# Calibrating X-ray binary luminosity functions via optical reconnaissance II.
The high-mass XLF and globular cluster population of X-ray binaries in the low
star-forming spiral M81

Qiana Hunt Department of Astronomy, University of Michigan, 1085 S University,
Ann Arbor, MI 48109, USA  Elena Gallo  Department of Astronomy, University of
Michigan, 1085 S University, Ann Arbor, MI 48109, USA  Rupali Chandar
Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606,
USA  Angus Mok  OCAD University, Toronto, Ontario, M5T 1W1, Canada  Andrea
Prestwich  Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138, USA

###### Abstract

We characterize the optical counterparts to the compact X-ray source
population within the nearby spiral galaxy M81 using multi-band Hubble Space
Telescope (HST) imaging data. By comparing the optical luminosities and colors
measured for candidate donor stars and host clusters to stellar and cluster
evolutionary models, respectively, we estimate the likely masses and upper age
limits of the field and cluster X-ray binaries. We identify 15 low-mass X-ray
binaries (i.e. donor star mass $\;\buildrel<\over{\sim}\;$3 $M_{\odot}$)
within ancient globular clusters, as well as 42 candidate high-mass X-ray
binaries (i.e. donor star mass $\;\buildrel>\over{\sim}\;$8 $M_{\odot}$). To
estimate the likelihood of misclassifications, we inject 4,000 artificial
sources into the HST mosaic image and conclude that our classifications of
globular clusters and high-mass X-ray binaries are reliable at the $>90$%
level. We find that globular clusters that host X-ray binaries are on average
more massive and more compact than globular clusters that do not. However,
there is no apparent correlation between the X-ray brightness of the clusters
and their masses or densities, nor are X-ray binary hosts more X-ray luminous
than the general field population of low-mass X-ray binaries. This work
represents one of the first in-depth analyses of the population of X-ray
binaries within globular clusters in a spiral galaxy.

X-rays: binaries – X-rays: galaxies – stars: luminosity function, mass
function – techniques: photometric

††software: AstroPy (The Astropy Collaboration 2013, 2018), DrizzlePac (Avila
et al. 2014), IRAF (Tody 1986, Tody 1993), Matplotlib (Hunter 2007), MSPECFIT
(Rosolowsky 2005), SAOImage DS9 (Joye & Mandel 2003)

##  1 Introduction

In the absence of an active galactic nucleus (AGN), the X-ray emission of
galaxies is dominated by X-ray binaries (XRBs), with only minor contributions
from coronally active binaries, cataclysmic variables, unresolved sources and
supernova remnants (Fabbiano 2006; Boroson et al. 2011, and references
therein). Early population studies of high-mass XRBs (HMXBs, here defined as
having donor masses in excess of $\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}8~{}M_{\odot}$) in star-forming
galaxies established quantitative scaling rations between the host galaxy star
formation rate (SFR) and the integrated X-ray luminosity of HMXBs (Grimm et
al., 2003; Ranalli et al., 2003; Gilfanov et al., 2004)). Along the same
lines, Gilfanov (2004) demonstrated that both the total number of low-mass
XRBs (LMXBs, with donor masses below $\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}3~{}M_{\odot}$) and their
integrated X-ray luminosity are proportional to the stellar mass ($M_{\star}$)
budget of the host galaxy, thereby establishing a universal X-ray luminosity
function (XLF) for LMXBs (see also Kim & Fabbiano 2004).

Since these pioneering works, the Chandra X-ray Observatory has collected
several Msec of sub-arcsec resolution X-ray imaging data for tens of nearby
galaxies. Updated XRB XLFs and their scaling relations are now routinely
employed for a variety of purposes under the assumption that each population’s
XLF has a universal shape. 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 can be used to argue in favor
or against a low-luminosity AGN on a statistical basis (Lehmer et al., 2010;
Gallo et al., 2010).

Recently, Lehmer et al. (2019) developed a global model to fit simultaneously
for the contributions from HMXBs, LMXBs, and background X-ray sources using
sub-galactic stellar-mass and star formation maps. This approach, applied to
38 nearby galaxies of varying morphological types and SFRs reveals a smooth
decline in the XLF normalization per unit SFR, along with a decrease in
normalization at the high-luminosity end with increasing specific SFR (sSFR,
defined as the ratio SFR/$M_{\star}$). Further, Lehmer et al. (2019) note a
possible discrepancy between the LMXB XLF slopes below $\log L_{\rm X}\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}38$ and above $\log L_{\rm X}\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}39$ compared to the results
obtained for early type ellipticals (Zhang et al., 2012). This is particularly
interesting in light of the fact that, prior to Lehmer et al. (2019),
virtually all HMXB XLF studies focused on galaxy samples with relatively high
sSFR, and, as a result, treated all the detected compact X-ray sources outside
of the bulge as HMXBs (e.g., Grimm et al. 2003; Gilfanov et al. 2004; Mineo et
al. 2012). It follows that, even two decades after the launch of Chandra, our
knowledge of LMXBs in actively star forming galaxies remains relatively
limited.

LMXBs are thought to form hundreds of times more efficiently in globular
clusters (GCs) than in the Galactic field (Clark & Parkinson, 1975; Katz,
1975), making GCs of particular interest in the study of LMXBs. Observations
of massive ellipticals with the Chandra X-ray Observatory and the Hubble Space
Telescope (HST), have shown that between 20% to 70% of bright LMXBs ($\log
L_{\rm X}\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}37$) currently
reside in GCs (Angelini et al., 2001; Kundu et al., 2002; Jordán et al., 2004;
Kundu et al., 2007; Humphrey & Buote, 2008; Peacock & Zepf, 2016), and that a
near constant 4% - 6.5% of GCs in ellipticals host bright LMXBs. Given these
extreme efficiencies, it has been suggested that field LMXBs may have formed
in GCs that subsequently dissolved (Grindlay, 1984), or were dynamically
ejected from their natal GCs (Grindlay & Hertz, 1985; Hut et al., 1992; Kremer
et al., 2018). Recent work by Lehmer et al. (2020) support this scenario,
although they also find evidence for an LMXB XLF component that scales with
$M_{\star}$, suggesting that a non-negligible fraction of the LMXB population
in ellipticals form ‘in-situ.’

The role that GCs play in the production of LMXBs in spiral galaxies remains
some 20 years behind our understanding in ellipticals. The key impediment to
progress in exploring the link between X-ray sources and GC in spirals has
been the lack of reliable GC catalogs in all but a handful of spirals. Owing
to on-going star-formation, the complex morphologies of spirals make it
extremely challenging to identify compact stellar clusters in general, let
alone to separate ancient GCs from reddened young clusters (Chandar et al.,
2004). The fraction of young HMXBs in late-type galaxies is also poorly known,
though $\approx 15$% of XRBs in M101 (Chandar et al., 2020) and $\approx 25$%
in the Antennae (Rangelov et al., 2012) are found in clusters younger than a
few 100 Myr.

There is tentative evidence that the GC specific frequency may affect the
shape and normalization of the LMXB XLF, since GC LMXBs and field LMXBs likely
have different evolutionary paths. In that case, late-type spiral galaxies,
which tend to have lower GC specific frequencies, may yield lower LMXB XLF
normalizations than in elliptical galaxies, (Jordán et al., 2004; Kim et al.,
2006; Sivakoff et al., 2007; Kim et al., 2013; Peacock et al., 2017; Luan et
al., 2018).

This Paper is a continuation of an ongoing investigation into the XRB
populations of nearby, late-type galaxies that leverages the combined imaging
power of Chandra and HST. We use multi-band HST imaging data to directly
identify candidate optical counterparts to compact X-ray sources identified by
Chandra. We previously applied this technique to classify XRBs within M101
(Chandar et al., 2020) and M83 (Hunt et al., 2021) and found that within a
distance of $\sim$10 Mpc HST is able to detect stars down to $\sim
3~{}$$M_{\odot}$, thereby allowing us to identify candidate donor stars of
IMXBs and HMXBs. The source-by-source nature of our procedure means that our
classification does not rely on any assumptions about the relationship with
the local environment, such as $M_{\star}$ and or SFR. On the other hand, it
is bound to suffer from some degree of contamination, as the accretion process
affects the evolution, color and overall brightness of the donor stars.

Here, we apply our methodology to M81 (NGC 3031), shown in Figure 1. M81 is a
spiral galaxy at an inclination of i = 58∘ (Okamoto et al., 2015) and a
distance of $\sim$3.6 Mpc (Lehmer et al., 2019; Lomelí-Núñez et al., 2021),
the nearest of our three galaxies sampled thus far. Compared to the previous
galaxies we investigated, M81 has a low SFR of 0.25 $M_{\odot}$ yr-1 (as
opposed to 1.07 and 2.48 $M_{\odot}$ yr-1 for M101 and M83 respectively) and a
relatively high GC specific frequency (SN) of 1.1 (as opposed to 0.43 and 0.17
for M101 and M83 respectively). Furthermore, M81 allows us to take a deeper
look into intermediate-mass XRB (IMXBs; with donor masses between 3-8
$M_{\odot}$) and how they are distributed throughout the galaxy.

We present an optically classified catalog of X-ray sources within M81. Each
source is identified as either an XRB (and tentatively classified by donor
star mass), a possible supernova remnant, a background galaxy, or a foreground
star. We quantify the likelihood of chance contamination using the results of
an artificial source simulation in §4.1. We describe the results of our
source-by-source classification with a special focusing on the XRB spatial
distribution (§3), the X-ray luminosity function of high-mass XRBs (which we
argue suffers from little contamination, §5.2), and the association between
XRBs and GCs in comparison to elliptical galaxies (§5.1).

##  2 Observations

###  2.1 X-ray Source Catalog

Following Hunt et al. (2021), we make use of the X-ray point source catalog
constructed by Lehmer et al. (2019, hereafter L19), in which deep Chandra
imaging data is examined for 38 nearby galaxies. This study includes thorough
estimates of the X-ray completeness limits for each galaxy — crucial for our
analysis. The Chandra data were reduced following the methods detailed in
Lehmer et al. (2017): the analysis was restricted to imaging data within 5′ of
the nominal center position of each galaxy, ensuring a sharp point spread
function across the field of view. The source detection and parameter
extraction were performed within 0.5-7 keV, where ACIS is best calibrated, and
fluxes were converted to between 0.5-8 keV for the purpose of comparing the
XLF analysis to previous studies (see L19 for details).

Within M81, L19 identify 252 compact X-ray sources. The L19 study restricts
its analysis of the subgalactic properties of the galaxy, and ultimately the
XRB population models that arise from them, to the ellipse that traces the
$K_{s}$=20 mag arcsec-2 surface brightness contour outlined in white in Figure
1 (see also Jarrett et al., 2003). The ellipse (hereafter referred to as the
L19 ellipse) has semi-major and semi-minor axes of 8.13 and 4.14 arcminutes
respectively, covering a total area of $\sim$106 square arcminutes (383,409
square arcseconds) and includes 199 X-ray sources, of which 150 are observed
down to the 90% completeness limit of $\ell_{X}\geq 36.3$ (where $\ell_{X}$
represents logarithmic X-ray luminosities in units of erg s-1). By comparison,
the HST footprint shown in Figure 1 includes 240 of the 252 compact X-ray
sources from L19 (see §2.2 below). These include 41 sources that fall outside
of the L19 ellipse, 36 of which are above the completeness limit. We will use
the full 240 sample in our analysis unless otherwise specified.

Figure 1: HST ACS/WFC mosaic image of M81, composed of 33 individual fields
numbered in red. The BVI color image is creating using F435W ($B$), F606W
($V$), and F814W ($I$) observations. The outer (white) ellipse traces the
$K_{s}\approx 20$ mag arcsec-2 galactic surface brightness contour (see
Jarrett et al., 2003). Within this region (which defines the chosen outer edge
of the weak disk), L19 identify 199 compact X-ray sources, of which 150 are
observed down to the (90%) completeness limit of $\ell_{X}~{}\geq 36.3$. The
inner (black) ellipse and circle represent the chosen edges of the bright disk
and the bulge, respectively.

###  2.2 Optical Data

Archival HST imaging downloaded from the Hubble Legacy Archive
(HLA111http://hla.stsci.edu/) was used for the identification and
classification of optical counterparts to the X-ray sources. For M81, a total
of roughly 35 hours worth of ACS/WFC observations spanning 33 fields in three
bands — F814W ($I$ band), F606W ($V$ band), and F435W for ($B$ band) — were
obtained between September 2004 and March 2006 by J. Huchra (Prop. ID 10250)
and A. Zezas (Prop. ID 10584). Of these, 27 fields have sufficient
observations for this Work. Each field spans $3.4\times 3.4$ arcminutes,
yielding roughly 674,000 arcsec2 of coverage over the entire galaxy (for
comparison, the L19 ellipse covers roughly 380,000 arcsec2 of the inner parts
of the galaxy). The 33 fields were combined into a single mosaic using
ASTRODRIZZLE from the STScI DrizzlePac software
package222https://www.stsci.edu/scientific-community/
software/drizzlepac.html. The full $BVI$ mosaic is shown in Figure 1. The
mosaic was used to correct the astrometry between the Chandra and HST data and
to identify the candidate counterparts, while the individual fields, which
preserved more reliable photometry, were used to measure source magnitudes.

A visual inspection of the HST image reveals a bright central bulge and an
outer disk. Unlike M83 and M101, the disk of M81 is marked by a region of
exponential increase in brightness towards the bulge. As such, we find it
useful to approach the X-ray source populations as members of 4 distinct
regions — bulge, bright disk, weak disk, and outskirts — since the background
brightness can drastically affect our ability to reliably classify the optical
counterparts of X-ray sources (see §4). The outer bounds of the weak disk is
well-described by the L19 ellipse (white ellipse in Figure 1). The edge of the
bright disk is defined by the smaller black ellipse in Figure 1, and has semi-
major and minor axes radii of 3.70 and 1.91 arcminutes, respectively, so as to
preserve the same aspect ratio as the L19 ellipse. The bulge (black circle in
Figure 1) is enclosed by a 1.18 arcminute radius circle as defined by
Fabricius et al. (2012).

###  2.3 Identifying Candidate Optical Counterparts

The first step to identifying candidate optical counterparts to X-ray sources
is to correct the astrometry between the Chandra and HST observations. 15
visually-identifiable background galaxies (i.e. those with clearly extended
morphologies) and stellar clusters were selected as known reference points
between the two data sets. We calculated a median relative positional offset
between the X-ray coordinates of each source, as given by L19, and their HST
optical counterparts to obtain a median shift of 0.059 and -0.016 arcseconds
along the HST x- and y-axes, respectively, and standard deviations of 0.207
and 0.413 arcseconds. The X-ray centroid coordinates of all L19 sources in our
sample were shifted by these offsets on the mosaic image.

1- and 2-$\sigma$ uncertainty radii were calculated by adding in quadrature
the standard deviation of the offsets with the positional uncertainties
associated with the X-ray observation as given by Equations 14 and 12 in Kim
et al. (2007), corresponding to the 68% and 95% confidence radii. These
equations take into account the total X-ray counts and the off-axis angle of
the X-ray observations, which is important given the degradation of the point
spread function of Chandra observations with distance from the pointing. The
resulting 1- and 2-$\sigma$ radii, which are unique to each source, represent
the regions within which we are most likely to detect an optical counterpart
to a given X-ray source.

We then identify all potential optical counterparts within 2-$\sigma$ using
the IRAF DAOFIND task to detect point-like sources on the composite images.
The IRAF IMEXAMINE task is used to plot the radial profile of each source,
which enables us categorize candidate counterparts as AGN, star clusters, or
single stars (see §3). To generate the magnitudes and colors needed for the
analysis of each source, we perform aperture photometry on each detected
source with IRAF PHOT. An aperture of 3 pixels is used on point sources, while
an aperture of 10 pixels is used for sources with radii much larger than 3
pixels (i.e. clusters). The photometry is performed on individual field images
rather than on the mosaic, due to the brightness rescaling that occurs during
the mosaic building process. The local background levels are determined in an
annulus with radii between 20 and 25 pixels and subtracted from the
photometric measurements. Aperture corrections of 0.357 ($V$), 0.329 ($B$),
and 0.413 ($I$) were calculated as the median difference between the 3 and 20
pixel aperture magnitudes of several bright, isolated stars with smooth radial
profiles that flatten towards the background sky magnitude. Similarly, the 10
pixel aperture corrections were 0.154 ($V$), 0.128 ($B$), and 0.160 ($I$). In
both cases, an additional correction term of 0.941 (B), 0.947 (V), and 0.949
(I) accounting for the flux missing within a 20 pixel aperture was also added
(see Encircled Energy Fractions from 20 pixels to infinity in Deustua et al.
2017). The magnitudes were converted to the VEGAMAG system by applying the
zero-point magnitude for each filter as reported in Table 2 of Deustua et al.
(2017). Finally, the optical photometry was converted to absolute magnitudes
at 3.63 Mpc, and we applied a blanket correction for foreground extinction
equal to $A_{V}\approx 0.255$ mag, assuming a galactic reddening of
$E(B-V)=0.08$ towards M81. As for M83 (Hunt et al., 2021), we do not account
for extinction intrinsic to each source, though we employ a confidence flag
scheme (see Table 3 in the Appendix) to indicate sources that may be
particularly susceptible to the effects of reddening and obscuration within
M81.

##  3 X-ray Source Classification

X-ray sources may be classified as one of several objects on the basis of
their detected optical counterparts: a foreground star, a background galaxy, a
supernova remnant (SNR), or an XRB donor (either within a cluster or in the
field). Foreground stars are identifiable by the bright diffraction spikes
centered on the point source. Similarly, the majority of background galaxies
that appear in the X-ray data can be identified by distinct morphological
features, such as their extended radial profiles and the presence of a disk
visible in the HST image. For reference, at the typical depth of the X-ray
observations that formed the basis for the L19 X-ray source catalog (X-ray
fluxes $\sim 10^{-15}-10^{-14}$ cgs), all optical counterparts of the X-ray
sources in the sub-regions of the Chandra Deep Field-S that were targeted with
HST are found and resolved at the resolution and depth corresponding to 1
orbit ACS exposure (Grogin et al., 2003, 2005).

When identifying the most likely optical counterpart to X-ray sources,
priority is given first to foreground stars and second to background galaxies
that fall within the 2-$\sigma$ confidence regions of each X-ray source. These
proximity-based classifications may be made with a high degree of confidence,
as we find the probability of an unassociated chance superposition with either
a foreground star or a background galaxy is rare within M81 (see §4.1 for an
in-depth analysis of chance superpositions with X-ray sources). We identify 5
foreground stars and 10 background galaxies in our sample. All other source
classifications require a more in-depth analysis to ascertain.

###  3.1 Supernova Remnants

SNRs are a source of contamination that likely plagues many current XLFs.
Recently, Galiullin & Gilfanov (2021) convincingly demonstrated that the vast
majority of so-called soft and quasi-soft X-ray sources are indeed SNRs; these
include soft X-ray sources both with and without an optical or radio
counterpart SNR. As a confirmation, soft X-ray sources are a factor $\sim$ 8
more abundant in star forming spiral galaxies compared to ellipticals.

In Hunt et al. (2021), we devised a quantitative X-ray-based criterion by
which to identify potential SNRs using the multi-wavelength SNR catalog
compiled by Long et al. (2014) for M83 as the basis. We found that the
majority of SNRs common between the Long et al. (2014) and L19 belong to a
distinct parameter space on an $L_{\rm X}$\- X-ray hardness ratio (HR, here
defined as the ratio of the sum of the counts in the 2-7 keV and 0.5-1.2 keV
bands to the difference of their counts) plot. Based on this phenomenological
approach, we adopt a minimum $L_{\rm X}$ and HR cuts to automatically select
out candidate SNRs in our catalog, which correspond to $\ell_{X}\leq 37.5$ and
HR$~{}\leq-0.75$.

We adopt the same $L_{\rm X}$ and HR cuts to identify potential SNRs in our
M81 catalog, yielding 19 SNR candidates — roughly a factor 5 less than in M83.
This is unsurprising considering the large difference in SFR between M81 and
M83. We exclude an additional 6 SNRs identified by Lee et al. (2015). Of the
25 total SNRs in our sample, 15 have optical counterparts, and 2 of these
appear to be associated with clusters.

Figure 2: Measured $B-V$ vs $V-I$ colors of XRB host clusters compared with
predictions for the color evolution of clusters from the Bruzual & Charlot
(2003) models. The black triangles mark cluster ages of 10 Myr (top) and 400
Myr (bottom). The arrow represents the direction of reddening following the
Milky Way extinction law with an example reddening of $E(B-V)=0.2$.

###  3.2 Stellar Cluster Hosts

We expect to find some fraction of XRBs to exist within stellar clusters, due
to the compact nature of clusters and increased likelihood of stellar
interactions. These are identified as candidate sources with full-width half-
maximums (FWHMs) that are broader than the point-spread function of a typical
field star within the M81 HST image; we find that GCs in M81 have FWHMs
greater than 4 pixels (0.2 arcseconds), whereas typical stars have FWHMs less
than 2 pixels (0.1 arcseconds). As a final confirmation, we compare our
selections with a number of catalogs that identify clusters and extended
sources in M81 (Nantais et al., 2010, 2011; Nantais & Huchra, 2010; Santiago-
Cortés et al., 2010), in which all but one of the sources we call a cluster
are identified as clusters or extended sources. The only source that was not
identified in any other catalog is found within the bulge region.

We assume that, unless identified as SNRs by our method outlined in §3.1,
X-ray emitting clusters are indeed XRB hosts. In order to classify a cluster
XRB by donor mass, we use the cluster age as a proxy; since high-mass stars
have hydrogen burning lifetimes of only $\sim 10$ Myr and intermediate-mass
stars have lifetimes of $\sim 400$ Myr, globular clusters that are older than
$400$ Myr are dominated by long-lived, low-mass stars, and their XRBs may be
confidently classified as LMXBs. Likewise, we classify classify clusters
younger than 10 Myr as HMXB hosts and those falling between 10-400 Myr as IMXB
hosts, since the most massive stars in a dense region are the most dynamically
active and most likely to form stable binaries (Bonnell & Bate, 2005).

We approximate the ages of these clusters by comparing their colors to those
predicted by the Bruzual & Charlot (2003) cluster evolution models at solar
metallicity, as shown in Figure 2. The models span 1 Myr to 13 Gyr in cluster
ages, moving from the upper left to the lower right. The black triangles
demarcate the bounds of 10 Myr and 400 Myr, and the arrow shows the direction
the colors would move due to reddening by dust. We find that 15 of the 17
clusters in our sample fall red-ward of the 400 Myr mark, distinguishing them
as ancient globular clusters that host LMXBs. 1 cluster appears younger than
10 Myr, and 1 cluster falls between the two age ranges. We classify these as
an HMXB and an IMXB respectively. By comparison, M83 had 4 HMXBs, 4 IMXBs, and
4 LMXBs found in clusters, while M101 had 2 HMXBs, 6 IMXBs, and 1 LMXBs. The
difference between these three galaxies is as expected given the SFR/SN number
of each.

###  3.3 Field X-ray Binaries

In the case where an X-ray source is neither a foreground star, background
galaxy, SNR, nor a cluster, we assume the source is a field XRB with a donor
star falling somewhere within the 2-$\sigma$ radius of the source. For sources
that contain multiple candidates, the most likely donor is chosen on a case-
by-case basis. Priority is given to high-mass stars that fall within or
nearest to the 1-$\sigma$ radius, since high-mass stars are more likely to
remain in a binary following a supernova kick (Kochanek et al., 2019). Low-
mass stars are given second priority over intermediate-mass stars, since IMXBs
are expected to be short-lived and are thus extremely rare (Podsiadlowski et
al., 2002; Pfahl et al., 2003).

To estimate the masses of candidate donor stars, we compare them against
Padova theoretical stellar evolutionary models on a color-magnitude diagram
(CMD, Figure 3). Following our definitions of each category of XRBs and in the
order of priority given, we classify sources with candidate donors above the 8
$M_{\odot}$ model line as HMXBs, those with donors below the 3 $M_{\odot}$
model line as LMXBs, and those falling between the two as IMXBs. The CMD
demonstrates that at the distance of M81, the HST image is deep enough to
detect stars down to 1 $M_{\odot}$. Thus, sources that do not have visible
donor stars are also categorized as LMXBs. This estimates implicitly assume no
contamination from the X-ray-irradiated accretion disk to the optical band.
This is further discussed in §4.

We note that M81 has regions of very intense star formation appearing as
bright green HII regions in the HST image. In these regions, it is difficult
to detect individual stars due to crowding and saturation. In these cases, the
donor star is assumed to be high-mass.

###  3.4 Final Classifications

Concluding the source classification, we identify 199 XRBs out of the total
240 X-ray sources that fall within the M81 HST footprint: 122 LMXBs, 35 IMXBs,
and 42 HMXBs. Of these, 17 exist within stellar clusters: 15 low-mass (within
GCs), 1 intermediate-mass, and 1 high-mass. Taking only XRBs above the 90%
completeness limit of $\ell_{X}\geq 36.3$ estimated by L19, there are 159
XRBs: 100 LMXBs (11 in clusters), 25 IMXBs (none in clusters), and 34 HMXBs (1
in a cluster). Of the remaining 41 sources, including the nucleus, 25 are
SNRs, 10 are background galaxies, and 5 are foreground stars.

Restricting the sample to those sources that fall within the L19 ellipse, we
find 88 LMXBs, 27 IMXBs, and 31 HMXBsin the field, with an additional 15
LMXBs, 1 IMXB, and 1 HMXB within clusters. Above the completeness limit, this
comes to 71 LMXBs, 19 IMXBs, and 26 HMXBs, with an additional 11 LMXBs in GCs.
The L19 ellipse also contains 22 SNRs, 9 background galaxies, and 4 foreground
stars (14, 5, and 4 above the completeness limit, respectively).

A complete description of the positions, $L_{\rm X}$, V-band magnitudes,
optical colors, and classifications of all 240 sources within the HST
footprint is given in Table 3. Full-color optical images of all sources — with
their 1- and 2-$\sigma$ radii outlined in red, candidate sources highlighted
with yellow dashed circles, and most likely counterpart/donor circled in red —
are shown in the Appendix, Figure 12.

The overall spatial distribution of the candidate XRB counterparts is shown in
Figure 6, where our classifications (not accounting for possible
misclassifications; see §4.1) of low-, intermediate-, and high-mass donors are
shown in red, green, and blue, respectively. The 15 cluster LMXBs are outlined
in yellow. As expected, the bulge of M81 is dominated by LMXBs: 39 total LMXBs
(2 of which are found in GCs) are found in the bulge compared to 1 HMXB. Above
the completeness limit, there are 38 bulge LMXBs (1 in a cluster) compared to
1 HMXB. The majority of HMXBs (31 out of 42) are within the disk; however,
roughly $\sim 52\%$ of all disk XRBs are LMXBs. When the disk is broken into a
bright and weak component, 80% of the bright disk XRBs are low-mass, while
nearly 40% of the weak disk XRBs are low-mass. The percentages may skew even
higher, considering the possibility that some (or all) of the sources we
classified as IMXBs may actually be LMXBs, as discussed in §4.1.

When compared with the stellar mass, SFR and specific SFR (sSFR) sub-galactic
maps generated by L19 (Figure 7), HMXBs appear to be concentrated in high SFR
regions, whereas most (albeit not all) LMXBs appear to follow the radial
profile of the stellar mass. The IMXBs population seems to be somewhat hybrid;
whereas their spatial distribution resembles more closely that of HMXBs, they
are found in larger proportions in the bright disk. As discussed in §4,
however, this population is likely affected by a high degree of contamination,
so we refrain from further speculating on their properties.

Figure 3: $V-I$ vs. $V$ color-magnitude diagram (CMD) of the donor stars of
field XRBs in M81, compared to theoretical evolutionary tracks modeled at
solar metallicity (Bertelli et al., 1994; Girardi et al., 2010; Marigo et al.,
2017). Donor stars in M81 are detectable with the HST down to $\lower
2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}1$ $M_{\odot}$.

##  4 Assessing Misclassifications

Here, we discuss a few of the most pressing sources of misclassification of
the optical counterparts in M81. For an additional discussion of potential
sources of misclassification inherent to our method, the reader is referred to
Chandar et al. (2020) and Hunt et al. (2021).

###  4.1 Quantifying Chance Superpositions

In this section we assess the likelihood that an X-ray source may have a
chance superposition (rather than physical association) with a high- or
intermediate-mass star, globular cluster, or background galaxy. Since low mass
stars dominate the stellar population of a galaxy, we seek to quantify how
certain can we be that, for any given region, the true donor is not an unseen
low-mass star. While our prioritization scheme for sources with multiple
point-source candidates places HMXBs above other classifications in any case
(due to the higher chance of binary survival post-supernova, Kochanek et al.
2019), this becomes a greater issue for IMXBs, which we would naturally de-
prioritize compared to LMXBs due to their rareness.

In order to quantify the frequency of chance superposition with a source that
is not a low mass star, we randomly populate the 4 regions of the galaxy
(bulge, bright disk, weak disk, and outskirts, as defined in § 2.2) with 1,000
artificial X-ray sources per region and classify each using the HST images and
photometry, as done with our ‘true’ X-ray sources. The $2\sigma$ positional
uncertainty used to search for an optical counterpart to each synthetic X-ray
source is assumed to be the median of the $2\sigma$ positional uncertainties
of the ‘true’ X-ray sources within that region; these values are compiled in
Table 1. As expected, these increase as one moves further from the center of
the galaxy, largely due to the degradation of the Chandra PSF farther from the
pointing.

The results of our artificial source experiment are compiled in Table 1 and
shown in Figure 4. For each region we estimate the probability of a chance
superposition with a high-mass star, an intermediate-mass star, a globular
cluster, and a background galaxy as a percentage.

In Table 2, we compile the number of observed XRBs that were classified as
HMXBs, IMXBs, and LMXBs in the same four regions, as well as X-ray sources
found in GCs and associated with background galaxies. The total number in each
region is given as the first number in the table, and the number of sources
above the completeness limit is given in parentheses.

One key result of the simulation is that the probability of finding a chance
superposition with a high-mass star, a globular cluster, or a background
galaxy is extremely low ($<1$% in total) in the bulge region. There is a
somewhat higher probability of a chance superposition with an intermediate-
mass star ($3.4$%). Because the bulge region of M81 is bright, it is
hypothetically possible for sources to be misclassified as an LMXB with no
optical counterpart, as the background brightness could outshine any potential
point source. However, the fact that we do see a handful of intermediate-mass
stars within our simulation in this region indicates that we are still able to
identify stars down to intermediate masses, though intermediate-mass stars
closer to the 3 $M_{\odot}$ limit may be lost. This, as well as the low
probability of chance superposition with non-low-mass sources, suggests that
our source classifications — particularly of any HMXBs — in the bulge are
likely accurate and are not prohibitively sensitive to background brightness
or chance superposition.

The bright disk also shows a low probability for a chance superposition with a
high-mass star (1.2%), a globular cluster ($<1$%), or a background galaxy
($<1$%). There is however, a more significant probability that an X-ray source
will have a chance superposition with an un-associated intermediate-mass star
($14.2$%). These probabilities increase in the weak disk, especially for high-
mass ($5.4$%) and intermediate-mass stars ($41.5$%). The probability of
overlapping with a background galaxy increased to 1.3%, while there is
virtually no chance superposition with a cluster in the weak disk. Potential
explanations for these increases is the inclusion of the spiral arms in these
regions, which tend to harbor bright, massive stars, the decreasing background
brightness, and (perhaps more importantly) the larger positional uncertainty
of the X-ray observations in this portion of the galaxy.

The outskirts of the galaxy also show substantial contamination by
intermediate-mass (23.6%) and — albeit to a lesser degree — high-mass stars
(6.8%). The chance of overlapping with a background galaxies triples (3.8%).
The increased frequency of background galaxies in our simulation with
galactocentric distance is not surprising, as many more background galaxies
are visible in the outskirts of M81, where the background brightness is lowest
and the density is most diffuse (see also §4.2).

Taken together, these results lead to the following conclusions:

  * •

The probability of finding a chance superposition with a globular cluster is
negligible all 4 regions of M81. This indicates that any X-ray source-GC
association is almost certainly physical.

  * •

X-ray sources classified as HMXBs in the bulge (1 source) or bright disk (2
sources) are almost certain to be correctly classified. The weak disk and
outskirts have relatively low probabilities of chance superposition with high-
mass stars ($<10\%$ each). There are 70 and 31 XRBs above the completeness
limit in the respective regions, with 23 and 7 identified as HMXBs in each
region, respectively. The artificial experiments suggest minor contamination,
with at most 4 possible misclassifications in the weak disk and 3 in the
outskirts.

We note that high-mass stars are more likely to survive in an X-ray binary
than those with lower masses, so in a galaxy with continuous star formation,
it may be reasonable to assume a greater fraction of XRBs identified as having
high-mass donors are truly HMXBs than this simple simulation suggests.

  * •

At face value, intermediate-mass stars are, after low-mass stars, the most
abundant potential counterparts within our simulation. This suggests a good
number of our XRBs may overlap with intermediate-mass stars that are un-
associated with the X-ray emission, simply by chance. In the bright and weak
disks, we classified 9 and 17 X-ray sources above the completeness limit as
IMXBs (there are only a handful of such sources in the outskirts and none in
the bulge). In the weak disk where the probability of chance superposition is
greatest, we may expect up to 30 of the 70 XRBs to be misclassified as IMXBs.
This suggests that we cannot trust our classified IMXB population to be truly
representative of the IMXB population of M81.

Evolutionary arguments further strengthen our conclusion that a large fraction
of XRBs with an associated intermediate-mass stars may not be reliable. Even
though the probability of forming an XRB with an initial intermediate-mass
donor is higher than that of a low-mass donor, population synthesis models
show that most intermediate-mass donors (those with neutron star accretor,
that is) evolve very quickly into low-mass stars through a short-lived thermal
mass transfer phase (Podsiadlowski et al., 2002; Pfahl et al., 2003). This
results into a population of abnormally hot and luminous LMXBs — albeit with
IMXB progenitors — which is bound to be misclassified through our method.

We check whether X-ray irradiated disks may contribute significantly to our
optical bands by comparing the colors of our HMXBs to other nearby, high-mass
stars. We identify a sample of 115 high-mass comparison stars located within
$\approx 3$ arcseconds of our 42 HMXBs, to account for potential environmental
effects that could alter the colors of the donor stars. We find that the B-V
and V-I colors of the candidate HMXB donor stars are entirely consistent with
typical field stars of similar brightness. We note, however, the discrepancies
arising from, e.g. X-ray irradiated disks, would become more prominent in the
UV band (Tao et al., 2011).

  * •

While remaining small, the probability of chance superposition with an
optically identified background galaxy in our simulated sample increases
radially towards the outskirts, as expected. In terms of our ‘true’ sample, we
find 3 X-ray sources associated with background galaxies in the bright disk
and 6 in the weak disk, and only a single such object in the outskirts. This
is addressed specifically in §4.2.

Figure 4: Results from our chance superposition simulation, in which 1,000 simulated sources were randomly distributed throughout each of our 4 regions — the bulge, the bright disk, the weak disk, and the outskirt, as defined in §2.2 — and their optical counterparts classified using the same methods as for the actual (‘true’) X-ray sources. These probabilities are also given in Table 1. Table 1: Probability of Chance Superposition (percentage) Region | Median | HMXB | IMXB | Globular | Background
---|---|---|---|---|---
in M81 | $2\sigma$ |  |  | Cluster | galaxy
Bulge | 0.′′54 | 0.1 | 3.4 | 0.1 | 0.6
Bright disk | 0.′′66 | 1.2 | 14.2 | 0.2 | 0.7
Weak disk | 0.′′78 | 5.4 | 41.5 | 0.0 | 1.3
Outskirts | 1.′′48 | 6.8 | 23.6 | 0.1 | 3.8
Table 2: Observed Populations (Total & Completeness limited) Region | LMXB | HMXB | IMXB | Globular | Background
---|---|---|---|---|---
in M81 | (Field) |  |  | Clusters | galaxy
Bulge | 37 (32) | 1 (1) | 0 (0) | 2 (1) | 0 (0)
Bright disk | 25 (14) | 2 (2) | 6 (2) | 7 (5) | 3 (1)
Weak disk | 26 (25) | 29 (23) | 22 (17) | 6 (5) | 6 (4)
Outskirts | 19 (18) | 10 (7) | 7 (6) | 0 (0) | 1 (1)
Figure 5: The contribution of X-ray sources to the total cumulative X-ray
luminosity function of M81 (grey). LMXBs (red), IMXBs (light green), HMXBs
(blue), and AGN (orange) are identified based on the radial profiles and
photometry of the optical counterparts as described in §3. The expected cosmic
X-ray background, derived from Kim et al. (2004) using the ChaMP survey
fitting parameters, is shown in dark green. The M81 90% completeness limit of
$\ell_{X}\lower 2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}36.3$ (from L19) is
shown as a vertical dashed line.

###  4.2 The Cosmic X-ray Background

In Figure 5, we plot the cumulative XLFs of the M81 X-ray sources classified
as low-, intermediate-, and high-mass XRBs (based on their candidate optical
counterparts) within the L19 ellipse, as well as the XLF of the optically
identified AGN. These are compared with the expected XLF of Cosmic X-ray
Background (CXB) sources, based on the log(N)-log(S) from the ChaMP Chandra
survey using the $0.5-8$ keV band fit, which has a limiting flux of $6.9\times
10^{-16}$ ergs cm-2 s-1 — intermediate between the Chandra Deep Fields and
previous surveys (Kim et al., 2004). The ChaMP survey covers an area of 9.6
square degrees, wider than many prior CXB studies, and detected $\sim 6500$
sources —the most detected in a single satellite survey. The wider field of
view means that cosmic variance will have less an impact on observations than
for smaller, deeper fields. At the same time, the flux limit of our X-ray data
is shallower than ChaMP’s.

Unlike in M83, where the contribution of the CXB is expected to be negligible
outside of the $K_{s}=20$ ellipse, the proximity and larger angular size of
M81 imply that the CXB can be expected to contribute significantly to the
detected X-ray source population (see also Figure 3 of L19). Specifically 55
CXB sources (that is, AGN) are expected down to the completeness limit within
the L19 ellipse (dark green line in Figure 5), whereas we directly identify
the host galaxies of only 10 sources. This implies that optically obscured AGN
are a non-negligible source of contamination to the compact X-ray source
population within the field of view of M81. We expect those will be mostly
associated with LMXB candidates with no detected optical counterparts.

To test this hypothesis, we conduct a thorough inspection of of 3 HST fields:
one covering the outskirts of M81 (outside of the weak disk/L19 ellipse), one
covering the weak disk, and one covering the bright disk and a portion of of
the bulge. We identify any optical source falling within the 3 fields with a
radial profile similar to a galaxy (i.e. non-point source, non-cluster, with
extended or unusual shapes, excluding sources that are clearly crowded stars)
as a potential galaxy. The aim of this exercise is to quantify the fraction of
optically identified galaxies that have an associated X-ray emitting source
(AGN), and to assess how that varies as a function of galactocentric distance.
The result is a high-end estimate of the number of background galaxies
captured within each field.

In the outskirt field, where background galaxies should be virtually
unabsorbed and easily identifiable, we identify 545 background galaxies, none
of which have an X-ray counterpart. For a field covering 37,913 arcsecs2, this
translates into a number density of less than 0.02 galaxies per arcsecs2, or 1
galaxy for every 70 arcsecs2. Across the same field there are 7 compact X-ray
sources (4 of which are above the X-ray completeness limit); none are
associated with an optical galaxy. Owing to increased absorption and crowding,
the number of optical galaxies goes down to 349 and 104 for the weak disk and
the bright disk/bulge HST fields, respectively; the number of compact X-ray
sources in these regions is 7 and 10 (4 and 8 above the completeness limit),
respectively. Again, none are identified as AGN.

This supports our hypothesis that the X-ray emitting AGN that make up the CXB
over the field of view of M81 have no detectable optical counterparts, and are
thus highly likely to be ‘hidden’ within the objects that we classify as
LMXBs. This, combined with our chance superposition assessment analysis (§4.1)
indicates that our HMXB population suffers from minimal (if any) CXB
contamination, whereas the LMXB population is likely contaminated,
particularly at the low luminosity end. Specifically, out of the 82 LMXBs that
we identified down to the completeness limit (71 of which are field XRBs)
within the regions mostly likely to be obscured (i.e. within the outer bounds
of the weak disk), a large fraction (of the order of 50) are expected to be
potential AGN.

Figure 6: Spatial distribution of LMXBs (red points), with globular cluster
hosts circled in yellow, IMXBs (green crosses), and HMXBs (blue boxes) on an
inverted image of M81. Background galaxies are also shown (orange X’s). The 4
regions (bulge, bright disk, weak disk, and outskirts) are marked by black and
white ellipses.  Figure 7: Overlays of LMXBs (red points), IMXBs (green
crosses), HMXBs (blue squares), and background galaxies (orange X’s) onto the
(a) stellar mass, (b) star formation rate, and (c) specific star formation
rate maps for M81 generated by L19 within the L19 ellipse. All three maps are
shown with a linear color scale.  Figure 8: The color-color diagram of
clusters from the SC10 catalog, compared to those that we determine are XRB
hosts. The black and orange lines represent the Bruzual & Charlot (2003)
cluster evolution models for solar and 20% solar metallicities, respectively.
Cluster colors are taken from the SC10 measurements. The arrow represents the
direction of reddening following the Milky Way extinction law with an example
reddening of $E(B-V)=0.2$.

Figure 9: Comparing the properties of X-ray emitting SC10 clusters to all GCs
in the SC10 catalog. The left shows the color magnitude diagram, with red
squares representing GCs that are XRB hosts. The magnitudes are taken from the
SC10 measurements. On the right, the radii and densities of the XRB-hosting
GCs are compared to the total GC population.

Figure 10: The X-ray properties of the SC10 XRB-hosting clusters. On the left,
histograms of the densities and masses of the XRB-hosting GCs from the SC10
catalog are compared to their L19 X-ray luminosities. On the right, a
histogram of the X-ray luminosities of the SC10 clusters is compared to our
total M81 LMXB population, not accounting for possible misclassifications (see
§4.1).

##  5 Discussion

###  5.1 LMXB Production in Globular Clusters

Extensive research has been done into the population of LMXBs found within GCs
in elliptical galaxies, in large part due to the abundance of GCs and the ease
with which LMXBs can be isolated in galaxies with old stellar and cluster
populations. Several early works found that GCs are especially efficient at
forming LMXBs thanks to the increased likelihood of dynamical interactions
within dense environments. Up to 70% of all LMXBs within any given early-type
galaxy are found within old star clusters, and some particularly luminous GCs
appear to harbor more than one LMXB (Angelini et al., 2001; Jordán et al.,
2004; Kundu et al., 2007). Furthermore, a significant fraction of field LMXBs
may have formed originally within GCs, only to be ejected later or deposited
within the field when the parent GC dissolved (Kundu et al., 2003; Lehmer et
al., 2020).

There is evidence to suggest metal-rich GCs form LMXBs 2-4 times more
efficiently than their metal-poor counterparts (Jordán et al., 2004; Kundu et
al., 2007; Humphrey & Buote, 2008). One explanation for this may be that,
because they have larger radii, metal-rich stars are better able to facilitate
both the formation of binaries and the Roche-lobe overflow that characterizes
LMXBs (Bellazzini et al., 1995). Alternatively, this effect may be explained
by the potentially longer lifetimes of metal-rich LMXBs due to stronger
stellar winds (and therefore faster evolution) of lower-metallicity stars
(Maccarone et al., 2004). On the other hand, metal-rich clusters tend to be
more compact, with may lead to more dynamical interactions within the cluster
environment (Peacock et al., 2010). Despite these hypotheses, a suitable
explanation for this apparent dependence is still a subject of much debate.

For all the uncertainty regarding the role of GCs in XRB production in early-
type galaxies, even less is known about their role in late-type galaxies.
Spiral galaxies tend to host GC populations with a range of ages, which makes
it difficult to pursue the effect of metallicity on XRB populations due to the
degenerate effects of both age and metallicity on cluster colors (Kundu et
al., 2003). In our previous work, we found only 1 LMXB in a GC in M101
(Chandar et al., 2020) and 4 within M83 (Hunt et al., 2021). These are much
lower fractions of the total LMXB population than expected in early-type
galaxies, since massive spiral galaxies like M83 and M101 are expected to have
on the order of $\sim 100$ GCs. Given that M81 is a spiral galaxy with a low
SFR (0.25 $M_{\odot}$yr-1) and relatively high SN (1.1), it is the ideal
target for analyzing the production of XRBs within the GCs of late-type
galaxies. Furthermore, the clusters in M81 have been well-studied, allowing us
to analyze the properties of XRB-hosting clusters compared to non-XRB clusters
and, along the same lines, the differences between field XRBs and cluster XRBs
using previously published works.

As a primary basis for our analysis we use an M81 cluster catalog by Santiago-
Cortés et al. (2010, hereafter SC10). Within this work, a total of 435 compact
stellar clusters were identified using HSTACS F435W, F606W, and F814W data in
combination with the source detection code SExtractor. They used bounds of
$2.4<$ FWHM $<10$ ACS pixels (or $2.1-9$ pc) for their definition of a compact
cluster. 10-pixel aperture magnitudes were also generated by SExtractor, from
which $B-V$ and $V-I$ colors are derived.

Of the 435 clusters in the SC10 catalog, 13 coincide with X-ray sources within
our catalog. Of these, 12 are located in GCs, and 1 (located in a young
cluster) is identified as a potential SNR by our methods outlined in §3.1,
which we remove. We also find an additional 3 GC LMXBs not included in the
SC10 catalog, which suggests that the SC10 catalog is not complete. To account
for these 3 missing GCs in our analysis of the cluster population in M81, we
compare the measured properties of the X-ray clusters in SC10, as measured by
SExtractor, to the values we measure by our methodology, as described in §2.3.
We find that, between the two catalogs, the FWHM measurements for the clusters
have a median difference of 0.33 pixels, and the V-band photometry has a
median offset of approximately 0.09 mags, while our B-band photometry is
fairly consistent with the SC10 measurements. Thus, by applying these offsets
to our 3 GCs that are missing in the SC10 catalog, we are able to calibrate
our measured values to the SC10 system, which will enable us to include our
full GC LMXB population in our analysis of M81 clusters.

Figure 8 shows all 435 SC10 clusters (grey points) compared to two models for
cluster evolution from Bruzual & Charlot (2003): a solar metallicity model,
and a model with metallicity $Z=0.004$, or 20% solar. As is the case for
Figure 2, cluster ages increase down and to the right, and the arrow
represents the direction of reddening for M81. The red squares represent X-ray
emitting clusters that appear in our source catalog, i.e. XRB hosts. All but
one fall towards the lower-right end of the model track, where we expect GCs.

Since we are interested in understanding the population of LMXBs within GCs,
we isolate the GCs in the SC10 sample by making a color cut corresponding to
minimum cluster age of 400 Myrs, based on the Bruzual & Charlot (2003) models.
220 of the 435 clusters meet these requirements. This cut successfully selects
the 12 clusters we classify as LMXB-hosts in our sample, which corresponds to
roughly 4.4% of the total GC population in SC10. The additional 3 GCs not
present in the SC10 catalog are also added to the total X-ray GCs population
for the remainder of our analysis. We calculate the masses of the GCs by
adopting a mass-luminosity ratio of 1.5 $M_{\odot}$/$L_{\odot}$ as presented
in Chandar et al. (2007). The mass of each cluster is estimated by converting
their V-band magnitudes using an absolute Vega magnitude of 4.66 for the Sun,
as viewed in the ACS F606W filter (Willmer, 2018). From these masses, we also
calculate cluster densities following Chandar et al. (2007), converting FHWMs
to effective radii using a pixel scale of 0.′′05 $\mathrm{pixel}^{-1}$ and a
conversion factor of 1.48 (Anders et al., 2006; Mulia et al., 2019).

In Figure 9, we compare the properties of GCs that host XRBs (red) with the
properties of those that do not (pink) — that is, the 15 X-ray emitting GCs
from our sample compared to the 208 GCs from the SC10 catalog that do not have
X-ray counterparts. We find that, within the spiral galaxy M81, GCs that host
XRBs tend to have higher V-band magnitudes than non-XRB GCs, as demonstrated
in the leftmost panel. Furthermore, when observing the sizes, masses, and
densities of the clusters (right panels), we find that GCs that host XRBs have
smaller radii, are more massive, and hence denser than GCs that do not. Higher
masses and densities may be more conducive for the formation of XRBs, since
dense environments allow for more close interactions between stars, increasing
the chances of capture. Similarly, higher masses correlate with more stars
and, therefore, more opportunities for dynamical interactions (Peacock et al.,
2010).

With only BVI photometry, it is hard to make definitive statements about the
metallicities of GCs in spiral galaxies, since small amounts of reddening
would significantly change the estimated metallicity. We do find however, that
the majority of GCs which host LMXBs in M81 are more centrally concentrated
than the full SC10 GC catalog. This is potentially indirect evidence that
LMXBs may prefer to form in more metal-rich GCs in spiral galaxies as well,
since metal-rich GCs tend to be associated with bulges (rather than halos),
and more concentrated towards the centers of their host galaxies as a result.

When we analyze the properties of the 15 X-ray emitting GCs (Figure 10, left),
we find no significant correlation between X-ray luminosity and the mass or
density of the host cluster. That is, more massive XRB-hosting GCs are not
more luminous in the X-rays, in line with what was found by Sivakoff et al.
(2007) for GCs in Virgo cluster elliptical galaxies. It is also interesting to
compare the population of LMXBs within GCs to the total number of XRBs and to
field LMXBs specifically, although the latter is quite uncertain in M81. Of
the 199 XRBs we identified within M81 (excluding SNR candidates), 15 are found
in GCs. 159 XRBs, 11 in GCs, are above the completeness limit. Taken at face
value, we classified 122 XRBs as low-mass (100 above the completeness limit).
However, as discussed in §4.2, this population likely has significant
contamination from CXB sources, and may be missing other sources classified as
IMXBs (due to, e.g., intense X-ray irradiation). The X-ray luminosities of
XRB-hosting GCs are consistent with field XRBs, independent of whether they
are compared to only low-mass field XRBs (blue sources in the right panel of
Figure 10) or to the total field XRB population. This may bolster the idea
that GCs are “seeding” the field population of LMXBs (Lehmer et al., 2020).

Overall, our observations of XRB-hosting GCs in M81 is consistent with
observations of those in early-type galaxies. However, as we noted, a more
complete sample of GCs in M81 is needed before any strong conclusions may be
drawn as to what fraction of GCs may host XRBs in star-forming galaxies.

Figure 11: Left: Fits to the HMXB XLF of M81 with a cumulative, un-binned
power-law function, with and without a truncation at high luminosities
(dotted-dashed and dotted lines, respectively). The functions are fitted down
to the completeness limit, $\ell_{X}=36.3$ (dashed line). Right: Maximum
likelihood fit to the cumulative HMXB XLF using a Schechter function. The
green triangle marks the X-ray luminosity of the brightest HMXB. Contours
represent the 1-, 2-, and 3$\sigma$ confidence level. The dashed lines
represent the ‘best fit’ at $-\beta=0.96$ and a knee log-luminosity of 37.84.

###  5.2 HMXB XLF in M81

In this section we will focus on the shape and normalization of the XLF of the
HMXB population, which our experiments in §4.1 show have negligible chance
superposition/background contamination. We are especially interested in how
our method for classifying HMXBs compares to state-of-the-art X-ray based
results (e.g., L19) both in terms of shape as well as normalization. Following
the analysis conducted in Hunt et al. (2021), we examine the HMXB XLF via two
methods: first, we fit the un-binned, cumulative XLF to a power-law (PL), with
and without a high-luminosity truncation, using the IDL script MSPECFIT
(Rosolowsky, 2005). Second, we perform a Maximum Likelihood (ML) fit of the
differential XLF to a Schechter function. The former enables us to potentially
detect a break (regardless of its functional shape) at high luminosities,
which may be expected to be present near the Eddington luminosity for a
stellar-mass compact object. The latter is a robust test for the presence of
an exponential break (Mok et al., 2019).

Figure 11 shows the results of these fits. The left panel shows the PL fit to
the cumulative HMXB XLF down to the 90% completeness limit (vertical dashed
line). The index of the PL fit is given by $-\beta$, while a value $N_{c}>1$
for the truncated PL indicates a statistically significant high-energy
downturn. The right panel of Figure 11 shows the results of the ML fit, where
the best-fit index ($-\beta$) is plotted against the best fit Schechter knee
luminosity, with the contours representing the 1-, 2- and 3$\sigma$ confidence
levels, and the green triangle marking the luminosity of the brightest HMXB.
The upper limit to the knee luminosity is set to be well in excess of the
brightest HMXB to ensure convergence of the fit.

The results of both fitting methods suggest a marginal cutoff or downturn at a
luminosity just below $\ell_{X}=38$, as indicated by $N_{c}=19.02\pm 8.48$
(left) and a closed $2\sigma$ but an open $3\sigma$ ML contour (right) with a
fit of $-\beta=0.96$ and $\ell_{\rm{knee}}=37.84$. This is similar to our
results for M83, in which only the HMXB population shows marginal evidence of
a downturn (at a $\sim 2.5\sigma$ level), albeit at a higher luminosity
($\ell_{X}\lower 2.15277pt\hbox{$\;\buildrel>\over{\sim}\;$}38$). In contrast,
we found that none of the XRB populations in M101 (high-, intermediate-, or
low-mass) required a truncation or Schechter-like cutoff (Chandar et al.,
2020). We note, however, that we did not excise the SNR population using the
X-ray luminosity and color cuts as for M81 and M83, so it is possible that the
inclusion of a large population of low-luminosity SNRs in the XLFs of M101
washed out any PL deviation at high-luminosity.

We compare our PL fit for HMXBs to that found by L19. Using sub-galactic SFR
and $M_{\star}$ maps (the same shown Figure 7), they construct both a global
HMXB XLF model that scales with enclosed SFR and a ‘standard’ XLF fit for each
individual galaxy in their sample (38 galaxies in total). These fits employ a
forward-fitting model that fits both the XRB and CXB contributions
simultaneously. They find that the individual galaxy HMXB XLFs are best fit
with a single PL with a fixed high-energy cutoffs of $\ell_{c}=40.3$. For M81,
L19 reports a best fit PL index of $-1.43\pm 0.06$, which is consistent within
the errors with our fitted value of $-\beta=1.55\pm 0.05$.

The L19 global HMXB XLF model gives a slightly steeper index of $-1.66\pm
0.02$. We can use the global model to estimate how many HMXBs are expected
within the L19 ellipse, given the enclosed SFR provided by the maps. L19 gives
a global HMXB normalization of $2.06^{+0.16}_{-0.15}~{}(M_{\star}{\rm
yr}^{-1})^{-1}$, with a galaxy-specific scaling factor of $\omega=0.90$ for
M81. We estimate a total SFR of 0.25 $M_{\star}$$\rm{yr^{-1}}$ enclosed within
the L19 ellipse (this excludes 0.01 $M_{\star}$$\rm{yr^{-1}}$ within 12 arcsec
of the bulge, which hosts a bright AGN). Based on these numbers and the
functions given by Equation 4 in L19, 10 HMXBs with $\ell_{X}\geq 36.3$ are
expected within the bounds of the L19 ellipse. This is to be compared with 26
HMXBs classified by our optical methods. As discussed in §4, these are highly
likely to be genuine counterparts as the chance superposition with a high-mass
star is negligible across the whole disk.

##  6 Summary and Conclusions

We make use of multi-wavelength HST imaging data to characterize the compact
X-ray source population of M81 (using the X-ray source catalog by Lehmer et
al. 2019), a nearby spiral galaxy with moderately low SFR. We directly
characterize each X-ray source as a foreground star, a background galaxy/AGN,
a SNR (based on the X-ray luminosity/hardness criterion developed by Hunt et
al. 2021) or an XRB. In the latter case, we use color-magnitude diagrams to
tentatively identify the most likely donor as a low-, intermediate- or high-
mass star, or colors to estimate age in cases where the XRB is associated with
a stellar cluster. In summary, we find the following:

  * •

199 out of 240 X-ray sources that are found over the HST footprint of M81 are
classified as XRBs (Figures 1 and 6). Out of these, 159 are above the X-ray
completeness limit of $\ell_{X}~{}>~{}36.3$. Based on color-magnitude diagrams
of the most likely counterpart(s), we identify 100 LMXBs (no visible
counterpart), 25 IMXBs (donor mass between 3-8 $M_{\odot}$), and 34 HMXBs
(donor mass above 8 $M_{\odot}$).

  * •

After a thorough misclassification assessment using artificial sources to
quantify chance superpositions, we conclude that the HMXBs population is
robust, with a very low probability that a X-ray source will have a chance
superposition with a massive star. In contrast, X-ray sources with no
detectable counterparts likely harbor a significant population of background
AGN with no visible optical host galaxy, whereas IMXBs suffer from a non-
negligible likelihood of chance superposition (additionally, intense X-ray
irradiation may contribute to enhance the brightness and alter the colors of
genuinely low-mass donors).

  * •

15 XRBs are found in old GCs, whereas 2 are associated with young star
clusters ($<400$ My old). GCs that host XRBs tend to be more massive and more
compact than GCs that do not, similar to earlier findings in elliptical
galaxies. These have X-ray luminosities consistent with the field population,
and there is no obvious correlation between the X-ray luminosities of XRBs in
GCs and the masses or densities of their host clusters.

  * •

The XLF of HMXBs in M81 shows a marginal high-luminosity break at
$\ell_{X}=37.84$, similar to that found for M83 (Hunt et al., 2021). We note
that the emergence of such a cut-off around the Eddington limit for a stellar-
sized accretor may depend on whether the contamination from SNR at the low-
luminosity end of the XLF is properly accounted for. While this effect may be
negligible in a low star forming galaxy, it is likely to affect the XLFs of
late types with high SFRs (such as M83).

QH is partially funded by a Rackham Merit Fellowship, awarded by the
University of Michigan Rackham Graduate School. QH thanks the LSSTC Data
Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining Grant
#1829740, the Brinson Foundation, and the Moore Foundation; her participation
in the program has benefited this work. We are also grateful to Xuheng Ding,
Tommaso Treu, and Tom Maccarone for useful comments and suggestions.

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Table 3: Properties and Classifications of M81 X-ray Sources

ID | CSC ID | R.A. | Dec | $L_{\rm X}$ | V | B-V | V-I | Class | CF
---|---|---|---|---|---|---|---|---|---
M81X003 | — | 148.579 | 69.07 | 36.5 | -2.393 | — | 1.199 | LM | 1.0
M81X006 | 2CXO J095422.6+690346 | 148.595 | 69.063 | 37.1 | -0.552 | — | 2.552 | LM | 1.0
M81X007 | — | 148.618 | 69.099 | 36.6 | -4.616 | 0.382 | 0.694 | Gal | 1.0
M81X008 | 2CXO J095431.1+690506 | 148.629 | 69.085 | 36.6 | -1.636 | — | 1.497 | LM | 1.0
M81X009 | 2CXO J095434.5+690452 | 148.644 | 69.081 | 36.7 | -5.612 | 1.194 | 1.045 | (SNR) | 1.0
M81X010 | 2CXO J095436.0+690856 | 148.651 | 69.149 | 37.0 | -2.934 | — | 1.389 | (SNR) | 1.0
M81X011 | — | 148.654 | 69.078 | 36.4 | -8.706 | 1.875 | 0.520 | Star | 1.0
M81X013 | — | 148.669 | 69.038 | 36.2 | -4.473 | 2.054 | 0.976 | HM | 1.0
M81X014 | 2CXO J095440.8+690548 | 148.67 | 69.097 | 36.4 | -3.081 | 1.997 | 1.263 | LM | 2.0
M81X015 | 2CXO J095442.0+690244 | 148.675 | 69.046 | 37.0 | -1.591 | — | 1.552 | LM | 1.0
M81X016 | 2CXO J095444.3+690454 | 148.685 | 69.082 | 37.0 | -2.633 | — | 1.636 | LM | 1.0
M81X018 | 2CXO J095446.4+690513 | 148.694 | 69.087 | 37.0 | -2.5 | — | 1.650 | LM | 1.0
M81X019 | 2CXO J095446.7+691123 | 148.695 | 69.19 | 37.1 | -2.169 | — | 1.135 | LM | 1.0
M81X020 | 2CXO J095447.2+690101 | 148.697 | 69.017 | 36.8 | -2.712 | 1.421 | 2.017 | LM | 1.0
M81X021 | 2CXO J095447.4+690322 | 148.698 | 69.056 | 36.2 | -8.6 | -0.009 | 0.658 | HM | 1.0
M81X022 | 2CXO J095449.2+690538 | 148.705 | 69.094 | 36.5 | -5.155 | 0.362 | 0.365 | HM | 1.0
M81X023 | — | 148.708 | 69.194 | 37.2 | -3.142 | — | 1.816 | IM | 1.0
M81X024 | 2CXO J095452.0+690455 | 148.717 | 69.082 | 36.4 | -3.703 | — | 1.954 | IM | 1.0
M81X025 | 2CXO J095455.0+690419 | 148.73 | 69.072 | 36.2 | -3.349 | — | 1.826 | IM | 1.0
M81X026 | 2CXO J095455.8+690517 | 148.733 | 69.088 | 36.3 | -4.379 | 0.423 | 0.256 | (SNR) | 1.0
M81X027 | — | 148.738 | 69.149 | 36.5 | -5.269 | -0.067 | -0.168 | HM | 1.0
M81X028 | 2CXO J095457.6+690241 | 148.74 | 69.045 | 37.5 | -3.578 | — | 0.281 | IM | 1.0
M81X029 | 2CXO J095458.4+685922 | 148.744 | 68.99 | 36.2 | -2.986 | 0.158 | 0.169 | IM | 1.0
M81X030 | 2CXO J095458.8+690521 | 148.745 | 69.089 | 36.1 | — | — | — | LM | 1.0
M81X031 | 2CXO J095458.8+690438 | 148.745 | 69.077 | 36.5 | — | — | — | LM | 1.0
M81X032 | 2CXO J095459.8+685817 | 148.75 | 68.972 | 36.2 | -5.095 | 0.268 | 0.101 | HM | 1.0
M81X033 | 2CXO J095500.0+690745 | 148.75 | 69.129 | 38.3 | -2.514 | 2.16 | — | LM | 1.0
M81X034 | 2CXO J095500.1+690437 | 148.751 | 69.077 | 36.5 | — | — | — | LM | 1.0
M81X035 | 2CXO J095500.3+690148 | 148.752 | 69.03 | 37.1 | -4.37 | 0.841 | 1.937 | Gal | 1.0
M81X036 | 2CXO J095501.0+690726 | 148.754 | 69.124 | 38.3 | -3.293 | — | 2.512 | Gal | 1.0
M81X037 | 2CXO J095501.0+685622 | 148.754 | 68.939 | 37.5 | — | — | — | Star | 1.0
M81X038 | 2CXO J095501.7+691040 | 148.757 | 69.178 | 37.3 | -6.276 | 0.685 | 0.157 | HM | 1.0
M81X039 | 2CXO J095502.6+685621 | 148.761 | 68.939 | 37.2 | — | — | — | Star | 1.0
M81X040 | 2CXO J095505.6+685852 | 148.774 | 68.981 | 36.8 | -4.358 | 1.842 | 0.942 | HM | 1.0
M81X041 | 2CXO J095506.3+690405 | 148.777 | 69.068 | 36.8 | — | — | — | LM | 2.0
M81X042 | 2CXO J095507.2+690314 | 148.78 | 69.054 | 35.9 | -4.06 | 0.939 | 1.029 | SNR | 1.0
M81X043 | 2CXO J095507.5+690713 | 148.781 | 69.12 | 35.9 | -7.397 | 0.206 | 0.266 | IM | 1.0
M81X044 | 2CXO J095508.8+685722 | 148.787 | 68.956 | 36.9 | — | — | — | Star | 1.0
M81X045 | — | 148.79 | 69.071 | 35.8 | — | — | — | SNR | 1.0
M81X046 | 2CXO J095509.6+690743 | 148.79 | 69.129 | 37.4 | -4.855 | 1.267 | 0.819 | HM | 1.0
M81X047 | 2CXO J095509.7+690407 | 148.791 | 69.069 | 37.1 | -10.368 | 0.94 | 0.526 | LM | 1.0
M81X048 | 2CXO J095509.6+690832 | 148.791 | 69.142 | 37.2 | -5.145 | 1.008 | 0.920 | HM | 2.0
M81X049 | 2CXO J095510.2+690502 | 148.793 | 69.084 | 38.5 | -3.411 | — | 1.713 | LM | 2.0
M81X050 | — | 148.793 | 68.99 | 35.6 | -4.884 | 0.058 | 0.011 | HM | 1.0
M81X051 | 2CXO J095510.6+690843 | 148.795 | 69.145 | 37.3 | -5.372 | 0.515 | 0.411 | HM | 1.0
M81X052 | 2CXO J095511.8+685748 | 148.799 | 68.963 | 36.9 | -1.538 | — | 2.194 | LM | 1.0
M81X053 | 2CXO J095512.2+690344 | 148.801 | 69.062 | 36.2 | — | — | — | LM | 2.0
M81X054 | 2CXO J095512.4+690411 | 148.802 | 69.07 | 35.9 | -2.529 | — | 2.212 | LM | 1.0
M81X055 | 2CXO J095512.4+690121 | 148.802 | 69.023 | 36.7 | — | — | — | LM | 1.0
M81X056 | 2CXO J095512.6+690141 | 148.803 | 69.028 | 36.0 | -6.722 | 0.408 | 0.252 | Gal | 1.0
M81X057 | 2CXO J095514.1+690740 | 148.809 | 69.128 | 36.3 | -4.388 | 0.216 | 0.282 | IM | 1.0
M81X058 | 2CXO J095514.5+690641 | 148.811 | 69.111 | 36.4 | -3.462 | 0.625 | 0.799 | IM | 1.0
M81X059 | 2CXO J095515.2+690230 | 148.813 | 69.042 | 36.6 | -2.752 | — | 1.415 | LM | 1.0
M81X060 | 2CXO J095515.2+690537 | 148.814 | 69.094 | 36.5 | — | — | — | LM | 2.0
M81X061 | 2CXO J095516.6+690512 | 148.819 | 69.087 | 36.4 | — | — | — | LM | 2.0
M81X062 | 2CXO J095518.0+685820 | 148.825 | 68.972 | 36.0 | -2.277 | — | 1.801 | LM | 1.0
M81X063 | 2CXO J095518.2+685930 | 148.826 | 68.992 | 36.4 | -5.193 | 0.615 | 0.860 | HM | 1.0
M81X064 | 2CXO J095519.6+690732 | 148.832 | 69.126 | 36.3 | -4.12 | 0.65 | 0.799 | SNR | 1.0
M81X065 | 2CXO J095519.9+690351 | 148.833 | 69.064 | 36.5 | — | — | — | LM | 2.0
M81X066 | 2CXO J095521.0+690313 | 148.838 | 69.054 | 36.1 | — | — | — | LM | 2.0
M81X067 | 2CXO J095521.1+685855 | 148.838 | 68.982 | 36.4 | -2.802 | — | 1.394 | LM | 1.0
M81X068 | 2CXO J095521.4+690831 | 148.84 | 69.142 | 36.6 | -5.571 | 1.543 | 0.924 | SNR | 1.0
M81X069 | 2CXO J095521.7+690345 | 148.841 | 69.062 | 36.6 | — | — | — | LM | 2.0
M81X070 | 2CXO J095521.8+690522 | 148.841 | 69.09 | 37.4 | — | — | — | LM | 2.0
M81X071 | 2CXO J095521.8+690637 | 148.841 | 69.11 | 37.7 | -10.613 | 0.92 | 0.864 | LM | 1.0
M81X072 | 2CXO J095521.9+690228 | 148.842 | 69.041 | 36.0 | -3.296 | — | 1.397 | LM | 2.0
M81X073 | 2CXO J095522.0+690518 | 148.842 | 69.089 | 36.7 | -9.921 | 1.234 | 0.775 | LM | 1.0
M81X074 | 2CXO J095522.1+690510 | 148.842 | 69.086 | 38.2 | — | — | — | LM | 2.0
M81X075 | 2CXO J095522.7+690237 | 148.845 | 69.044 | 35.8 | -3.98 | — | 1.438 | IM | 2.0
M81X076 | 2CXO J095523.7+685849 | 148.849 | 68.98 | 37.2 | -2.347 | — | 2.225 | LM | 1.0
M81X077 | 2CXO J095524.2+690957 | 148.851 | 69.166 | 38.8 | -2.534 | — | 1.242 | LM | 1.0
M81X078 | 2CXO J095524.2+690439 | 148.851 | 69.078 | 36.7 | — | — | — | LM | 2.0
M81X079 | 2CXO J095524.7+690113 | 148.853 | 69.02 | 38.2 | -7.485 | 1.003 | 0.601 | HM | 1.0
M81X080 | 2CXO J095525.6+690458 | 148.857 | 69.083 | 36.1 | — | — | — | (SNR) | 2.0
M81X081 | — | 148.86 | 69.067 | 36.6 | — | — | — | LM | 2.0
M81X082 | 2CXO J095526.6+690523 | 148.861 | 69.09 | 36.2 | — | — | — | LM | 2.0
M81X083 | 2CXO J095526.9+690541 | 148.863 | 69.095 | 36.5 | — | — | — | LM | 3.0
M81X084 | 2CXO J095527.2+690247 | 148.864 | 69.047 | 37.3 | — | — | — | LM | 2.0
M81X085 | 2CXO J095527.2+690250 | 148.864 | 69.047 | 36.3 | — | — | — | LM | 3.0
M81X086 | 2CXO J095527.5+690631 | 148.865 | 69.109 | 36.0 | -1.982 | — | 2.010 | LM | 2.0
M81X087 | 2CXO J095527.7+690704 | 148.866 | 69.118 | 36.3 | -3.491 | -0.087 | 0.323 | IM | 1.0
M81X088 | 2CXO J095527.7+690400 | 148.866 | 69.067 | 37.1 | — | — | — | LM | 2.0
M81X089 | 2CXO J095528.2+690541 | 148.867 | 69.095 | 35.9 | — | — | — | LM | 2.0
M81X090 | 2CXO J095528.4+690244 | 148.869 | 69.046 | 36.7 | — | — | — | (SNR) | 2.0
M81X091 | 2CXO J095528.8+690613 | 148.87 | 69.104 | 37.2 | -2.861 | — | 0.422 | LM | 2.0
M81X092 | 2CXO J095529.1+690320 | 148.871 | 69.056 | 36.8 | — | — | — | LM | 2.0
M81X093 | — | 148.873 | 69.047 | 35.8 | — | — | — | LM | 2.0
M81X094 | 2CXO J095530.1+690318 | 148.876 | 69.055 | 36.9 | — | — | — | LM | 2.0
M81X095 | 2CXO J095530.2+690246 | 148.876 | 69.046 | 36.5 | — | — | — | LM | 2.0
M81X096 | 2CXO J095530.3+690039 | 148.877 | 69.011 | 35.9 | -2.849 | — | 1.372 | IM | 1.0
M81X097 | — | 148.877 | 69.071 | 36.5 | — | — | — | LM | 2.0
M81X098 | — | 148.878 | 69.062 | 35.9 | — | — | — | LM | 2.0
M81X099 | — | 148.878 | 69.062 | 36.2 | — | — | — | LM | 2.0
M81X100 | 2CXO J095531.0+690055 | 148.879 | 69.015 | 35.8 | -4.512 | 0.092 | 0.006 | (SNR) | 1.0
M81X101 | 2CXO J095531.1+690144 | 148.88 | 69.029 | 35.9 | -4.377 | — | 1.695 | Gal | 1.0
M81X102 | 2CXO J095531.2+690418 | 148.881 | 69.072 | 37.6 | — | — | — | LM | 2.0
M81X103 | — | 148.885 | 69.069 | 36.3 | — | — | — | LM | 2.0
M81X104 | 2CXO J095532.6+690231 | 148.886 | 69.042 | 37.1 | -3.244 | — | 2.022 | IM | 1.0
M81X105 | 2CXO J095532.6+690352 | 148.886 | 69.065 | 37.8 | — | — | — | LM | 2.0
M81X106 | 2CXO J095532.6+690513 | 148.886 | 69.087 | 36.3 | — | — | — | (SNR) | 2.0
M81X107 | — | 148.886 | 69.073 | 36.1 | — | — | — | LM | 2.0
M81X108 | 2CXO J095532.8+690639 | 148.887 | 69.111 | 35.9 | -9.241 | 1.173 | 0.874 | LM | 1.0
M81X110 | 2CXO J095532.9+690033 | 148.887 | 69.009 | 39.2 | -4.326 | 0.066 | -0.025 | IM | 1.0
M81X111 | — | 148.888 | 69.067 | 36.9 | — | — | — | LM | 2.0
M81X112 | — | 148.888 | 69.068 | 36.8 | — | — | — | LM | 2.0
M81X113 | 2CXO J095533.1+690354 | 148.888 | 69.065 | 39.4 | — | — | — | Nucleus | 1.0
M81X117 | 2CXO J095533.7+690124 | 148.891 | 69.023 | 36.3 | — | — | — | LM | 1.0
M81X118 | — | 148.892 | 69.065 | 36.8 | — | — | — | LM | 2.0
M81X119 | 2CXO J095534.0+690713 | 148.892 | 69.12 | 37.1 | -6.572 | 0.297 | 0.267 | HM | 1.0
M81X120 | 2CXO J095534.1+690618 | 148.892 | 69.105 | 35.9 | -3.622 | 0.695 | 0.146 | IM | 1.0
M81X121 | 2CXO J095534.3+690350 | 148.893 | 69.064 | 37.5 | — | — | — | LM | 2.0
M81X122 | — | 148.893 | 69.063 | 37.0 | — | — | — | LM | 2.0
M81X123 | — | 148.894 | 69.061 | 36.6 | -8.698 | 1.319 | 0.983 | LM | 1.0
M81X124 | 2CXO J095534.5+690250 | 148.894 | 69.047 | 37.4 | — | — | — | LM | 2.0
M81X125 | 2CXO J095534.6+690453 | 148.894 | 69.082 | 37.5 | — | — | — | LM | 2.0
M81X126 | 2CXO J095534.7+690351 | 148.895 | 69.064 | 37.8 | — | — | — | LM | 2.0
M81X127 | 2CXO J095534.8+690408 | 148.895 | 69.069 | 37.5 | — | — | — | LM | 2.0
M81X128 | 2CXO J095534.9+690342 | 148.896 | 69.062 | 38.2 | — | — | — | LM | 2.0
M81X129 | 2CXO J095535.2+690316 | 148.897 | 69.054 | 37.8 | — | — | — | LM | 2.0
M81X130 | 2CXO J095535.3+690352 | 148.897 | 69.065 | 37.7 | — | — | — | LM | 2.0
M81X131 | 2CXO J095535.3+690638 | 148.898 | 69.111 | 37.2 | -4.819 | 0.88 | 1.699 | HM | 1.0
M81X132 | 2CXO J095535.4+690557 | 148.898 | 69.099 | 36.8 | — | — | — | LM | 2.0
M81X133 | 2CXO J095536.2+690245 | 148.901 | 69.046 | 36.5 | — | — | — | (SNR) | 2.0
M81X134 | 2CXO J095536.6+690632 | 148.903 | 69.109 | 37.2 | -7.988 | 1.351 | 1.010 | LM | 1.0
M81X135 | 2CXO J095536.9+685656 | 148.904 | 68.949 | 36.9 | -2.325 | 0.508 | 1.195 | LM | 1.0
M81X136 | 2CXO J095536.9+690439 | 148.904 | 69.078 | 37.0 | — | — | — | LM | 2.0
M81X137 | 2CXO J095536.9+690433 | 148.904 | 69.076 | 37.5 | — | — | — | LM | 2.0
M81X138 | 2CXO J095537.2+690207 | 148.905 | 69.035 | 36.1 | -9.593 | 1.304 | 1.006 | LM | 1.0
M81X139 | 2CXO J095537.5+690457 | 148.907 | 69.083 | 36.9 | — | — | — | LM | 2.0
M81X140 | 2CXO J095537.6+685833 | 148.907 | 68.976 | 36.6 | -4.106 | 0.853 | 0.945 | HM | 1.0
M81X141 | 2CXO J095537.7+690327 | 148.907 | 69.058 | 36.1 | -9.272 | 1.016 | 0.758 | LM | 1.0
M81X142 | — | 148.91 | 68.943 | 36.5 | -2.544 | — | 1.228 | LM | 2.0
M81X143 | 2CXO J095538.9+690423 | 148.912 | 69.073 | 36.4 | — | — | — | LM | 2.0
M81X144 | 2CXO J095539.9+690348 | 148.916 | 69.064 | 36.5 | — | — | — | LM | 2.0
M81X145 | 2CXO J095540.3+690314 | 148.918 | 69.054 | 36.4 | — | — | — | LM | 2.0
M81X146 | 2CXO J095540.6+690105 | 148.92 | 69.018 | 36.1 | — | — | — | LM | 3.0
M81X147 | 2CXO J095540.7+690258 | 148.92 | 69.05 | 36.1 | — | — | — | LM | 2.0
M81X148 | 2CXO J095541.8+690301 | 148.925 | 69.051 | 35.9 | — | — | — | LM | 2.0
M81X149 | 2CXO J095541.9+690504 | 148.925 | 69.085 | 36.2 | — | — | — | LM | 3.0
M81X150 | 2CXO J095542.1+690336 | 148.926 | 69.06 | 38.0 | -6.606 | 0.307 | 0.364 | HM | 1.0
M81X151 | — | 148.926 | 69.116 | 36.2 | -2.067 | — | 1.567 | SNR | 1.0
M81X152 | 2CXO J095542.5+690320 | 148.927 | 69.056 | 37.1 | — | — | — | LM | 2.0
M81X153 | 2CXO J095542.5+691127 | 148.928 | 69.191 | 36.8 | -4.71 | 1.782 | 0.899 | (SNR) | 1.0
M81X154 | 2CXO J095542.9+690522 | 148.929 | 69.09 | 36.0 | — | — | — | LM | 1.0
M81X155 | 2CXO J095543.1+690445 | 148.93 | 69.079 | 36.6 | — | — | — | LM | 2.0
M81X156 | 2CXO J095543.2+690423 | 148.93 | 69.073 | 36.5 | — | — | — | LM | 2.0
M81X157 | 2CXO J095543.5+690355 | 148.932 | 69.065 | 36.3 | — | — | — | LM | 2.0
M81X158 | 2CXO J095543.8+690551 | 148.932 | 69.098 | 36.5 | -4.485 | 2.117 | 1.364 | IM | 1.0
M81X159 | 2CXO J095543.7+685905 | 148.932 | 68.985 | 37.4 | — | — | — | LM | 1.0
M81X160 | 2CXO J095544.5+690534 | 148.936 | 69.093 | 36.8 | -5.657 | 0.723 | 1.113 | HM | 1.0
M81X161 | 2CXO J095544.6+691003 | 148.936 | 69.168 | 36.9 | -6.616 | 0.128 | 0.049 | HM | 1.0
M81X162 | 2CXO J095545.3+690253 | 148.939 | 69.048 | 36.1 | -4.253 | 0.58 | 0.838 | (SNR) | 3.0
M81X163 | — | 148.939 | 69.038 | 35.9 | — | — | — | Gal | 1.0
M81X164 | 2CXO J095545.8+690300 | 148.941 | 69.05 | 37.4 | -10.078 | 1.154 | 0.829 | LM | 1.0
M81X165 | 2CXO J095547.0+690551 | 148.946 | 69.098 | 37.9 | -9.11 | 1.519 | 1.164 | LM | 1.0
M81X166 | 2CXO J095546.9+690536 | 148.946 | 69.093 | 36.3 | -3.238 | — | 1.865 | IM | 1.0
M81X167 | 2CXO J095547.9+685928 | 148.95 | 68.991 | 36.3 | -5.454 | 0.433 | 0.016 | SNR | 1.0
M81X168 | 2CXO J095548.2+685915 | 148.951 | 68.988 | 36.4 | -3.217 | — | 1.696 | IM | 2.0
M81X169 | 2CXO J095548.7+690140 | 148.953 | 69.028 | 36.2 | -2.954 | — | 2.318 | IM | 2.0
M81X170 | 2CXO J095549.3+685836 | 148.956 | 68.977 | 37.6 | -6.873 | 0.694 | 0.438 | HM | 1.0
M81X171 | 2CXO J095549.4+690811 | 148.956 | 69.137 | 38.0 | -2.223 | — | 1.808 | LM | 1.0
M81X172 | 2CXO J095549.7+690531 | 148.958 | 69.092 | 38.7 | -7.053 | 1.218 | 0.915 | LM | 1.0
M81X173 | 2CXO J095549.8+690300 | 148.958 | 69.05 | 36.1 | -3.744 | — | 0.797 | IM | 2.0
M81X174 | 2CXO J095550.0+690714 | 148.959 | 69.121 | 36.5 | -5.162 | 0.162 | 0.104 | HM | 2.0
M81X175 | 2CXO J095550.1+690540 | 148.959 | 69.095 | 36.3 | — | — | — | LM | 1.0
M81X176 | 2CXO J095550.5+685832 | 148.961 | 68.976 | 36.7 | -2.688 | — | 1.234 | LM | 1.0
M81X177 | 2CXO J095551.0+690512 | 148.963 | 69.087 | 36.4 | — | — | — | (SNR) | 2.0
M81X178 | 2CXO J095551.5+691104 | 148.964 | 69.185 | 36.7 | -2.902 | 2.969 | 1.241 | IM | 1.0
M81X179 | 2CXO J095551.5+685910 | 148.965 | 68.986 | 36.0 | -5.353 | 0.356 | 0.416 | HM | 2.0
M81X180 | 2CXO J095551.8+690739 | 148.966 | 69.128 | 36.7 | -9.302 | 1.285 | 0.951 | LM | 1.0
M81X181 | 2CXO J095552.4+685625 | 148.968 | 68.94 | 36.5 | -2.508 | -2.176 | 2.398 | IM | 1.0
M81X182 | 2CXO J095552.4+690306 | 148.969 | 69.052 | 38.2 | — | — | — | LM | 2.0
M81X183 | 2CXO J095553.1+685926 | 148.971 | 68.991 | 37.8 | -3.545 | -0.28 | -0.302 | HM | 1.0
M81X184 | 2CXO J095553.2+690207 | 148.972 | 69.035 | 36.9 | -5.731 | 1.087 | 1.019 | HM | 1.0
M81X185 | 2CXO J095553.3+690446 | 148.972 | 69.08 | 36.1 | -4.86 | 1.256 | 0.993 | (SNR) | 1.0
M81X186 | 2CXO J095553.6+690434 | 148.973 | 69.076 | 37.1 | — | — | — | LM | 1.0
M81X187 | 2CXO J095554.2+690346 | 148.976 | 69.063 | 36.3 | — | — | — | (SNR) | 1.0
M81X188 | 2CXO J095554.9+690055 | 148.979 | 69.016 | 37.5 | -9.38 | 1.376 | 1.098 | LM | 1.0
M81X189 | 2CXO J095554.9+690239 | 148.979 | 69.044 | 36.9 | -5.432 | 1.408 | 1.348 | Gal | 2.0
M81X190 | 2CXO J095555.5+691007 | 148.981 | 69.169 | 36.7 | -4.442 | 0.875 | 0.815 | HM | 1.0
M81X191 | 2CXO J095555.3+685859 | 148.981 | 68.983 | 36.1 | -4.784 | 0.355 | 0.353 | (SNR) | 2.0
M81X192 | 2CXO J095555.6+690814 | 148.982 | 69.137 | 36.9 | -2.299 | — | 1.085 | LM | 1.0
M81X193 | 2CXO J095555.7+690901 | 148.982 | 69.15 | 36.4 | -3.554 | 0.545 | 0.422 | IM | 1.0
M81X194 | 2CXO J095555.9+690515 | 148.983 | 69.088 | 36.3 | -2.578 | — | 1.946 | LM | 2.0
M81X195 | 2CXO J095556.0+690358 | 148.984 | 69.066 | 36.1 | — | — | — | (SNR) | 2.0
M81X196 | 2CXO J095556.0+690312 | 148.984 | 69.053 | 36.6 | — | — | — | (SNR) | 1.0
M81X197 | 2CXO J095556.5+690802 | 148.986 | 69.134 | 37.8 | -5.53 | 1.17 | 1.417 | LM | 2.0
M81X198 | 2CXO J095557.6+690436 | 148.99 | 69.077 | 37.8 | -4.561 | 0.024 | — | IM | 1.0
M81X199 | 2CXO J095558.5+690525 | 148.994 | 69.091 | 37.6 | — | — | — | LM | 1.0
M81X200 | 2CXO J095559.1+690617 | 148.997 | 69.105 | 37.2 | -3.48 | — | 1.190 | IM | 1.0
M81X201 | — | 149.0 | 69.093 | 36.2 | -6.115 | 2.352 | 1.376 | Gal | 1.0
M81X202 | 2CXO J095600.1+690418 | 149.001 | 69.072 | 36.5 | -3.374 | -0.105 | — | (SNR) | 1.0
M81X203 | — | 149.001 | 69.021 | 35.6 | -4.979 | 2.101 | 1.158 | HM | 2.0
M81X204 | — | 149.007 | 69.005 | 35.8 | -5.234 | -0.184 | 0.055 | HM | 1.0
M81X205 | 2CXO J095601.9+685859 | 149.008 | 68.983 | 37.0 | -6.296 | 0.283 | 0.324 | HM | 1.0
M81X206 | 2CXO J095602.6+685935 | 149.011 | 68.993 | 37.6 | -4.437 | 0.137 | 0.810 | HM | 2.0
M81X207 | 2CXO J095602.7+685844 | 149.011 | 68.979 | 37.1 | -5.699 | 1.976 | -0.487 | HM | 1.0
M81X208 | 2CXO J095602.6+690547 | 149.011 | 69.096 | 36.6 | -2.912 | — | 1.610 | IM | 1.0
M81X209 | 2CXO J095602.9+690217 | 149.013 | 69.038 | 36.7 | -3.485 | 1.138 | 1.664 | IM | 2.0
M81X210 | 2CXO J095603.2+690107 | 149.013 | 69.019 | 36.4 | -1.603 | — | 2.348 | LM | 1.0
M81X211 | — | 149.014 | 69.001 | 36.2 | -6.076 | 0.629 | 0.506 | HM | 1.0
M81X212 | 2CXO J095604.0+690726 | 149.017 | 69.124 | 36.3 | -2.56 | — | 2.097 | LM | 1.0
M81X213 | 2CXO J095604.8+690344 | 149.02 | 69.062 | 36.3 | -8.314 | 0.044 | 0.120 | (SNR) | 1.0
M81X214 | 2CXO J095604.7+685840 | 149.02 | 68.978 | 36.9 | -3.822 | 3.515 | 1.616 | IM | 1.0
M81X215 | — | 149.023 | 69.112 | 36.2 | -8.904 | 1.192 | 0.918 | LM | 1.0
M81X216 | 2CXO J095606.0+685941 | 149.025 | 68.995 | 37.0 | -4.358 | 1.851 | 1.720 | Gal | 1.0
M81X217 | 2CXO J095606.0+690833 | 149.025 | 69.143 | 36.8 | -5.335 | 0.712 | 0.606 | HM | 1.0
M81X218 | 2CXO J095607.7+690325 | 149.032 | 69.057 | 37.0 | -4.637 | 0.74 | 1.172 | HM | 1.0
M81X219 | 2CXO J095608.1+690142 | 149.034 | 69.029 | 36.0 | -3.381 | 1.961 | 1.163 | IM | 1.0
M81X220 | 2CXO J095608.9+690106 | 149.037 | 69.019 | 37.6 | -5.432 | -0.141 | 0.149 | HM | 1.0
M81X221 | — | 149.038 | 68.993 | 36.0 | -3.922 | -0.058 | -0.181 | HM | 2.0
M81X222 | — | 149.052 | 69.104 | 36.4 | -2.258 | — | 1.823 | LM | 2.0
M81X223 | 2CXO J095613.6+690631 | 149.056 | 69.109 | 37.3 | -2.259 | 0.716 | 1.094 | LM | 1.0
M81X224 | 2CXO J095613.7+685724 | 149.057 | 68.957 | 37.4 | — | — | — | Star | 1.0
M81X225 | 2CXO J095614.3+690248 | 149.06 | 69.047 | 37.1 | — | — | — | LM | 1.0
M81X226 | 2CXO J095614.6+690339 | 149.061 | 69.061 | 36.8 | -4.918 | 1.272 | 1.047 | Gal | 1.0
M81X227 | 2CXO J095614.9+685732 | 149.062 | 68.959 | 37.3 | -5.357 | 0.913 | 0.523 | HM | 1.0
M81X228 | 2CXO J095616.3+690119 | 149.068 | 69.022 | 36.4 | -2.977 | — | 1.805 | IM | 1.0
M81X229 | 2CXO J095616.5+685649 | 149.069 | 68.947 | 37.1 | -3.034 | 0.886 | 0.936 | IM | 1.0
M81X230 | 2CXO J095617.0+685820 | 149.071 | 68.972 | 37.5 | -5.536 | 0.901 | 0.374 | HM | 1.0
M81X231 | — | 149.076 | 69.052 | 36.8 | -2.407 | — | 2.423 | LM | 1.0
M81X232 | 2CXO J095619.7+690201 | 149.083 | 69.034 | 36.9 | -3.746 | 0.79 | 0.482 | IM | 1.0
M81X233 | 2CXO J095622.2+690220 | 149.092 | 69.039 | 36.5 | -3.226 | — | 1.395 | IM | 1.0
M81X234 | 2CXO J095622.3+690446 | 149.093 | 69.08 | 36.6 | -2.734 | — | 1.652 | (SNR) | 2.0
M81X235 | — | 149.098 | 69.03 | 36.1 | -2.855 | 1.09 | 2.473 | IM | 1.0
M81X236 | 2CXO J095624.0+690009 | 149.1 | 69.003 | 36.6 | -4.584 | 0.512 | 0.778 | HM | 1.0
M81X237 | 2CXO J095628.0+690102 | 149.117 | 69.017 | 37.4 | -5.536 | 0.273 | 0.599 | HM | 1.0
M81X238 | 2CXO J095630.8+690222 | 149.128 | 69.04 | 36.8 | -2.48 | — | 1.762 | LM | 1.0
M81X239 | 2CXO J095631.0+685837 | 149.129 | 68.977 | 37.0 | -2.224 | 1.037 | 2.038 | LM | 1.0
M81X240 | 2CXO J095632.5+685714 | 149.135 | 68.954 | 36.9 | — | — | — | LM | 1.0
M81X241 | 2CXO J095633.4+690035 | 149.139 | 69.01 | 36.5 | -2.098 | — | 1.464 | LM | 2.0
M81X242 | 2CXO J095633.5+690331 | 149.14 | 69.059 | 37.3 | -1.704 | 1.187 | 1.972 | LM | 1.0
M81X243 | 2CXO J095636.4+690028 | 149.152 | 69.008 | 37.9 | -8.657 | 1.029 | 0.779 | HM | 1.0
M81X244 | 2CXO J095642.0+685858 | 149.174 | 68.983 | 36.7 | -4.448 | -0.224 | -0.081 | HM | 1.0
M81X245 | 2CXO J095645.2+690108 | 149.189 | 69.019 | 36.7 | -2.038 | -0.169 | 1.207 | LM | 1.0
M81X246 | — | 149.198 | 69.064 | 36.9 | -2.889 | 1.17 | 0.746 | IM | 1.0
M81X248 | — | 149.214 | 68.977 | 36.6 | -4.075 | 0.378 | 0.588 | IM | 1.0
M81X249 | 2CXO J095651.4+685606 | 149.214 | 68.935 | 37.8 | -2.469 | — | 1.652 | LM | 1.0
M81X250 | — | 149.227 | 69.032 | 36.9 | -2.051 | — | 1.344 | LM | 1.0
M81X251 | 2CXO J095658.2+690046 | 149.243 | 69.013 | 37.5 | -7.659 | 0.517 | 0.760 | HM | 1.0

Note. — Properties and classifications of all M81 X-ray sources identified in
Lehmer et al. (2019) that fall within the footprint of the HST image. For each
source, the ID is the galaxy name and the ID number assigned in Lehmer et al.
(2019). X-ray luminosities are in units log erg s-1, and magnitudes are
absolute mags estimated at a distance of 3.63 Mpc. The classification for each
source is given, with (SNR) representing SNRs identified using our HR-LX
criterion, and italics indicating XRBs associated with clusters. A confidence
flag (CF) is assigned to each source based on the “strength” of the
identification of the X-ray emitter: a CF of 1 represents the most certain
classifications (i.e. those determined in other studies, or XRBs with a clear
donor, with multiple candidates of similar mass, or a clear absence of a
donor); CF ratings of 2 or 3 may indicate that a source is in a dust-obscured
region, such as near the nucleus or along a dust lane, since the presence of
heavy dust could potentially mask high-mass stars, background galaxies, and
clusters, leading to possible misidentifications.

Figure 12: Identified point sources within the 1- and 2-$\sigma$ radii for
each X-ray source, with the most likely donor circled in red. The
classifications of each source are also given, with LM, IM, and HM
representing our LMXBs, IMXBs, and HMXBs, respectively, and those in italics
represent cluster XRBs. Sources classified as (SNR) represent SNRs identified
using our HR-LX criterion; all other SNRs are identified within published
catalogs (Nantais et al., 2010, 2011; Santiago-Cortés et al., 2010, see §3.1).
The size of each image is roughly $3.7\times 3.7$ arcseconds. Figure 12:
(continued) Figure 12: (continued) Figure 12: (continued) Figure 12:
(continued) Figure 12: (continued) Figure 12: (continued) Figure 12:
(continued)