to 3 M_⊙. These sources would be misclassified as HMXBs in studies that use a spatial approach, since they fall within a region of high sSFR (L19) and also within the “disk” region, as defined by Mineo et al. (2012), typically believed to be dominated by HMXBs. Overall, the spatial distribution of the XRB population is fairly mixed: whereas HMXBs and (to a much lesser extent) IMXBs seem to track higher SFR regions than LMXBs, LMXBs can be found in the bulge as well as the outer disk, and the bulge itself is home to a large HMXB population.

A key goal of characterizing the XLF(s) of XRBs is to ascertain whether a statistically significant downturn exists at high luminosities. Theoretically, such a “cutoff” is expected near the Eddington luminosity for stellar-mass compact objects, but observations have yet to confirm this prediction with high confidence. Assessing the presence and robustness of such a downturn is inherently dependent upon the chosen functional shape of the XLFs. Virtually all investigations of XRB XLFs perform either single power law (PL) or broken power law (BPL) fits to the differential and/or cumulative XLFs, often with an assumed cutoff luminosity. To first order, most studies conclude that a single PL with a high-energy cutoff at or above the maximum measured XRB luminosity adequately describes the shape of the luminosity distribution of HMXBs in highly star-forming galaxies (Mineo et al. 2012). For LMXBs, the XLF is modeled with either a single PL or BPL (Kim & Fabbiano 2004; Kim et al. 2009; Zhang et al. 2012; Lehmer et al. 2019), plus a high-luminosity cutoff.

There is, however, little physical motivation for adopting a BPL shape for the LMXB XLF; this approach dates back to the seminal work by Gilfanov (2004), who first noted that the XLF of LMXBs in external galaxies “is consistent with a power law with differential slope of ≃1 at low luminosities, gradually steepens above ℓ = 37.0–37.5 and has a rather abrupt cutoff at ℓ = 39.0 − 39.5.” In later works, the best-fit values of the break and cutoff luminosities fall near ℓ ≃ 38 and ℓ ≃ 40, respectively (e.g., Mineo et al. 2012, L19). However, the lack of a unified approach (e.g., fitting cumulative versus differential and/or binned versus un-binned distributions; fixing versus fitting for the cutoff luminosity) makes it somewhat difficult to compare results across different studies. Furthermore, whether the presence of a break and/or a cutoff in the XLFs is required by the data with high statistical confidence remains an open, key question, whose answer is again intertwined with the choice of the XFL functional shape.

As shown by Mok et al. (2019) in their thorough exploration of the mass function of young star clusters (see also C20, and references therein), methods that bin the differential distribution in luminosity (or mass) intervals result in stable fits for the power-law indices, while fits to the un-binned distributions give the most robust detection of any downturn at higher luminosities.

Guided by the above considerations, we approximate the shape of the XLF for XRBs in M83 with two functional shapes: a single PL, and a Schechter function (Schechter 1976). We fit the X-ray luminosity distribution of the (a) composite sample (i.e., all XRBs), as well as (b) HMXBs, (c) IMXBs, and (d)LMXBs, separately. Whereas the compact source fluxes were originally extracted over the 0.5–7 keV energy range, for the purpose of XLF fitting, L19 converts the source fluxes to a 0.5–8 keV range, as appropriate, i.e., using either a template spectral shape or the actual source spectrum, depending on the number of counts. This was meant to facilitate a comparison with the literature; we adhere to the same choice in this paper.

To assess the presence of a truncation—here defined as a luminosity above which no sources exist— we adapt the methodology developed by Rosolowsky (2005) to investigate the shape of the mass function of giant molecular clouds. To account for the presence of a maximum luminosity value (L_c ) in the distribution, we approximate the cumulative distribution as:

where N_C is the number of XRBs more luminous than 2^1/(β+1) L_c , at which point the distribution shows a significant deviation from a single PL of index (β + 1). In the case where N₀ ≃ 1, there is no significant deviation, and the distribution is consistent with sampling from a single PL. With this formalism, the cumulative mass distribution below L_c is proportional to .

The differential Schechter luminosity distribution is proportional to (L/L_⋆), where L_⋆—known as the Schechter “knee”—corresponds to a characteristic luminosity above which the distribution declines exponentially, as follows:

where N_⋆Γ(1 + β, 1) is the number of galaxies with L > L_⋆, and Γ(−b, y) is the incomplete gamma function. This well-known functional shape provides a good analytical approximation to the measured luminosity (and/or mass) distribution of astronomical objects across a wide dynamic range.

We examine the shape of M83's XLFs with three methods:

• (i)  
  We perform a single PL fit to the differential luminosity distributions, binned in intervals with an equal number of sources. This method yields the most stable and robust constraints to the power-law index of the distribution (Mok et al. 2019).
• (ii)  
  We utilize the IDL script MSPECFIT (Rosolowsky 2005) to fit a single PL—with and without truncation—to the un-binned, cumulative luminosity distributions. This method is sensitive to the presence of a downturn at high luminosities, i.e., it serves to identify a characteristic luminosity above which the distribution declines sharply (if any).
• (iii)  
  We perform a maximum likelihood (ML) fit with a Schechter function to the un-binned differential luminosity distributions, following Mok et al. (2019). This method does not use binned data (which can hide weak features at the ends of the distribution), nor cumulative distributions (where the data points are not independent of one another). It thus gives the most robust test for the presence of a statistically significant exponential decline at high luminosities.

The top, middle, and bottom panels of Figure 7 illustrate the results of methods (i), (ii), and (iii), respectively. Unless otherwise noted, fits are performed above the 90% completeness limit of ℓ = 36.2 identified by L19.

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Fitting the differential XLF of M83 (composite sample) with method (i), using bins by 10 sources each, yields a slope of −β = 1.40 ± 0.05. The inferred slopes for the HMXB, IMXB, and LMXB XLFs are, respectively, −β = 1.30 ± 0.08, 1.58 ± 0.12, and 1.55 ± 0.12, suggesting that the HMXBs are characterized by a somewhat shallower overall distribution (top panels of Figure 7; adopting bins of 3, 5, and 7 sources yields consistent results, within the uncertainties).

With respect to the presence of a break, methods (ii) and (iii) give consistent—and interesting—results. Fits to the cumulative XLF with a truncated power law (TPL), with MSPECFIT, indicate that the HMXB XLF is the only distribution that shows any statistically significant evidence, at the ∼2.5σ level, for a high-energy cutoff (this is indicated by values of the N_c parameter in excess of unity in the middle panels of Figure 7).

The ML fits with a Schechter function confirm this trend. The bottom panels in Figure 7 show the 1σ, 2σ, and 3σ confidence contours for the best-fit values of the Schechter slope and knee luminosity. The best-fit values are indicated by the dashed black lines (the upper limit to the knee luminosity was set to be 100 times higher than that of the brightest XRB in each sample, ensuring convergence in all cases). A formally statistically significant detection of the exponential cutoff would be seen as closed 3σ contours in these diagrams. We find only marginally significant evidence (at the 1σ-to-2σ level) for an exponential cutoff at the bright end of the composite XLF, suggesting that M83's XLF is formally consistent with the expectations of sampling statistics from a single PL. This is true for the composite XLF as well as individual donor classes. Interestingly though, in line with the conclusions from method (ii), the presence of a (marginally significant) exponential cutoff appears to be driven by the HMXB population, which exhibits a knee at (at the 1σ-to-2σ level), whereas the LMXB and IMXB XLFs show no evidence for a statistically significant dive (as indicated by the open 1σ contours in the third and fourth plots of the bottom panel of Figure 7).

In summary, we find that, when approximated by a single PL, the composite XRB XLF of M83 has an index of −1.40 ± 0.05; the shapes of the XLFs for the HMXB, LMXB, and IMXB populations show marginal deviations, with HMXBs having a shallower slope than both LMXBs and IMXBs. Our ML fits to the Schechter function do not find formally statistically significant evidence for an exponential cutoff at the bright end of the luminosity functions. However, the presence of a high-energy cutoff in the HMXB XLF above ℓ = 38 (at the ∼2.5σ level) is indicated by both the ML and cumulative XLF fits.

In Section 5.2, we compare our fit results for the XLFs of different populations in M83 with those from previously published results for M83, as well as average XLFs derived from large samples of (star-forming) galaxies.

5.1. The Nature of Donor Stars in IMXBs and HMXBs

5.2. Comparison with X-Ray-based XLFs

Building on the methodology developed by C20 for M101, we carry out an optical reconnaissance study of the XRB population in the nearby, star-forming spiral galaxy M83. This method allows us to directly characterize the donor stars of each Chandra-detected compact X-ray source as low-, versus intermediate- versus high-mass stars (here defined as ≲3M_⊙, 3–8 M_⊙, and ≳8M_⊙, respectively) by comparing their donor stars to stellar evolutionary models or by estimating the ages of their parent clusters using optical photometry from multiband high-resolution HST imaging, while also enabling a direct identification of background contaminants. Similar to what was found by C20 for M101, we show that high-quality HST imaging of the star-forming spiral M83 enables the direct detection of an optical counterpart down to about 3 M_⊙.

After accounting for SNR contamination (which is especially severe in the case of M83), the differential XRB XLF of M83's (between 0.5 and 8 keV) is best fit by a single PL with slope − β = 1.40 ± 0.05. At variance with previous studies, we also explore a Schechter function as a physically motivated alternative to the cutoff and/or BPLs that are typically adopted to approximate XRB XLFs. Our Schechter modeling (the results of which are illustrated in the bottom panel of Figure 7) only identifies a marginally significant (at the 1σ-to-2σ level) exponential downturn for the HMXBs XLF in M83, . In contrast, the LMXB and IMXB distributions, as well as the total XLF, are formally consistent with sampling statistics from a single PL.

That the HMXB XLF in M83 deviates somewhat from a single PL is confirmed by our cumulative distribution analysis, for which we adopt a formalism that was developed for the mass function of giant molecular clouds (Rosolowsky 2005). Through this method, we identify a marginally significant truncation at ℓ = 38.67 ± 0.18, at the 2.5σ level. Again, we find that no deviations from a single PL are required for either the LMXB or IMXB population.

Lastly, our optical reconnaissance methodology enables us, for the first time, to make direct inferences on the role of IMXBs in the XRB XLFs. The assumption that the SFR-tracing XRB population maps into truly high-mass donors is typically predicated upon the notion that the adopted SFR tracer is sensitive to instantaneous, and hence very-short-lived, star formation episodes. However, we note that the survival rate of IMXBs is arguably dependent on the host galaxy star formation history. For spiral galaxies like M83, which had fairly constant (high) rates of star formation over at least the last gigayear (Chandar et al. 2010), IMXBs are likely to yield a non-negligible contribution to the XRB population. At the same time, X-ray binary evolutionary models show that, after sustaining a highly super-Eddington mass-loss phase on thermal timescales, these will quickly evolve into low-mass donors with unusually hot spectral types. Owing to this effect, we estimate a non-negligible contribution from low- and possibly intermediate-mass XRBs to the global XLF of the star-forming galaxy M83, i.e., between 20% and 50% (to be compared with an estimated contribution from LMXBs at the 30% level based on the L19 X-ray XLFs). Finally, we caution against a sizable contribution from X-ray emitting SNRs to the published XLFs for M83, and possibly other star-forming galaxies (for the case of M83, more than 30% of the compact X-ray sources that fall within the HST footprint have been identified by Long et al. 2014 as SNRs).

In future papers, we will extend our methodology to a sample of several tens of nearby galaxies with high-quality HST and Chandra coverage, so as to increase our number statistics and deliver a direct census of the XRB population based on our novel optical reconnaissance of the donor type.

Q.H. is partially funded by a Rackham Merit Fellowship, awarded by the University of Michigan Rackham Graduate School. We are grateful to Tom Maccarone for useful comments and suggestions.

To facilitate a direct comparison with the literature, where the XRB XLFs are typically fit with single or broken power laws (PLs and BPLs), here we approximate M83's XRB luminosity distribution as follows:

where N(>L) is the cumulative XLF, L_b is the break luminosity of the BPL, and the κ values are normalization constants (note, κ is defined differently than the normalization constants of the differential XLF fits, K, discussed in Section 5). All luminosities are in units log erg per second. We choose to fit un-binned cumulative distributions here, as they tend to be more sensitive to the presence of a downturn at high luminosities. At the same time, the choice to represent the power-law indices as (α − 1) is meant to facilitate a direct comparison to those studies that adopt a differential, rather than cumulative, form of the XLF. Apart from the break luminosity, which is fixed to ℓ_b = 38.0 for consistency with L19, all variables are fitted for, using the Python scipy.curve_fit function. We are primarily interested in comparing our fits to the results reported by L19. However, since previous studies do not take into account the SNR contamination to the compact X-ray source population, we also examine the effects of removing (secure and candidate) SNRs to the shape of the XLF. For completeness, we also report the results of fitting the HMXB, LMXB, and IMXB samples separately. Table A1 and Figure A1 summarize the results of our fits.

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View extended figure (16 panels)

Our “fiducial sample” (from the main paper, sample (a)) includes a total of 120 sources above the 90% completeness limit of ℓ = 36.2. This excludes 103 sources identified as SNRs either by (Long et al. 2014, 76 in total) or by their X-ray properties (27 additional sources), as described in Section 2.4. For this sample, we find a PL index of 1.51 ± 0.02, and BPL indices of 1.42 ± 0.01 and 2.03 ± 0.07, respectively, below and above the break. This is to be compared with the values inferred by L19: a PL index of , and BPL indices of and below and above the break, all of which are formally consistent with our best-fit values, within the uncertainties.

Including the SNRs to the sample (“With SNRs”, sample (b)) yields a single PL index 1.62 ± 0.02, whereas the BPL indices are 1.57 ± 0.01 and 2.06 ± 0.07. Not surprisingly, the inclusion of these (low-luminosity) sources slightly steepens the inferred PL slope, as well as the BPL slope below the break. The X-ray-based diagnostics we developed to identify and reject SNR candidates (see Section 2.4) may be too aggressive in that it may lead to the rejection of faint, X-ray soft XRBs. To fully illustrate the effects of our rejection criteria, we present the results of our fits to a sample in which only the 76 X-ray sources that were directly identified by Long et al. (2014) are removed (“With spec. SNRs”, sample (c)), while the additional 27 SNR candidates that we reject from the fiducial sample on the basis of the X-ray color are included in the XLF. However, it should be noted that, in terms of the inferred slopes, all three fits are consistent with the values reported by L19, within 2σ. This suggests that, though strict, our SNR filtering method does not drastically alter the overall shape of the XLF. It does, however, alter the normalization.

For completeness, we compare our BPL fits to those of Zhang et al. (2012), who studied the LMXB XLF using a sample of 20 nearby elliptical galaxies. A comparison to this study is also conducted in L19. They fit the XLF to a BPL model with two breaks (at 5.5 × 10³⁷ and 6 × 10³⁸ erg s⁻¹), as opposed to a single break used both by L19. L19 find no improvement in the quality of the fit when adopting two breaks; therefore, they focus only on the parameters around the first break, a prescription we follow here. The indices of the LMXB XLF found by Zhang et al. (2012) are and , which yields ∼32 expected LMXBs within the HST footprint of M83. By our methods, we find 23 LMXBs in our fiducial sample (a), 30 LMXBs in sample (b), and 26 LMXBs in sample (c). Like other studies that indirectly estimate the contribution of LMXBs in late-type galaxies, the Zhang et al. (2012) XLF most likely includes SNR contamination, as well as contamination from IMXBs. Like L19, we obtain slopes that are steeper in the faint end by a statistically significant margin for all fits. At higher luminosities, however, rather than steepening, our LMXB XLF becomes much shallower. There are two possible explanations for these observations: first, this may be due to the fact that M83 is a late-type galaxy, and at higher sSFRs, young LMXBs may achieve higher luminosities (Fragos et al. 2013; Kim & Fabbiano 2010; Lehmer et al. 2014, 2017; L19); or second, a BPL is simply a poor representation of the LMXB XLF, as demonstrated in Section 4. The classifications of each X-ray source in our catalog are given in Figure A2 and Table A2, extended versions of which are available.