# Chandra and HST studies of the X-ray sources in the Globular Cluster NGC 362

Gourav Kumawat,1,2 Craig O. Heinke,2 Haldan N. Cohn,3 Phyllis M. Lugger3
1Department of Physics, Indian Institute of Science Education and Research,
Bhopal 462066, India
2 Department of Physics, University of Alberta, Edmonton, AB T6G 2G7, Canada
3 Department of Astronomy, Indiana University, 727 E. Third St., Bloomington,
IN 47405, USA E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We analyse a Chandra observation of the rich globular cluster NGC 362, finding
33 X-ray sources within 1’ (1.2 half-mass radii) of the cluster center.
Spectral analysis of the brightest source (X1) shows blackbody-like emission,
indicating it is likely a quiescent low-mass X-ray binary; we find a possible
counterpart that falls in the sub-subgiant region. We use HST UV Globular
Cluster Survey (HUGS) photometry to identify 15 potential optical/UV
counterparts to these X-ray sources, including two background AGN. We identify
no likely CVs, probably due to crowding in optical filters in the core, though
we predict of order 8 CVs among the detected X-ray sources. We identify three
other sub-subgiants and two red straggler counterparts, which are likely
powered by coronal activity, along with five other potential coronally active
binary counterparts to three X-ray sources. Finally, we note two unusual
counterpart candidates that lie to the red of the red giant branch in
$V_{606}-I_{814}$, and shift well to the blue of the red giant branch in
ultraviolet colour-magnitude diagrams. These systems seem to contain a red
giant with a distorted evolutionary history, plus a bright blue light source,
either a blue straggler star (an Algol-like system) or an accreting white
dwarf (a long-period CV, or a symbiotic star).

###### keywords:

globular clusters: individual: NGC 362 – binaries: close – X-rays: binaries –
novae, cataclysmic variables – stars: activity – Hertzsprung-Russell and
colour-magnitude diagrams

††pubyear: 2023††pagerange: Chandra and HST studies of the X-ray sources in
the Globular Cluster NGC 362–A13

##  1 INTRODUCTION

Globular clusters (GCs) are stellar systems characterized by high densities,
leading to frequent gravitational interactions between stars. These
interactions give rise to various dynamical processes, including collisions
and mass transfers, which can result in the formation of exotic binary star
systems such as millisecond pulsars (MSPs), cataclysmic variables (CVs), and
low-mass X-ray binaries (LMXBs), among others. Early observations of bright
LMXBs (in Galactic globular clusters, generally neutron stars accreting from
low-mass companion stars via an accretion disc) showed that they were of order
100 times more common in globular clusters per unit mass than the rest of the
Galaxy (Clark, 1975), and indeed the clusters with the highest predicted rates
of stellar interaction are the most likely to contain LMXBs (Verbunt & Hut,
1987). This can be attributed to the tendency of LMXB progenitor binaries to
become unbound gravitationally when the more massive star goes supernova; this
makes LMXBs rare in the field, but neutron stars can gain a new partner in
globular clusters.

The study of faint X-ray binaries with $L_{X}$ < 1034.5 erg/s in GCs was
pioneered by Hertz & Grindlay (1983). The advent of the Chandra X-Ray
Observatory and the Hubble Space Telescope (HST) with their enhanced
resolution and improved sensitivity made it feasible to investigate faint
X-ray binaries within the dense stellar environments of GCs. Among these faint
X-ray binaries, the brightest are classified as quiescent LMXBs (qLMXBs),
which are LMXBs in which accretion onto the neutron star is low to
nonexistent. X-ray emission from qLMXBs can occur through thermal emission
from the neutron star surface or continued low-level accretion onto the
neutron star. Many qLMXB X-ray spectra are dominated by bright, soft
blackbody-like X-ray emission, enabling clear identification in globular
clusters (Rutledge et al., 2002; Heinke et al., 2003a; Guillot et al., 2009).
These systems are primarily formed in GCs through stellar encounters, and
their numbers are correlated with the total encounter rate of the cluster
(Heinke et al., 2003a; Pooley & Hut, 2006). While their optical counterparts
appear blue, the accretion disk is generally faint, as their mass transfer
rates are low (e.g. Haggard et al., 2004), leading to high X-ray/optical flux
ratios (Verbunt et al., 2008).

MSPs are believed to be the descendants of LMXBs (Alpar et al., 1982), as the
neutron star magnetic field is reduced and the neutron star spin increased
during the recycling process. Their X-ray emission may include hard nonthermal
synchrotron pulsed emission from their magnetosphere (Saito et al., 1997),
hard nonthermal shock emission from a collision between the pulsar wind and a
stellar wind (Wadiasingh et al., 2017). However, X-rays from most MSPs are
dominated by thermal blackbody-like emission from the heated polar caps of the
neutron star, such that they are typically soft X-ray sources with $L_{X}\sim
10^{30-31}$ erg/s (Zavlin et al., 2002; Bogdanov et al., 2006). MSP numbers
are also correlated with the total encounter rate of the cluster (Bagchi et
al., 2011; Bahramian et al., 2013). Their optical counterparts may be helium
white dwarfs (e.g. Edmonds et al., 2001; Chen et al., 2023), or nondegenerate
stars, so-called ’spiders’, which may show unusual evolution and heating
(Ferraro et al., 2001; Cadelano et al., 2015).

Cataclysmic variables (CVs) are white dwarfs (WDs) accreting from a main-
sequence or subgiant companion star, via Roche Lobe Overflow (RLOF). Their
X-rays are produced by thermal hot plasma, leading to relatively hard X-ray
spectra and X-ray luminosities of typically $L_{X}<10^{32}$ erg/s (e.g. Heinke
et al., 2005). While CVs are formed in the densest globular clusters, their
progenitors are also destroyed in many globular clusters, and the effects of
dynamics on their population is the subject of current research (Cool et al.,
2013; Cheng et al., 2018; Belloni et al., 2019; Heinke et al., 2020). White
dwarfs may accrete from evolved (red giant or subgiant) stars via either
Roche-lobe overflow or from a stellar wind. In the latter case, they are known
as symbiotic stars (Luna et al., 2013). (If a neutron star or black hole
accretes from a red giant wind, this is termed a symbiotic X-ray binary.) No
confirmed symbiotic stars have been identified in globular clusters
(Henleywillis et al., 2018; Bahramian et al., 2020), which may be explained by
the destruction of wide binaries in clusters (Belloni et al., 2020).

Active binaries (ABs) consist of main-sequence or (sub)giant stars in a binary
system that emit X-rays due to coronal activity on one or both stars (Güdel,
2004). Their numbers are not increased by dynamical processes in clusters;
instead, they are likely decreased by the destruction of wide binaries in all
clusters (Verbunt, 2000; Cheng et al., 2018; Heinke et al., 2020). To first
order, their numbers appear to scale with the total mass of the cluster (Bassa
et al., 2004, 2008).

Active binaries may be identified in several unusual places in colour-
magnitude diagrams (CMDs); above the main sequence, below the subgiant branch,
or to the red of the giant branch. Binary stars will naturally appear above
the main sequence, by up to 0.75 magnitudes (or a factor of 2). Sub-subgiants
(SSGs) are redder than the main-sequence, but fainter than subgiant stars,
while red straggler stars (RSS) lie to the red of the red giant branch (Geller
et al., 2017). Their unusual CMD locations may result from rapid rotation in
subgiants or giants due to tidal synchronization in a close binary system. The
strong magnetic fields generated in these stars inhibit convection, leading to
the formation of large starspots, radius inflation, and lower-than-expected
average surface temperatures and luminosities (Leiner et al., 2022). The
emission of X-rays from SSGs is a consequence of these strong magnetic fields.

The globular cluster NGC 362 is located 8.8 kpc away (Baumgardt & Vasiliev,
2021), $\sim$1 degree north of the northern end of the Small Magellanic
Cloud’s (SMC) bar. The cluster experiences a reddening of approximately 0.05
mag, and its half-mass radius is determined to be 0.82 arcmin (Harris, 1996,
2010 revision). Its metallicity is [Fe/H]=-1.3, and its age is estimated at 11
Gyr (Vasiliev & Baumgardt, 2021). It has a relatively high mass ($2.5\times
10^{5}$ $\mathrm{M_{\sun}}$, Vasiliev & Baumgardt 2021), may be core-collapsed
Harris (1996, 2010 revision), and has one of the highest estimated stellar
encounter rates among Galactic globular clusters, $0.74\pm 0.13$ the rate for
47 Tucanae (Bahramian et al., 2013). A preliminary report of Chandra and HST
analyses of NGC 362 X-ray binaries was made by Margon et al. (2010), who
suggested that one X-ray source is a qLMXB. Here we analyse the archival
Chandra exposure and use photometric catalogues produced by the HST UV
Globular Cluster Survey (Piotto et al., 2015a; Nardiello et al., 2018) to
identify probable optical/UV counterparts.

##  2 HST CATALOGUES USED

NGC 362 was observed by the Wide Field Camera 3 (WFC3; GO-12605) and Advanced
Camera for Surveys (ACS; GO-10775) on board the HST. GO-12605 (PI: Piotto)
contains exposures in two UV filters, F275W (hereafter $UV_{275}$) and F336W
($U_{336}$), along with an exposure in F438W ($B_{438}$) taken in 2012, while
GO-10775 (PI: Sarajedini) is comprised of exposures in F606W ($V_{606}$) and
F814W ($I_{814}$) taken in 2006 (see Table 1). For all the filters, we
retrieved photometric and astrometric catalogues and astrometrised stacked
images from the HST UV Globular Cluster Survey ("HUGS", Piotto et al.
(2015b)).

Table 1: HST Observations of NGC 362 Telescope/ | Date of | Proposal | Filter | Exposure
---|---|---|---|---
instrument | Observation | ID |  | time (s)
HST/WFC3 | 2012 Sep 09 | GO-12605 | F275W | 1557
HST/WFC3 | 2012 Sep 09 | GO-12605 | F336W | 700
HST/WFC3 | 2012 Sep 09 | GO-12605 | F438W | 108
HST/ACS | 2006 Jun 02 | GO-10775 | F606W | 610
HST/ACS | 2006 Jun 02 | GO-10775 | F814W | 690

The HUGS data reduction procedure is extensively described in Anderson et al.
(2008) and Bellini et al. (2017); we summarise it briefly here. In the initial
"first-pass" photometry stage, these authors utilized the FORTRAN program
HST1pass to generate perturbed PSFs for each image. Bright, unsaturated, and
isolated stars were selected, and their fluxes and positions were measured
using the library PSFs. A model of each star was then subtracted from the real
star. Preliminary catalogues were extracted using the HST1pass program on
these PSF arrays. In the subsequent "multi-pass" photometry stage, the authors
employed the images, PSF arrays, and transformations obtained during the
"first-pass" stage to simultaneously detect and measure stars in all
individual exposures, using the FORTRAN software kitchen_sync2 (KS2; Bellini
et al. 2017). To calibrate the photometry output from KS2, the authors
compared aperture photometry on _drc images (normalized to an exposure time of
1 s) with their PSF-based photometry. The KS2 software generated astrometric
and photometric catalogues of stars using three different methods. Method 1
works best for bright stars generating star-like profiles in single exposures,
Method 2 works well for faint stars and crowded environments, and Method 3
works well for highly crowded environments. In this paper, we used Method 3
photometry, since this is a crowded cluster.

The astrometric solution was based on the Gaia Data Release 1 catalogue (Gaia
Collaboration et al., 2016) as the reference frame. To determine the
membership probabilities of the target stars, the authors employed the local-
sample method (Bellini et al., 2009). For each target star, membership
probability was estimated by considering a sub-sample of 500 reference stars
from the catalogue. The selection of these reference stars was based on their
proper motion error (typically $\pm$ 0.25 mas yr-1) and a magnitude similar to
that of the target star. The catalogue indicates whether a membership
probability calculation is not possible (value -1), or gives a probability
estimate for belonging to the cluster.

##  3 X-ray Observations and Data Reduction

The X-ray data utilized in this study comprised two Chandra X-ray Observatory
observations of NGC 362 in 2004, totaling an exposure time of 78.82 ks (see
Table 2). For both observations, the core of NGC 362 was positioned on the
back-illuminated ACIS-S3 chip and configured in FAINT mode.

Table 2: Chandra Observations of NGC 362 Telescope/ | Date of | Observation | Exposure
---|---|---|---
instrument | Observation | ID | time (ks)
Chandra/ACIS-S | 2004 Jan 30 | 4529 | 65.85
Chandra/ACIS-S | 2004 Jan 27 | 5299 | 12.97

We performed data reduction and analysis using CIAO111Chandra Interactive
Analysis of Observations; available at https://cxc.cfa.harvard.edu/ciao/
(version 4.15.1, CALDB 4.10.4) provided by the Chandra X-ray Center (CXC). The
data were reprocessed using the chandra_repro script, which generated new
level 2 event files for each observation incorporating the latest calibration
updates and bad pixel files. We applied fine astrometric shifts to the shorter
observation (ID 5299) using the reproject_aspect script, aligning it with the
longer observation (ID 4299). Finally, the event files from both observations
were merged using the reproject_obs script.

###  3.1 Source Detection

We utilized the CIAO package wavdetect for the detection of X-ray sources. Two
regions were defined around the cluster’s center: a larger region with an 8
arcminute radius and a smaller region with a radius of 1 arcminute ($\approx
1.2\times$ the cluster’s half-mass radius). The data in the larger region were
filtered to the energy range of 0.5-8 keV. The wavelet scales were specified
as a series from 1 to 8, increasing by a factor of $\sqrt{2}$, and a
significance threshold for source detection was set at $10^{-6}$ (false
sources per pixel).

To refine the astrometry of the Chandra dataset, we cross-matched the detected
X-ray sources with the Gaia DR3 dataset (Gaia Collaboration et al., 2023)
within a search radius of 1 arcsec. The offset between Gaia and Chandra
astrometry was found to be significantly smaller than the position
uncertainties of the Chandra sources (see section 4). Therefore, this method
did not yield further improvements in astrometric accuracy. We note that the
proper motion offset between Gaia DR1 and DR3 positions is small compared to
our X-ray positional uncertainties.

Within the smaller region, the data were filtered into three distinct energy
ranges: 0.5-2 keV, 2-8 keV, and 0.5-8 keV. For each energy range, the same
wavelet scales as in the case of the larger region were employed. The
detection signal threshold was set to $10^{-5}$. The unique X-ray source
detections from each energy range were subsequently combined, resulting in a
master file containing 33 X-ray sources (see Table 3). The X-ray sources are
shown in Figure 1.

Figure 1: Merged Chandra ACIS-S 0.5–8 keV image of NGC 362. The 33 detected X-ray sources are marked with red circles of 1 arcsec radius and labeled with their source IDs. The inner black circle represents the core radius, r_c (0.18 arcmin), and the larger black circle represents the half-mass radius, r_h (0.82 arcmin), of the globular cluster NGC 362. The left panel shows all detected Chandra sources, while the right panel shows the detected sources in and around the core of NGC 362. Additional diffuse emission (likely faint point sources) is also visible in the core. Table 3: Properties of Chandra sources. The right ascension (R.A.), declination (Decl.), and net counts in 0.5-8 keV are provided by the wavdetect algorithm. The RA and Decl. are corrected for the offset between Chandra and HST positions of three sub-subgiants. The unabsorbed luminosities are derived from power-law spectral fitting, as discussed in Section 3.3. For sources with net counts $\leq$ 10, the luminosities are extrapolated using a linear relation between net counts and luminosity. The positional uncertainty is given in arcseconds (see text). Source | R.A. | Decl. | Net | $L_{X(0.5-10)}$ | Uncert.
---|---|---|---|---|---
ID | (J2000.0) | (J2000.0) | Counts | ($10^{32}$ erg/s) | (")
X1 | 1:03:14.880 | -70:50:56.00 | 598 $\pm$ 25 | 4.56 | 0.16
X2 | 1:03:16.529 | -70:51:00.79 | 125 $\pm$ 12 | 1.60 | 0.20
X3 | 1:03:15.542 | -70:50:59.53 | 81 $\pm$ 9 | 1.49 | 0.22
X4 | 1:03:01.716 | -70:50:17.34 | 71 $\pm$ 9 | 0.88 | 0.29
X5 | 1:03:16.339 | -70:50:48.48 | 55 $\pm$ 8 | 0.91 | 0.26
X6 | 1:03:14.674 | -70:50:53.66 | 41 $\pm$ 7 | 0.68 | 0.28
X7 | 1:03:15.312 | -70:50:54.92 | 40 $\pm$ 7 | 0.73 | 0.29
X8 | 1:03:13.390 | -70:51:01.44 | 34 $\pm$ 6 | 0.37 | 0.31
X9 | 1:03:12.725 | -70:50:53.45 | 32 $\pm$ 6 | 0.33 | 0.32
X10 | 1:03:22.154 | -70:50:44.95 | 17 $\pm$ 4 | 0.27 | 0.48
X11 | 1:03:12.914 | -70:51:06.98 | 13 $\pm$ 4 | 0.12 | 0.48
X12 | 1:03:16.476 | -70:50:56.15 | 11 $\pm$ 3 | 0.13 | 0.51
X13 | 1:03:16.234 | -70:51:05.18 | 11 $\pm$ 4 | 0.51 | 0.52
X14 | 1:03:14.026 | -70:50:45.24 | 11 $\pm$ 3 | 0.12 | 0.52
X15 | 1:03:13.354 | -70:50:46.50 | 10 $\pm$ 3 | 0.10 | 0.54
X16 | 1:03:12.950 | -70:50:58.02 | 10 $\pm$ 3 | 0.10 | 0.55
X17 | 1:03:14.095 | -70:50:41.35 | 7 $\pm$ 3 | 0.07 | 0.63
X18 | 1:03:12.571 | -70:51:04.07 | 6 $\pm$ 3 | 0.06 | 0.68
X19 | 1:03:14.933 | -70:51:28.51 | 6 $\pm$ 2 | 0.06 | 0.76
X20 | 1:03:12.766 | -70:51:17.86 | 6 $\pm$ 2 | 0.06 | 0.74
X21 | 1:03:10.606 | -70:50:58.70 | 6 $\pm$ 2 | 0.06 | 0.73
X22 | 1:03:21.917 | -70:50:30.34 | 5 $\pm$ 2 | 0.05 | 0.84
X23 | 1:03:14.071 | -70:50:55.64 | 5 $\pm$ 2 | 0.05 | 0.74
X24 | 1:03:24.694 | -70:51:49.25 | 5 $\pm$ 2 | 0.05 | 1.02
X25 | 1:03:13.846 | -70:51:06.30 | 5 $\pm$ 2 | 0.05 | 0.78
X26 | 1:03:12.434 | -70:50:57.55 | 5 $\pm$ 2 | 0.05 | 0.77
X27 | 1:03:17.462 | -70:50:50.96 | 3 $\pm$ 2 | 0.03 | 0.93
X28 | 1:03:14.614 | -70:51:03.49 | 3 $\pm$ 2 | 0.03 | 0.91
X29 | 1:03:21.605 | -70:51:51.16 | 3 $\pm$ 2 | 0.03 | 1.23
X30 | 1:03:12.595 | -70:50:18.42 | 3 $\pm$ 2 | 0.03 | 1.10
X31 | 1:03:14.962 | -70:50:40.16 | 3 $\pm$ 2 | 0.03 | 1.00
X32 | 1:03:03.199 | -70:51:03.28 | 3 $\pm$ 2 | 0.03 | 1.22
X33 | 1:03:14.131 | -70:50:51.07 | 3 $\pm$ 2 | 0.03 | 1.00

###  3.2 Spectral Extraction

We utilized the specextract script to extract spectra for the detected Chandra
sources with "Net Counts" > 10 (see Table 3) for both observations 4529 and
5299 (see Table 2). The specextract script is designed for creating source and
optional background spectra in Chandra imaging mode.

For the background region, we selected a source-free area with a radius of 25
arcsec near the cluster. As for the source regions, they were chosen to have a
radius of 1 arcsec for each source. To combine the spectra from the two
observations, we utilized the combine_spectra script. This script performs the
summation of multiple PHA spectra and combines the associated background PHA
spectra, as well as the source and background ARF and RMF response files.

###  3.3 Spectral Fitting

We utilized CIAO’s modelling and fitting application, SHERPA222
https://cxc.cfa.harvard.edu/sherpa/ for all spectral fits. To account for the
limited number of counts in the X-ray spectra, we employed the
WSTAT333https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html
statistic, which is a Poisson log-likelihood function that includes a Poisson
background component. Considering the limited counts, we grouped the spectral
data to ensure that each bin contains at least one photon (Humphrey et al.
(2009)).

Initially, we performed fits on all spectra using a combination of a power law
with pegged normalization (xspegpwrlw) and XSpec photoelectric absorption
(xsphabs) as the source model. The hydrogen column density ($N_{H}$) was set
to $4.4\times 10^{20}$ cm-2, calculated by multiplying the optical extinction
E(B-V)=0.05 (Harris, 2010) by a factor of 3.1 to convert to $A_{V}$, and by a
conversion of $2.81\times 10^{21}$ cm-2 to convert to $N_{H}$ (Bahramian et
al., 2015). The energy range for the normalization was chosen to be 0.5 to 10
keV. We set the elemental abundances used by XSpec models to wilm (Wilms et
al., 2000). This initial model yielded satisfactory results for all sources,
except for source X1 (see Table 4, and below). We extrapolated a relation
between the net counts and power-law $L_{X}$ to infer estimated $L_{X}$ for
the fainter sources as well, in Table 3. We do not provide formal $L_{X}$
error estimates in Table 3; the dominant $L_{X}$ error should be small-number
count statistics, but uncertainty in spectral shape is also substantial.

Table 4: Spectral fit parameters of the Chandra sources with NET_COUNTS > 10\. The model used is a power law with pegged normalization (xspegpwrlw) and photoelectric absorption (xsphabs) fixed to $N_{H}=4.4\times 10^{20}$ cm-2, and $L_{X}$ values reported are corrected for absorption. Source ID | Photon Index |  $L_{X(0.5-10)}$ (1032 erg/s)
---|---|---
X1 | 3.2 $\pm$ 0.1 | 4.56 $\pm$ 0.18
X2 | 1.7 $\pm$ 0.1 | 1.60 $\pm$ 0.21
X3 | 1.3 $\pm$ 0.2 | 1.49 $\pm$ 0.25
X4 | 1.7 $\pm$ 0.2 | 0.88 $\pm$ 0.15
X5 | 1.4 $\pm$ 0.2 | 0.91 $\pm$ 0.18
X6 | 1.5 $\pm$ 0.2 | 0.68 $\pm$ 0.16
X7 | 1.4 $\pm$ 0.2 | 0.73 $\pm$ 0.17
X8 | 1.8 $\pm$ 0.2 | 0.37 $\pm$ 0.10
X9 | 2.0 $\pm$ 0.2 | 0.33 $\pm$ 0.09
X10 | 2.0 $\pm$ 0.3 | 0.27 $\pm$ 0.07
X11 | 2.5 $\pm$ 0.3 | 0.12 $\pm$ 0.04
X12 | 2.5 $\pm$ 0.2 | 0.13 $\pm$ 0.04
X13 | 0.7 $\pm$ 0.3 | 0.51 $\pm$ 0.20
X14 | 1.9 $\pm$ 0.3 | 0.12 $\pm$ 0.06

Source X1 showed an unusually steep power-law spectrum, with a photon index of
3.2 $\pm$ 0.1, which suggests that it might be better fit by a blackbody-like
neutron star atmosphere model. To address this, we used an XSpec photoelectric
absorption model (xsphabs) with a low-magnetic-field NS hydrogen atmosphere
model (xsnsatmos, Heinke et al. 2006). In this fit, the neutron star
gravitational mass (M_ns) was fixed at 1.4 M⊙, while the neutron star radius
(R_ns) was fixed at 11.5 km. The distance to the neutron star (dist) was set
to 8.8 kpc (Baumgardt & Vasiliev, 2021). This modified model successfully fit
Source 1, resulting in a fraction of the neutron star surface emitting (norm)
of 1.30$\pm$0.26 and a logarithm of the unredshifted effective temperature
(Log_Teff) of 6.01$\pm$0.02 K, and $L_{X}$(0.5-10 keV)$=4.2\times 10^{32}$
erg/s. We interpret the close match of the neutron star normalization with the
model value of 1.0 as evidence for consistency with the model. We do not
attempt to constrain the neutron star radius independently with this data.

During our analysis, we encountered fainter sources that exhibited soft
spectra with steep power-law indices ranging between 2 and 2.5 (see Table 4).
However, when attempting to fit these sources using the xsnsatmos model, we
observed that the resulting normalization parameter (norm) was much smaller
(0.0004 to 0.001) than the expected value of $\sim$1 (indicating emission from
the full surface). This does not seem to match observations of quiescent LMXB
spectra; though they may be consistent with hot polar spots on millisecond
pulsars, typically radio millisecond pulsars showing thermal spectra are not
observed to be this luminous (Zhao & Heinke, 2022).

##  4 COUNTERPART IDENTIFICATION

We performed a search for the optical counterparts of the Chandra X-ray
sources by crossmatching them with the HST HUGS catalogue using TOPCAT
(Taylor, 2005). We initially used a search radius of 0.6 arcsec for
crossmatching. We identified three promising sub-subgiant candidate
counterparts (X15, X16, and X20, see Table 5) with $<$0.2 arcsecond
separations. Sub-sub-giants are often identified with X-ray sources (see
details below and Geller et al. 2017), so we identified these as promising
counterparts.

To refine the Chandra astrometry, we shifted the Chandra positions to match
the HST positions for these three sub-subgiants. The average R.A. offset
between the Chandra and HST catalogues was 0.04", with a standard deviation of
0.13". The average Decl. offset was -0.11", with a standard deviation of
0.02", producing an uncertainty in the optical/X-ray alignment of 0.13".

Table 5: List of interesting HST counterparts to the Chandra source detections. The $\Delta$RA and $\Delta$Decl. columns represent the differences between the positions of the HST source and the associated Chandra source in arcsec. Photometry is from HUGS (’–’ if not detected). The PROB column indicates the cluster membership probability provided in the HUGS catalogue (-1 indicates the probability could not be determined). Source ID | HUGS ID |  $\Delta$RA |  $\Delta$Decl. | UV275 | U336 | B438 | V606 | I814 | PROB | NOTES
---|---|---|---|---|---|---|---|---|---|---
X1 | R0077953 | -0.02 | 0.00 | 19.29 | 18.50 | 18.83 | 18.15 | 17.50 | 75.4 | qLMXB
X4 | R0113456 | -0.06 | 0.01 | 22.20 | 21.87 | 23.81 | 22.40 | 21.63 | 0 | Galaxy
X9 | R0005396 | 0.13 | -0.03 | 18.71 | 17.76 | 17.91 | 17.05 | 16.34 | 98 | RG+B
X10 | R0006360 | -0.09 | 0.10 | 18.46 | 17.28 | 17.24 | 16.19 | 15.44 | 96.5 | RG+B
X12 | R0005116 | 0.05 | 0.11 | 19.72 | 18.21 | 18.24 | 17.19 | 16.44 | 97.8 | RSS
X15 | R0089306 | -0.02 | 0.00 | 20.38 | 19.09 | 18.95 | 18.02 | 17.19 | 93.3 | SSG
X16 | R0078991 | -0.12 | 0.02 | 20.75 | 19.37 | 19.40 | 18.72 | 17.80 | 99.4 | SSG
X20 | R0002866 | 0.14 | -0.04 | 20.39 | 19.10 | 19.03 | 17.83 | 17.11 | 97.8 | SSG
X21A | R0004837 | 0.22 | 0.10 | 19.32 | 17.83 | 17.73 | 16.82 | 16.06 | 95.5 | RSS?
X21B | R0077004 | -0.20 | 0.65 | – | 23.98 | 23.16 | 21.97 | 21.00 | 97.9 | AB?
X23A | R0078618 | 0.20 | 0.35 | 19.27 | 18.53 | 18.92 | 18.44 | 17.84 | 95.9 | AB?
X23B | R0078683 | 0.39 | 0.38 | 23.16 | 21.16 | 21.27 | 20.27 | 19.56 | 97.1 | AB?
X23C | R0078681 | 0.50 | 0.18 | 20.90 | 20.14 | 20.53 | 20.03 | 19.36 | 99.2 | AB?
X24 | R0029822 | -0.26 | 0.14 | 22.46 | 22.38 | 22.57 | 21.60 | 20.86 | -1 | Galaxy
X26 | R0078462 | 0.00 | 0.19 | 21.86 | 20.79 | 21.05 | 20.31 | 19.65 | 99.2 | AB

Next, we searched for interesting HST sources located within the positional
uncertainty regions of the Chandra X-ray detections shown in Table 3. The
selection of these sources was based on their positions in the HUGS color-
magnitude diagrams (see Figures 2, 3, & 4).

We calculated the Chandra 95% confidence positional uncertainties using
equation 1 from Kim et al. (2007), and summing in quadrature the positional
uncertainty for each X-ray source with the uncertainty in the X-ray/optical
alignment (0.13"). The positional uncertainty, PU, is in arcseconds, and off
axis angle, OAA, is in arcminutes. Source counts, C, are as extracted by
wavdetect. The final positional uncertainties are listed in Table 2.

$logPU=\begin{cases}0.1145\times OAA-0.4958\times\log C+0.1932,\\\ 0.0000<\log
C\leq 2.1393\\\ 0.0968\times OAA-0.2064\times\log C-0.4260,\\\ 2.1393<\log
C\leq 3.3000\end{cases}$ (1)

Figure 2:  $V_{606}$ vs $V_{606}-I_{814}$ color-magnitude diagram (CMD) from
the HST ACS HUGS data on NGC 362. The coloured markers are the positions of
the interesting HST counterparts to the Chandra source detections. Figure 3:
$U_{336}$ vs $U_{336}-B_{438}$ CMD of the HST WFC3 HUGS data on NGC 362. The
coloured markers are the positions of the interesting HST counterparts to the
Chandra source detections. Figure 4: $UV_{275}$ vs $UV_{275}-U_{336}$ CMD of
the HST WFC3 HUGS observations of NGC 362. The coloured markers are the
positions of the interesting HST counterparts to the Chandra source
detections.

###  4.1 Interesting Candidates

We identified a number of candidate counterparts in unusual CMD positions in
the three HUGS CMDs. We discarded potential counterparts if the star appeared
significantly blended with another star in the relevant images. We include
finding charts for all our candidate counterparts in Appendix A. We also
constructed a plot (Fig. 5) of 0.5-10 keV X-ray luminosity vs. $M_{V}$
(assuming a distance of 8.8 kpc and $m_{V}-M_{V}$ of 14.7). We include on the
$L_{X}$/$M_{V}$ plot equations 2.2 and 2.3 of Verbunt et al. (2008), which are
empirical limits on the $L_{X}$ of ABs at a given $M_{V}$ estimated from
reported matches in the globular cluster X-ray source population literature,
and from ROSAT observations of nearby ABs, respectively.

Figure 5: X-ray luminosity as a function of absolute visual magnitude for the
interesting stars given in Table 5. Equations 2.2 and 2.3 are taken from
Verbunt et al. (2008).

X1 is the brightest X-ray source in NGC 362 ($L_{X(0.5-10)}$ = 4.2$\times
10^{32}$ erg/s), and it is well-fit by the NS hydrogen atmosphere model (see
section 3.3). This indicates that X1 is a quiescent low-mass X-ray binary
(qLMXB). We identify a potentially interesting candidate star within the error
circle, which falls within the SSG region in the $V_{606}-I_{814}$ CMD (Fig.
2). As the environment is rather crowded (see figure A1), it is possible that
the photometry is affected. While SSG companion stars have not previously been
identified in globular cluster qLMXBs, at least two redback MSPs in NGC 6397
show similar CMD positions (Ferraro et al., 2001; Grindlay et al., 2001; Zhao
& Heinke, 2022; Zhang et al., 2022), and qLMXB accretion discs could be faint
enough not to show up against a relatively bright star. Alternatively, the
true qLMXB counterpart may be fainter (or obscured; Fig. A1 shows that one
other star within the error circle is not detected in HUGS) and lacking HUGS
photometry.

X4’s candidate counterpart lies near the main-sequence in the
$V_{606}-I_{814}$ CMD, but is 1.5 magnitudes bluer than the main sequence in
the $U_{336}-B_{438}$ and $UV_{275}-U{336}$ CMDs, suggesting it might be a CV.
However, X4 has a zero membership probability in the HUGS database, due to its
distinctly different proper motion (visible in Figure A1, compared to the
cluster stars). X4’s proper motion in the Libralato et al. (2022) HUGS proper
motion database is the opposite of NGC 362’s motion (Gaia Collaboration et
al., 2018), verifying that X4 is a background active galactic nucleus (AGN).

X9 and X10 have candidate counterparts that are located slightly to the right
of the red giant branch in $V_{606}-I_{814}$, on or just to the left in
$U_{336}-B_{438}$, and significantly blueward ($\sim$0.5 magnitudes) in
$UV_{275}-U{336}$ (we label them "RG+B" in Table 5). X-ray counterparts with
such characteristics have not been identified in globular clusters previously,
to our knowledge. We interpret the colour evolution to indicate a combination
of a red straggler star (a giant with unusual evolution) along with a bright,
blue source of light. The blue light could be produced by either a blue
straggler star (suggesting the system is similar to Algol), or an accreting
white dwarf star, in which case the system would be either a long-period CV,
if the giant fills its Roche lobe (similar to AKO9 in 47 Tuc, Knigge et al.
2003), or a symbiotic, if it accretes from a wind. The $L_{X}$/$M_{V}$ plot
does not provide evidence against any of these possibilities (the X-rays could
be produced by accretion onto a white dwarf, or by coronal emission from the
giant).

However, additional evidence comes from the variability study of Rozyczka et
al. (2016), who associated X10 (in the Chandra Source Catalogue as
X010322.09-705044.7) with their variable V24, an eclipsing binary of period
8.14 days. They obtained radial velocity measurements of V24, identifying it
as a pair of 0.8 $\mathrm{M_{\sun}}$ stars with similar radial velocities.
However, they also observed a highly variable lightcurve. The primary eclipse
(its length implies the giant is filling its Roche lobe) is stable, but the
secondary eclipse width varies by a factor of three on a timescale of years;
Rozyczka et al. (2016) suggest an accretion disk is sometimes present. The
deeper, stable eclipse must be the eclipse of the bluer object by the giant
star. Optical spectroscopy could verify whether an accreting white dwarf is
present (some high-accretion-rate CVs show absorption-line spectra, e.g.
Beuermann et al. 1992), or the accreting blue object is a blue straggler star.

The candidate counterpart to X12, and the brighter candidate counterpart to
X21 (labeled X21A), both appear to the right of the red giant branch in
$V_{606}-I_{814}$, and are consistent with the red giant branch in
$U_{336}-B_{438}$. X12 also appears redward of the red giant branch in
$UV_{275}-U{336}$, while X21A falls on this branch in $UV_{275}-U{336}$. We
identify these counterparts as red straggler stars, with X-rays likely powered
by coronal activity; they are consistent with the AB region in the
$L_{X}$/$M_{V}$ plot.

X15, X16, and X20 are candidates for sub-subgiants, as previously discussed.
All three sources have candidate counterparts slightly lower and to the right
of the subgiant branch in all three CMDs, with X16 showing a colour bluer than
the other two in $U_{336}-B_{438}$, but redder than them in $UV_{275}-U{336}$
and $V_{606}-I_{814}$, suggestive of variability during the HUGS observations.

The candidate counterpart for X24 has a very blue $UV_{275}-U{336}$ colour,
shifting redwards towards the main sequence in $V_{606}-I_{814}$, which could
suggest a CV nature. However, the HST images show that this blue object is
significantly extended (see Figure A4), indicating that it is a background
galaxy. The HUGS catalogue does not provide a proper motion or membership
probability for this object, likely due to its extended nature.

We identify five candidate ABs as potential counterparts to X21 (this we label
X21B, with the X21A candidate a red straggler), X26, and X23 with three
potential counterparts (X23A, X23B, X23C). All lie above the main sequence in
$V_{606}-I_{814}$, with the candidate X23A lying $>1$ magnitude above the main
sequence, and the rest lying $<$0.75 magnitudes above it. The candidates for
X17 and X23B lie off the main sequence in $UV_{275}-U{336}$ also (X23B lying a
magnitude off), while most lie on the main sequence in $UV_{275}-U{336}$ and
all lie on the main sequence in $U_{336}-B_{438}$ (this CMD is significantly
more vertical at the relevant magnitudes than the others). All but X21B lie
below the lower empirical Verbunt et al. (2008) equation setting an upper
limit on AB $L_{X}$ values (Fig. 5), and all lie below the higher empirical
Verbunt et al. (2008) upper limit, making them plausible AB candidates.

##  5 Chance coincidence calculation

To identify how many of our identifications may be expected to be produced by
chance, we select regions of the $UV_{275}-U_{336}$ and $V_{606}-I_{814}$ CMDs
where we expect to find different types of X-ray counterparts (Fig. 6). We
select regions in the $UV_{275}-U_{336}$ CMD to identify CVs (blueward of the
main sequence) and sub-subgiants (below the subgiant branch). In the
$V_{606}-I_{814}$ CMD we select regions for ABs (above the main sequence) and
red stragglers (right of the giant branch). Sub-subgiant and AB
identifications can overlap, as may some others. As a control, we also count
the number of main-sequence (MS) stars in both filters. Finally, we identify
stars that lie in the CV region in $UV_{275}-U{336}$ but on the MS in
$V_{606}-I_{814}$ (which match our expectation that CVs will typically have
blue and red light components).

Figure 6: CMDs showing the selected regions for main-sequence (MS),
cataclysmic variable (CV), sub-subgiant (SSG), red straggler star (RSS), and
binary sequence (Binary) stars in $UV_{275}-U_{336}$ and $V_{606}-I_{814}$
CMDs.

The density of stars varies substantially within our considered region, and
X-ray sources are concentrated in the core. We therefore count the numbers of
these stars within three spatial regions: the core; an annulus of 1.0 to 1.5
core radii; and an annulus from 1.5 core radii to 1 arcminute. Finally, we
count the numbers of stars within the X-ray error circles (within these 3
regions) fitting these criteria. The results of these calculations are in
Table 6.

We note that we do not identify and discuss (in 4.1) many of the stars which
lie within X-ray error circles and also have interesting colours (e.g. the CV
regions), as these stars typically appear crowded in one or more images, often
with a neighbouring star which also has unusual colours (indicating that the
HUGS photometry has shifted flux between the stars in different filters).
Thus, our chance coincidence calculations will overstate the likelihood of a
particular object being a spurious match to an X-ray source, as we cannot sift
out all stars that appear crowded in all CMDs. Nevertheless, this exercise is
useful to roughly estimate the degree of chance coincidences.

Table 6: Chance Coincidence results. Observed numbers are taken from the error circles, while predicted numbers are calculated from the relevant regions and area ratios, selected using TOPCAT. Region 1 includes the core radius. Region 2 is an annulus from the core radius to 1.5 times the core radius. Region 3 is an annulus from 1.5 times the core radius to 1 arcminute. Type | Observed | Predicted
---|---|---
| Region 1 | Region 2 | Region 3 | Region 1 | Region 2 | Region 3
CV in UV-U | 4 | 2 | 2 | 3.9 | 1.4 | 0.7
CV in UV-U & MS in V-I | 2 | 0 | 1 | 1.2 | 0.4 | 0.2
Binary in V-I | 28 | 15 | 5 | 22.7 | 10.3 | 4.2
RSS in V-I | 2 | 0 | 1 | 1.3 | 0.2 | 0.1
MS in V-I | 58 | 50 | 58 | 89.2 | 63.1 | 80.3
SSG in U-V | 2 | 1 | 1 | 0.8 | 0.1 | 0

First, the numbers of MS stars predicted and observed in the three regions are
similar, though not identical (the predicted numbers average 1.4 times larger
within each region). This suggests that the chance coincidence predictions
give small overestimates, and should be taken as upper limits.

We see that the numbers of objects observed in X-ray error circles in the CV
region in $UV_{275}-U_{336}$ ("Observed") in Table 6) are similar to those
predicted based on the CMD ("Predicted"), suggesting these could all be chance
coincidences. However, when restricting consideration to objects in the CV
region in $UV_{275}-U_{336}$ and on the MS in $V_{606}-I_{814}$, only 0.2 are
predicted in region 3, where 1 is seen (X24). We are confident that both X24
and X4 (which lies just off the MS in $V_{606}-I_{814}$) are AGN, in the outer
cluster region.

Stars in the AB region in $V_{606}-I_{814}$ are more likely to be observed
than is predicted, in all three regions. As the numbers of chance coincidences
are predicted to be substantial (23 in the core), we cannot be highly
confident that any of our matches with AB candidates are secure. However, the
facts that we identify a number of good candidates, and that the predicted
number of chance coincidences is less than we see, suggests that several of
these ABs are real counterparts.

Finally, the predicted numbers of spurious matches to red straggler stars and
sub-subgiants are quite small, though the predictions are of order one false
match of each within the core. Subtracting the predicted from observed values,
we anticipate 1-2 real red straggler matches, and 3 real sub-subgiant matches
in NGC 362, which happens to match the numbers of candidate counterparts that
we advance in 4.1. We conclude that most of our red straggler and sub-subgiant
candidate counterparts are likely to be real counterparts.

##  6 Discussion

As is clear from Fig. 1, NGC 362 is rich in X-ray sources, which are
concentrated into the cluster core. Although we have detected 33 sources
within 1’ of the cluster (1.2 half-mass radii; note that 4 of these lie
outside the current best-estimate half-mass radius), excess X-ray emission
within the cluster core can be seen in Figure 1. We estimate a total of 85
counts of excess emission (0.5-8 keV) in the cluster core (outside our 1"
source regions, subtracting background and the wings of the point-spread-
function for known sources), which (assuming the same spectrum as our faint
sources) would convert to $L_{X}$(0.5-10 keV)$=8.5\times 10^{31}$ erg/s. We
estimate that our X-ray detection is complete down to about 10 counts, or
$L_{X}$(0.5-10 keV)$=10^{31}$ erg/s, above which we find 16 sources.

###  6.1 Radial distributions

We can use the radial distribution of X-ray sources to estimate the number of
X-ray sources that are background objects, and (assuming that the sources have
gravitationally relaxed) to infer the average mass of the cluster X-ray
sources. Our approach has most recently been applied to M4, as described by
Lugger et al. (2023). This analysis assumes that the radial profile of the
cluster is reasonably well described by a King (1966) model. This has been
demonstrated for NGC 362 by a number of studies, e.g. Trager et al. (1995),
and we have verified it from the HUGS star counts for stars near the main-
sequence turnoff (MSTO) mass. A key input to the X-ray source mass
determination is the core radius value from the optical surface brightness
profile fit. There is good agreement on this number in the literature. The
published values are 10.2 arcsec (Trager et al., 1995), 10.8 arcsec (Harris,
1996, 2010 online version), and 10.1 arcsec (Baumgardt et al., 2023). Since
the Harris (1996) value is based on Trager et al. (1995), we adopt a value of
10.2 arcsec.

The analysis method used by Lugger et al. (2023) computes the ratio of the
typical mass $m_{X}$ of an X-ray source to that of a MSTO star
$m_{\textsc{msto}}$ by a maximum likelihood fit of a generalised King model

$S(r)=S_{0}\left[1+\left(\frac{r}{r_{c}}\right)^{2}\right]^{(1-3q_{X})/2}$ (2)

to the surface density profile of the X-ray sources, where $q_{X}\equiv
m_{X}/m_{\textsc{msto}}$ (see Heinke et al., 2005). In order to do this, it is
necessary to correct for the extragalactic background X-ray source
contribution. We use the extragalactic source counts of Giacconi et al.
(2001), their eqn. 1, which gives an estimated background level of 0.69
arcmin-2 for a 5-count source detection threshold.

Figure 7: Cumulative radial distribution of excess source counts over the
background predicted from the Giacconi et al. (2001) extragalactic source
counts. Error bars represent the statistical uncertainty of the background
correction. The dashed curve is the cumulative background distribution for the
expected background density of 0.69 arcmin-2 The red line is a least-squares
fit to the profile for $r\geq 0.5\,\mathrm{arcmin}$.

Figure 7 shows the cumulative excess source number over the estimated
background as function of the radial distance from the cluster centre; we use
the centre determination by Goldsbury et al. (2010). As expected, the inferred
cluster source distribution (excess over the background) becomes
asymptotically flat beyond about 2 core radii. Thus, there is no evidence for
an excess source population in the cluster halo, and this suggests that most
of the eight X-ray sources farther than 2 core radii are background. Among
these sources, we indeed identify X4 and X24 with background AGN, but we
identify X10 with a cluster member at high confidence.

For the adopted parameter values of $r_{c}=10.2^{\prime\prime}$,
$n_{\mathrm{bkgd}}=0.69\,\mathrm{arcmin}^{-2}$, and a 5-count detection
threshold, the maximum-likelihood mass ratio is $q_{X}=1.72\pm 0.21$. This is
in good agreement with the well-determined value of $q_{X}=1.63\pm 0.11$ that
we obtained for 47 Tuc in Heinke et al. (2005). This mass ratio value also
agrees with the values we have found for M71 ($1.36\pm 0.47$; Elsner et al.,
2008), M4 ($1.53\pm 0.24$; Lugger et al., 2023), and M30 ($1.61\pm 0.20$;
Lugger et al., 2007).

For an assumed MSTO mass of $0.80\,\mathrm{M_{\sun}}$, the inferred typical
_Chandra_ source mass in NGC 362 is $1.38\pm 0.17\,\mathrm{M_{\sun}}$. This is
a reasonable result for a mixture of ABs, CVs, MSPs, and qLMXBs, all of which
should be somewhat more massive on average than a typical turnoff star (Heinke
et al., 2005).

###  6.2 Comparison to other clusters

NGC 362 happens to lie in a similar direction on the sky as 47 Tucanae (47
Tuc), though it is roughly twice as far away. 47 Tuc is 3.4 times as massive
as NGC 362, but as NGC 362 has a denser core, NGC 362 has a stellar encounter
rate 0.74$\pm 0.20$ that of 47 Tuc (Bahramian et al., 2013). It is interesting
to compare their X-ray source content; above $L_{X}=10^{32}$ erg/s, 47 Tuc has
6 X-ray sources (3 qLMXBs, 2 CVs, and an AB), while NGC 362 has 3 (1 qLMXB; 2
unknown). Above $L_{X}$(0.5-6 keV)$=10^{31}$ erg/s, 47 Tuc has 39 total
sources (from Heinke et al. 2005, but assuming a 4.5 kpc distance, and
separating MSPs 47 Tuc-F and 47 Tuc-S into two sources), while NGC 362 has 16
(one of those a background AGN). The total numbers of X-ray sources above
$L_{X}=10^{31}$ erg/s are lower than we might expect based purely on stellar
encounter rates–38% as many as in 47 Tuc, when we might expect 74$\pm
20$%–which may reflect other factors (metallicity, destruction of binaries in
denser clusters, etc), or could be just small-number statistics.

47 Tuc’s sources above $10^{31}$ erg/s include 6 qLMXBs, 21 CVs (or
candidates), 4 ABs, and 4 MSPs (or candidates). Thus, we may predict that if
NGC 362 is similar, the majority of its sources above $10^{31}$ erg/s should
be CVs. However, we have not identified any good candidate CVs among our X-ray
sources. This at first seems odd, since we have the X-ray sensitivity (down to
$L_{X}=10^{31}$ erg/s) and ultraviolet sensitivity (e.g. a $U_{336}-B_{438}$
CMD reaching over 4 magnitudes below the turnoff) that would be sufficient to
identify a dozen CVs in 47 Tuc (see Edmonds et al. 2003), and thus we would
predict identification of $\sim$8 CVs in this range in NGC 362. We do identify
2 AGN in the relevant CMD spaces, indicating that we have sensitivity to such
sources in the cluster outskirts. However, the core is substantially more
crowded especially in the optical. Fig. 9 shows that the HUGS photometry is
highly incomplete even a few magnitudes below the turnoff (visible at
$M_{R}\sim 3$). As inclusion in the HUGS photometry database relies on
detection in $V_{606}$ or $I_{814}$, most CVs, which are likely to be located
within $\sim$15" of the centre and be fainter than $M_{R}\sim 6$, are likely
to be missed. Future work may identify the likely CV population through a new
photometric analysis of archival UV and $H-\alpha$ HST imaging of X-ray error
circles.

Cluster | Distance | $r_{h}$ | $\Gamma$ |  $\Gamma$ err | X-ray srcs, $L_{X}>10^{31}$ erg/s | Refs
---|---|---|---|---|---|---
| kpc | arcmin |  |  | Total | Fg/Bg (pred) |
Terzan 5 | 6.6 | 0.72 | 6800 | 1000 | 102 | 33 | 1,2
NGC 6266 | 6.4 | 0.92 | 1670 | 710 | 39 | 2 | 3
47 Tuc | 4.52 | 3.17 | 1000 | 15 | 33 | 1 | 4
NGC 2808 | 10.1 | 0.80 | 923 | 67 | 16 | 1 | 5
NGC 6388 | 11.2 | 0.52 | 900 | 240 | 52 | 1 | 6
NGC 362 | 8.8 | 0.82 | 740 | 140 | 15 | 0 | 7
NGC 6626 | 5.4 | 1.97 | 650 | 80 | 30 | 12 | 1,8
NGC 6093 | 10.3 | 0.61 | 530 | 60 | 18 | 1 | 9
NGC 6752 | 4.13 | 1.91 | 400 | 180 | 7 | 0 | 10
NGC 7099 | 8.5 | 1.03 | 320 | 120 | 8 | 0 | 11, 12
NGC 5904 | 7.5 | 1.77 | 160 | 40 | 12 | 3 | 1
NGC 5139 | 5.43 | 5.00 | 90 | 27 | 32 | 14 | 13,14,15
NGC 6397 | 2.48 | 2.90 | 84 | 18 | 9 | 1 | 16
NGC 6656 | 3.30 | 3.36 | 78 | 32 | 8 | 3 | 1
NGC 6121 | 1.85 | 4.33 | 27 | 12 | 1 | 0 | 17
Table 7: Information about several globular clusters, including predicted
stellar encounter rates (Bahramian et al., 2013) and observed numbers of X-ray
sources, divided into likely members and nonmembers. We use Baumgardt &
Vasiliev (2021) for distances, and Harris (1996, 2010 revision) for half-mass
radii and extinctions. References: 1: Bahramian et al. (2020), 2: Cheng et al.
(2019), 3: Oh et al. (2020), 4: Heinke et al. (2005), 5: Servillat et al.
(2008), 6: Maxwell et al. (2012), 7: this work, 8: Cheng et al. (2020), 9:
Heinke et al. (2003b), 10: Cohn et al. (2021), 11: Lugger et al. (2007), 12:
Zhao et al. (2020), 13: Haggard et al. (2009), 14: Cool et al. (2013), 15:
Henleywillis et al. (2018), 16: Bogdanov et al. (2010), 17: Bassa et al.
(2004).

We also compare NGC 362 to other clusters with significant X-ray source
populations. We collect information from 14 other clusters with published
surveys down to $L_{X}$(0.5-10 keV)$=10^{31}$ erg/s, which we list in Table 7.
If the published paper quoted a different energy range, we converted fluxes
assuming a power-law of photon index 1.7. For most of the clusters, we
estimate the number of background AGN based on the log N-log S estimate of
Giacconi et al. (2001). In a few clusters (NGC 6397, NGC 6752, NGC 6121),
every source in this $L_{X}$ range has been identified. However, in some
clusters, especially at low Galactic latitude, the dominant contaminant is
Galactic stars. For Terzan 5 and M28, we use estimates of the Galactic source
contamination rate by Cheng et al. (2019, 2020).

We plot the stellar encounter rates with errors from Bahramian et al. (2013),
vs. the observed numbers of X-ray sources with $L_{X}$(0.5-10 keV)$>10^{31}$
erg/s, in Figure 8. We calculate Gehrels (1986) errors on the total number of
sources. NGC 362 is labeled in red, while other clusters marked as core-
collapsed or possibly core-collapsed by Harris (1996) are indicated in blue.
NGC 362’s X-ray population appears similar to those of other clusters with
similar encounter rates.

Figure 8: Stellar encounter rates from Bahramian et al. (2013) vs. observed
numbers of X-ray sources with $L_{X}$(0.5-10 keV)$>10^{31}$ erg/s (see Table
7). NGC 362 is in red, while other core-collapsed clusters are indicated in
blue. Figure 9: Radial distribution, relative to NGC 362’s center, of HUGS
stars, vs. their estimated $M_{R}$ absolute magnitude (using
$m_{V}-M_{V}=14.725$, Harris 1996, 2010 revision, and assuming $R=(V+I)/2$).
The vertical blue line represents the core radius. The horizontal blue line
represents the absolute magnitude separating the bright and faint CV
populations in NGC 6752 (Cohn et al., 2021). The core of NGC 362 is severely
incomplete at fainter magnitudes due to crowding.

###  6.3 Interesting objects

The three sub-subgiants that we confidently identify have similar X-ray
luminosities (0.5-10 keV $L_{X}$ of $6\times 10^{30}$ to $10\times 10^{30}$
erg/s) as the four sub-subgiant coronally active systems identified in 47 Tuc
(Albrow et al., 2001; Heinke et al., 2005), which have $L_{X}$(0.5-6 keV) of
$4.5\times 10^{30}$ to $8.2\times 10^{30}$ (excluding the more X-ray luminous
CV AKO9). The qLMXB X1 may also be associated with a sub-subgiant optical
counterpart, which would suggest an orbital period of 10-20 hours. Although
most sub-subgiant systems are likely powered by coronal activity, placement in
the sub-subgiant location in some CMDs may be a general feature of close-orbit
nuclear evolution of close binaries, as illustrated by the variety of objects
found there, including redback MSPs (Ferraro et al., 2001), CVs (Knigge et
al., 2003), black hole candidates (Shishkovsky et al., 2018), as well as both
short-orbit and longer-orbit binaries composed of non-degenerate stars
(Mathieu et al., 2003).

X9 and X10 show evidence of both red and blue components to their light. They
could be Algol-type active binaries (where the stars include a red giant and a
blue straggler), CVs containing a red giant filling its Roche lobe, or
symbiotic stars. No symbiotic stars have yet been verified in any globular
cluster, though there is a candidate in $\omega$ Cen; (Henleywillis et al.,
2018). X10’s optical lightcurve, presented by Rozyczka et al. (2016), shows
eclipses with an 8.14 day period and large variability, suggesting a variable
accretion disk.

##  7 Conclusions

Our analysis of the X-ray sources in NGC 362 finds 33 sources down to a
limiting $L_{X}$(0.5-10 keV)$=3\times 10^{30}$ erg/s, likely complete to
$L_{X}=10^{31}$ erg/s. The numbers of X-ray sources are slightly lower than
expected if scaling from 47 Tuc’s X-ray content based on their relative
stellar encounter rate, and their radial distribution is concentrated towards
the core as appropriate for a stellar population with mass of 1.38$\pm 0.17$
$\mathrm{M_{\sun}}$, consistent with known X-ray source populations. We
identify the brightest X-ray source, X1, as a qLMXB based on its distinctive
X-ray spectrum. NGC 362’s X-ray source characteristics are not surprising
compared to similar globular clusters.

The optical/UV counterpart source population, however, does offer surprises.
We do not identify any compelling CV candidates, although extrapolation by
stellar encounter rate from 47 Tuc would suggest of order 8 CVs may exist
among our detected X-ray sources. We infer that our lack of identified CVs is
due to optical crowding in the core. This suggests that CVs may be identified
using a new reduction of the deep HST F225W UV imaging of this cluster that is
available in the archive, since the HUGS source list was prepared using less
deep, longer wavelength data. We find several plausible AB candidate
counterparts. On the other hand, we find numerous relatively bright likely
optical counterparts with unusual CMD positions; 3 plausibly coronally-powered
sub-subgiants, a possible sub-subgiant optical counterpart to the qLMXB, 2
objects in the red straggler location in all CMDs, and 2 objects that lie in
the red straggler location in our optical CMD but shift well to the blue of
the giant branch in ultraviolet CMDs. Chance coincidence tests indicate that
few if any of these are false matches, and one of the last group (X10) has an
optical lightcurve showing eclipses on an 8.14 day orbit with strong
variability indicative of a variable accretion disk around the bluer star
(Rozyczka et al., 2016). The majority of these bright optical counterparts are
likely to be powered by coronal activity, but other explanations are possible.
Optical spectroscopy of these various bright optical X-ray counterparts could
be very helpful in understanding their nature.

## Acknowledgements

GK is supported by a Mitacs Globalink Research Internship. CH is supported by
NSERC Discovery Grant RGPIN-2023-04264.

## Data Availability

The Chandra data used in this work is available via the Chandra Data Archive,
at http://cda.harvard.edu/chaser/, while the HST HUGS catalogues are available
at https://archive.stsci.edu/prepds/hugs/.

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##  8 Appendix A

$U_{336}$ $V_{606}$

Figure A10: Finding charts: X1, X4, and X9. The field size is 1.2 arcsec on a
side. North is up and east is to the left. HUGS stars are indicated by yellow
circles labelled by the HUGS sequence number. The red circles are the
_Chandra_ error circles as computed (see text and Table 3). The cyan circles
indicate the locations of the proposed counterparts.

$U_{336}$ $V_{606}$

Figure A11: Finding charts: X10, X12, and X15. The field size is 1.2 arcsec on
a side.

$U_{336}$ $V_{606}$

Figure A12: Finding charts: X16, X20, and X21. The field size is 1.2 arcsec on
a side for X16, and 1.8 arcsec on a side for X20 and X21.

$U_{336}$ $V_{606}$

Figure A13: Finding charts: X23. X24, and X26. The field size is 1.8 arcsec on
a side for X23 and X26, and 2.7 arcsec on a side for X24.