# An XMM-Newton View of the ANdromeda Galaxy as Explored in a Legacy Survey
(New-ANGELS) I: the X-ray Source Catalogue

Rui Huang Department of Astronomy, Tsinghua University, Beijing 100084, China
Jiang-Tao Li Department of Astronomy, University of Michigan, 311 West Hall,
1085 S. University Ave, Ann Arbor, MI, 48109-1107, U.S.A.  Wei Cui Department
of Astronomy, Tsinghua University, Beijing 100084, China  Joel N. Bregman
Department of Astronomy, University of Michigan, 311 West Hall, 1085 S.
University Ave, Ann Arbor, MI, 48109-1107, U.S.A.  Xiang-Dong Li School of
Astronomy and Space Science, Nanjing University, Nanjing 210023, People’s
Republic of China  Key Laboratory of Modern Astronomy and Astrophysics,
Nanjing University, Ministry of Education, Nanjing 210023, People’s Republic
of China  Gabriele Ponti INAF-Osservatorio Astronomico di Brera, Via E.
Bianchi 46, 23807 Merate (LC), Italy  Max-Planck-Institut für
Extraterrestrische Physik, Giessenbachstrasse, 85748 Garching, Germany  Zhijie
Qu Department of Astronomy & Astrophysics, The University of Chicago, Chicago,
IL 60637, U.S.A  Q. Daniel Wang Department of Astronomy, University of
Massachusetts, Amherst, MA 01003, U.S.A.  Yi Zhang INAF-Osservatorio
Astronomico di Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy Jiang-Tao Li
<EMAIL_ADDRESS>
###### Abstract

We introduce the New-ANGELS program, an _XMM-Newton_ survey of $\sim
7.2\rm~{}deg^{2}$ area around M 31, which aims to study the X-ray populations
in M 31 disk and the X-ray emitting hot gas in the inner halo of M 31 up to 30
kpc. In this first paper, we report the catalogue of 4506 detected X-ray
sources, and attempt to cross-identify or roughly classify them. We identify
352 single stars in the foreground, 35 globular clusters and 27 supernova
remnants associated with M 31, as well as 62 AGNs, 59 galaxies, and 1 galaxy
clusters in the background. We uniquely classify 236 foreground stars and 17
supersoft sources based on their X-ray colors. X-ray binaries (83 LMXBs, 1
HMXBs) are classified based on their X-ray colors and X-ray variabilities. The
remaining X-ray sources either have too low S/N to calculate their X-ray
colors or do not have a unique classification, so are regarded as
unclassified. The X-ray source catalogue is published online. Study of the
X-ray source populations and the contribution of X-ray sources in the
unresolved X-ray emissions based on this catalogue will be published in
companion papers.

longtable

##  1 Introduction

X-ray studies of stellar sources provide a direct probe of the formation and
evolution of different stellar populations (e.g., Fabbiano 2006). Compared to
X-ray sources in the MW (e.g., Liu et al. 2007; Revnivtsev et al. 2007, 2011;
Zhu et al. 2018) with large distance uncertainties (e.g., Jonker & Nelemans
2004), sources in a nearby galaxy are essentially at the same distance and are
thus optimized to study the science based on accurate luminosity measurements
[e.g., the X-ray source luminosity functions (Gilfanov 2004).]. For a local
galaxy with a distance of a few Mpc and a typical _Chandra_ or _XMM-Newton_
exposure time of a few hundred ks, a point source detection limit of $\sim
10^{36-37}\rm~{}ergs~{}s^{-1}$ in the 0.5-7 keV band, for example, is
typically reached (e.g., Kim & Fabbiano 2004; Kim et al. 2009; Fabbiano 2006;
Liu et al. 2007; Revnivtsev et al. 2008; Lehmer et al. 2010; Mineo et al.
2012). This detection limit is insufficient to characterize the properties of
individual X-ray binaries down to the LF break at $\lesssim
10^{37}\rm~{}ergs~{}s^{-1}$ (e.g., Gilfanov 2004). Most nearby galaxies with
moderate X-ray observations only have about $\sim 10^{2}$ detected X-ray
sources (e.g., Irwin et al. 2002; Li et al. 2008; Li & Wang 2013a), which is
too few for many follow-up analyses, such as estimating the X-ray-stellar mass
ratio ($N_{\rm X}/M_{*}$ or $L_{\rm X}/M_{*}$; the latter could be highly
biased by one or two luminous X-ray sources; e.g., Revnivtsev et al. 2008;
Lehmer et al. 2010). This highlights the importance of an X-ray survey of a
nearby galaxy to a detection limit as low as $\lesssim
10^{36}\rm~{}ergs~{}s^{-1}$.

The Andromeda galaxy M 31 is the closest massive spiral galaxy to the MW
(distance $d=761\rm~{}kpc$, $\mathrm{5^{\prime\prime}\approx 18\rm~{}pc}$; Li
et al. 2021b). It is the most massive galaxy in the Local Group and one of the
most massive spiral galaxy in the local Universe, with a stellar mass of
$M_{*}=(1-1.5)\times 10^{11}\rm~{}M_{\odot}$ and a dark matter halo mass of
$M_{\rm 200}=(8-11)\times 10^{11}\rm~{}M_{\odot}$ (Tamm et al., 2012). M 31 is
very quiescent in star formation, with a star formation rate of only $\rm
SFR\sim 0.4\rm~{}M_{\odot}~{}yr^{-1}$ (Barmby et al., 2006). The Galactic
foreground absorption toward M 31 ($N_{\mathrm{H}}\sim 5\times
10^{21}~{}\mathrm{cm^{-2}}$) is not too high (HI4PI Collaboration et al.,
2016). The small distance, large stellar and gravitational mass, low SFR, and
large galactic disk inclination make M 31 ideal to study the population,
luminosity function, and vertical distribution of old stellar X-ray sources in
a large luminosity range.

X-ray sources toward the direction of M 31 has been extensively studied with
various X-ray telescopes (e.g., van Speybroeck et al. 1979; Trinchieri &
Fabbiano 1991; Supper et al. 1997, 2001), especially the bulge (e.g., Voss &
Gilfanov 2007, Stiele et al. 2008) and disk area (e.g., Kong et al. 2003,
Sasaki et al. 2018). The first catalogue of the _XMM-Newton_ survey of M 31
was published by Pietsch et al. (2005b), which consisted of 856 sources.
Stiele et al. (2011) then updated the catalogue which contains 1948 sources.
However, these observations toward the disk and bulge are insufficient to
characterize the spatial variation of X-ray sources over large physical
scales, which could be affected by the formation, evolution, and migration of
different source populations (e.g., Zuo et al. 2008).

An XMM-Newton View of the ANdromeda Galaxy as Explored in a Legacy Survey
(New-ANGELS) is a legacy X-ray survey of the M 31 disk and bulge, as well as
its inner halo around the disk. The program is based on an _XMM-Newton_ AO-16
large program surveying the M 31 halo at $r\lesssim 30\rm~{}kpc$ (PI: Li,
Jiang-Tao), plus many archival data mainly covering its disk and bulge (Figs.
1, 2; Table LABEL:table:XMMDatalist). The major scientific goals include not
only the population, spatial distribution, and X-ray/IR ratio of stellar
sources, but also the survey of foreground/background sources, as well as the
large-scale diffuse X-ray emission from the hot gas (e.g., Li & Wang 2007,
Bogdán & Gilfanov 2008,Bogdán & Gilfanov 2010, Kavanagh et al. 2020), the hot
CGM potentially produced by accretion instead of galactic feedback in a
representative massive quiescent spiral galaxy (e.g., Li et al. 2016, 2017,
2018).

As the first paper of the New-ANGELS project, we herein present by far the
most comprehensive X-ray source catalog extracted from a
$\approx\mathrm{7.2~{}deg^{2}}$ field around M 31, down to a flux limit of
$F_{\rm 1.0-2.0keV}=3.6\times 10^{-15}\rm~{}ergs~{}s^{-1}~{}cm^{-2}$ (reached
in 90% of the sky area covered in the survey) and the luminosity limit of
$L_{\rm 1.0-2.0keV}=\mathrm{2.5\times 10^{35}~{}ergs~{}s^{-1}}$ for M 31
sources. Further statistical analysis and scientific discussions based on this
X-ray source catalog (X-ray source LFs, spatial distribution, and the X-ray/IR
ratio of different X-ray source populations), as well as analysis of the
diffuse X-ray emission from the hot gas, will be presented in follow-up
papers. The present paper is organized as follows: In §2, we introduce the
_XMM-Newton_ observations used in the New-ANGELS project, as well as the data
reduction and source detection procedures. We then discuss the source
identification and classification based on either the multi-wavelength cross-
identification or the multi-band color and/or extent in §3. The complete
source catalog is described in detail in §4. All errors are quoted at 1
$\sigma$ confidence level throughout the paper unless specially noted.

##  2 Observations and Data Reduction

In order to have a complete survey of the X-ray sources in and around M 31, we
make use of all the available _XMM-Newton_ observations which have a pointing
position within the projected radius $r\leq 30\rm~{}kpc$ ($\approx
2.2^{\circ}$, adopting a distance of $d=761\rm~{}kpc$; Li et al. 2021b) around
the center of M 31. In summary, there are 137 observations matching our
selection criteria, but 28 of them are significantly impacted by strong
background flares. Eleven observations pointing to the center of M 31, with
less than 20 ks of exposure time, are excluded as the central region already
had sufficient exposure time, resulting in a final selection of 98
observations for subsequent analysis. Table LABEL:table:XMMDatalist in
Appendix A provides a summary of them. The total/net (after removing strong
background flares) exposure time is $\approx 3.1/2.5$, $3.1/2.6$, and
$2.7/1.9\rm~{}Ms$ for MOS-1, MOS-2, and PN, respectively. The mosaicked _XMM-
Newton_ exposure map of all the observations is presented in Fig. 1.

Figure 1: Left: All-EPIC exposure map of the _XMM-Newton_ observations around
M 31. The color denotes the effective exposure time accounting for the
vignetting. The pink circles represent observations that are excluded from
data reduction and analysis due to background flaring. Right: The sky coverage
of the observations above the given all-EPIC exposure time. The sky coverage
of this work, Stiele et al. (2011), and Pietsch et al. (2005b) are shown in
black solid line, blue dashed line, and green dotted line, respectively.

We reprocess the _XMM-Newton_ data using the _XMM-Newton_ Science Analysis
Software (SAS) v19.1.0. SAS does not have a fixed version of calibration
files. Instead, these files are updated continuously. We use the latest
calibration files until May 2022. We first reproduce the event lists of the
three EPIC cameras (MOS-1, MOS-2, and PN) using the SAS tools emchain and
pnchain for MOS and PN, respectively. We then identify and tag the MOS CCDs
which are in anomalous states with emtagnoise. The registered events from
these tagged CCDs are removed in the following analysis. We identify good time
intervals (GTIs) by removing strong background flares mainly caused by
elevated soft proton contamination using mos-filter and pn-filter. We further
filter the events with the #XMMEA_EM filter in evselect for MOS and “FLAG ==
0” for PN which provide a canned screening set of FLAG values for the event.
These filters exclude ‘wrong’ or ‘suspicious’ events, e.g., near hot pixels or
outside the field of view (FOV) of the telescope. The GTIs of different
observations (identified with the observation ID: ObsID) after these cleanings
are summarized in Table LABEL:table:XMMDatalist.

After reprocessing the event list, we perform standardized EPIC source
detection with the task edetect_stack111http://xmm-
tools.cosmos.esa.int/external/sas/current/doc/eboxdetect/ (Traulsen et al.
2019, 2020) in five bands: 0.2-0.5 keV, 0.5-1.0 keV, 1.0-2.0 keV, 2.0-4.5 keV,
and 4.5-12.0 keV, which are the standard bands used in many _XMM-Newton_
catalogues (e.g., the 4XMM-DR12 catalog; Webb et al. 2020). The count rates
measured in these bands are also used to define the hardness ratios of the
source. The hardness ratio is defined as
${HR}_{\mathrm{i}}=(R_{\mathrm{i+1}}-R_{\mathrm{i}})/(R_{\mathrm{i+1}}+R_{\mathrm{i}})$,
where the $R_{\mathrm{1}},R_{\mathrm{2}},R_{\mathrm{3}},R_{\mathrm{4}}$, and
$R_{\mathrm{5}}$ are the count rates of all-EPIC in 0.2-0.5 keV, 0.5-1.0 keV,
1.0-2.0 keV, 2.0-4.5 keV, and 4.5-12.0 keV, respectively. edetect_stack is a
tool chain to perform source detection on multiple mosaicked or stacked
observations. It greatly improves the sensitivity of the source detection in
the overlapping areas of different observations. Considering the efficiency,
the source detection edetect_stack is not applied to the entire New-ANGLES
footprint. Instead, we split the _XMM-Newton_ survey area around M 31 into
five smaller areas (North, South, East, West, and Center, as summarized in
Table 1 and plotted in different colors in Fig. 3) and perform source
detection separately in each of them. For each of these five areas, we only
include observations whose pointing direction is within or $\leq 10^{\prime}$
from the boundary of different areas in the source detection procedure.

Table 1: Definition of sky areas used for source detection Region | Definition
---|---
North | $\rm d1\geq 30^{\prime}$
South | $\rm d1\leq-30^{\prime}$
East |  $\rm-30^{\prime}<d1<30^{\prime}$, $\rm d2<0^{\prime}$ and $\rm R>12^{\prime}$
West |  $\rm-30^{\prime}<d1<30^{\prime}$, $\rm d2\geq 0^{\prime}$ and $\rm R>12^{\prime}$
Center | $\rm R\leq 12^{\prime}$

Figure 2: Mosaicked false-color image of the _XMM-Newton_ observations of M
31. We also show three zoom-in $30^{\prime}\times 30^{\prime}$ regions in the
center, disk, and halo. The count rate images are background subtracted,
exposure corrected, adaptively smoothed, but not vignetting corrected. The
scale bars of $10^{\prime}=2.2~{}\mathrm{kpc}$ in the inserted panels are
calculated at the distance of M 31 (761 kpc). Because the center region is
much brighter, we adjust the color scale of the upper left panel to capture
more details.

We use edetect_stack to detect sources with a two-stage procedure. We first
run edetect_stack to the original cleaned data, which calls evselect, eexpmap,
and emask to create the counts, exposure, and mask maps, respectively. We
further modify the mask maps to limit the source detection area within the
boundary as defined in Table 1 and Fig. 3 to speed up the source detection. In
the second stage, we run edetect_stack again to perform the source detection
within the five sub-areas, separately. It first calls eboxdetect to search
sources in two steps: in the first step we use a local background to detect
and remove the sources, then create global background maps; while in the
second step, we use these global background files to perform sliding box
search again. After this initial source searching, edetect_stack then calls
emldetect to acquire the parameters of the sources by performing joint maximum
likelihood point spread function (PSF) fitting on all the involved images of
the given source simultaneously (see more detail in Traulsen et al. 2019,
Traulsen et al. 2020). edetect_stack then produce the final EPIC summary
source list by calling srcmatch.

Sometimes a faint source could fall into the gaps or bad pixels of one of the
three EPIC cameras. In this case, edetect_stack still performs maximum
likelihood multi-source PSF fitting (by calling emldetect) at the same
position based on the detection on the other one or two cameras. It may obtain
a zero flux of the source on a certain camera. This will significantly bias
the final parameters of the source in the summary list. Therefore, we mark the
‘zero flux’ of detected sources as non-detection due to their falling into the
CCD gaps or bad pixels in one or two cameras. We then recalculate the combined
parameters of the sources based only on the detection on other cameras (flux,
detection likelihood with an updated degree of freedom, etc.).

Figure 3: Location of detected X-ray sources. Sources detected in different
areas as defined in Table 1 are plotted in different colors.

##  3 X-ray Source Identification and Classification

M 31 is unique for systematic studies of different populations of X-ray
sources either associated with the galaxy or in the foreground/background
(e.g., Fabbiano 2006), including low- and high-mass X-ray binaries (LMXBs and
HMXBs), ultra-luminous X-ray sources (ULXs), and other accreting or non-
accreting stellar binary X-ray sources (e.g., supersoft sources, SSSs), open
or globular clusters, isolated neutron stars and magnetars, supernova remnants
(SNRs) and pulsar wind nebulae (PWNe), background galaxies/groups/clusters,
AGN, and transient X-ray sources (e.g., SNe, GRB), etc. In this section, we
will identify or classify the detected X-ray sources around M 31 in two ways:
either by identification of the sources based on cross-matching them with
other firmly identified multi-wavelength counterparts (§3.2), or by rough
classification of the sources based on their multi-band (including X-ray)
colors, morphology, and/or variability (§3.3). The former way is often a firm
unique identification of the nature of the source, while the latter one is
just a rough classification of the source, and a single source may be
classified as candidates of different types of objects.

###  3.1 Multi-wavelength catalogues and cross-match criteria

We compare our _XMM-Newton_ source catalogue in and around M 31 to other
multi-wavelength catalogues to cross-identify the sources. The multi-
wavelength catalogues used in the cross-identification include (as summarized
in Table 2): the SIMBAD (Wenger et al., 2000), Pan-STARRS (PS1) DR1 (Chambers
et al., 2016), and AllWISE (Cutri et al., 2021) databases for various types of
objects; the Local Group Galaxies Survey (LGGS; Massey et al. 2006) for
optical sources on the M 31 disk; GAIA DR3 for stars (Gaia Collaboration et
al., 2016, 2021); the Revised Bologna Catalog (Galleti et al. 2004) for
globular clusters (GlCs); Jennings et al. (2014) and Lee & Lee (2014) for
SNRs; the Million Quasars (Milliquas) catalog v7.2 (an update of Flesch 2015)
for AGN.

We adopt different cross-match criteria for different types of sources based
on their different spatial extension and multi-wavelength properties. Details
of the cross-identification procedure for different types of sources will be
described in §3.2.1, 3.2.2, and 3.2.3, while a brief summary of the criteria
is listed in Table 2. In most of the cases, we define the cross match criteria
based on the X-ray position uncertainty $\sigma_{\mathrm{pos}}$ of the _XMM-
Newton_ sources (joint fit in five bands), which is determined via PSF
fitting. To include the additional position uncertainty, we use the following
empirical formula:

$\sigma_{\mathrm{combined}}=\sqrt{0.89\times\sigma_{\mathrm{\mathrm{pos}}}^{2}+0.42^{2}}$
(1)

More information can be found in Appendix B. For most of the point-like
sources, we cross match the multi-wavelength counterparts with
$\Delta{\mathrm{pos}}<3.44\sigma_{\mathrm{combined}}$ from the detected X-ray
sources. For extended sources such as galaxies, galaxy clusters, or SNRs,
however, in addition to an initial cross-match in a larger radial range, we
manually check each cross-matched sources on the multi-wavelength images to
avoid mis-match.

A more complicated case is the foreground (fg) star, which we use the Gaia DR3
catalogue to identify (Gaia Collaboration et al., 2016, 2021). As the number
density of foreground star is very high, we often identify multiple stars
within $3.44~{}\sigma_{\mathrm{combined}}$ from the X-ray sources. We
therefore adopt a different procedure to cross match the stars to our X-ray
sources. We generate a foreground star catalogue from Gaia DR3 with PSS $>$
90% (PSS is the column in GAIA DR3 referring to the probability as a single
star). We then use the NWAY222https://github.com/JohannesBuchner/nway(a
Bayesian algorithm for cross-matching multiple catalogs, Salvato et al. 2018;
Buchner et al. 2021) algorithm to cross-match the foreground stars to our
X-ray catalogue by considering their X-ray/optical locations, the X-ray-to-
optical flux ratio, and the X-ray hardness ratio HR2. Details of the cross-
matching procedure is presented in the appendix (§C). We use the NWAY
parameter p_any which is the probability that the X-ray source has at least a
reliable counterpart, instead of just the separation between the X-ray and
optical sources, to describe the likelihood of a GAIA source being the
counterpart of an X-ray source. Typically, p_any$>$0.9 corresponds to a false
detection rate of $<5\%$.

Table 2: Summary of the criteria and results of source identification and
classification in and around M 31

Type |  Cross-Matched Catalogs |  Identification |  Classification |  Confirmed |  Candidates
---|---|---|---|---|---
fg star |  GAIA DR3 |  1\. NWAY p_anya$>0.9$; 2. PSSb$>90\%$; 3. point source |  1\. softc in X-ray; 2. not AGN or confirmed fg star; 3. point source |  352 |  236
AGN |  The Million Quasars (Milliquas) catalog, v7.2 |  $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$d from a confirmed AGN |  $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from an AGN candidate |  62 |  505
Globular cluster (GlC) in M 31 |  Revised Bologna Catalog, v5; SIMABD |  $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from a confirmed GlC |  $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from a GlC candidate |  35 |  0
Supernova remnant (SNR) in M 31 |  Jennings et al. (2014); Lee & Lee (2014) |  1\. no AGN or confirmed fg star at $\Delta\mathrm{pos}<10^{\prime\prime}$; 2. $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from a SNR candidate; 3. manual check |  1\. no AGN or confirmed fg star at $\Delta\mathrm{pos}<10^{\prime\prime}$; 2. $3.44\sigma_{\mathrm{combined}}\leq\Delta\mathrm{pos}<10^{\prime\prime}$ from a SNR candidate; 3. manual check |  27 |  4
Galaxy (Gal) |  SIMABD |  1\. no AGN or confirmed fg star at $\Delta\mathrm{pos}<6^{\prime\prime}$; 2. $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from a galaxy; 3. manual check |  1\. no AGN or confirmed fg star at $\Delta\mathrm{pos}<6^{\prime\prime}$; 2. $3.44\sigma_{\mathrm{combined}}\leq\Delta\mathrm{pos}<6^{\prime\prime}$ from a galaxy; 3. manual check |  59 |  3
Galaxy cluster (GCl) |  SIMBAD |  1\. extendede source in X-ray; 2. close to a confirmed galaxy cluster based on manual check |  1\. extended source in X-ray; 2. close to a galaxy cluster candidate based on manual check |  1 |  5
Super soft source (SSS) |  N/A |  1\. HR1$<$0, HR2$<$-0.9; 2. point source |  1\. only detected in 0.2-0.5 keV; 2. point source |  11 |  6
High mass X-ray binary (HMXB) |  1\. Pan-STARRS DR1; 2. LGGS |  1\. hardc in X-ray; 2. bluef in optical but not AGN or confirmed fg star; 3. coincided with OB association or strongly variableg; 4. point source |  see unclassified sources |  1 |  0
Low mass X-ray binary (LMXB) |  1\. Pan-STARRS DR1; 2. LGGS |  1\. hard in X-ray; 2. red or no confirmed optical counterpart, but not AGN or confirmed fg star; 3\. strongly variable; 4. point source |  see unclassified sources |  83 |  0
total classified (with unique classification) |  |  |  |  631 |  759
unclassified (with no or more than one classification) |  |  1\. not uniquely classified; 2. low S/Nh or extended |  1\. not uniquely classified; 2. hard in X-ray; 3a. blue in optical: AGN or HMXB; 3b. red or no confirmed optical counterpart: AGN or LMXB; 4. Additional labels added to distinguish AGNs and XRBs based on HR2 and HR3i. |  2327 |  789

The table summarizes the multi-wavelength catalogues used for cross-
identification of different types of X-ray sources, as well as the criteria of
identifying confirmed sources, or classifying source candidates. The number of
different types of firmly identified or roughly classified sources are listed
in the last two columns.

Table 2 —continued.
a. We use the NWAY algorithm to match the GAIA sources to our X-ray sources,
considering both the X-ray to optical flux ratio and the X-ray hardness (see
text for details). p_any is the matching probability defined by NWAY. The
false matching rate is $<5\%$ when p_any$>$0.9.
b. PSS (between 0 and 100%) is the parameter in GAIA defining the probability
of a source being classified as a star.
c. We define X-ray sources with HR2-HR1+0.53$>$0 ($\leq$0) as ‘hard’ (‘soft’).
HR1 (HR2) is the X-ray hardness ratio between the 0.2-0.5 keV and 0.5-1.0 keV
(0.5-1.0 keV and 1.0-2.0 keV) bands, as detailed in the §2.
d. $\sigma_{\mathrm{combined}}$ is the modified position uncertainty defined
in Equ. 1
e. We define sources as “extended”, when the detected extent radius (EXTENT,
see Appendix D) of sources exceed $6^{\prime\prime}$.
f. We define Pan-STARRS counterpart with $g-r>0$ ($<0$) as ‘red’ (‘blue’).
g. We define sources with FLUXVAR$>$10 as ‘strongly variable’.
h. We only use HR1 and HR2 in high S/N detections to classify sources, when
$\sigma_{\mathrm{HR1}}<0.2$ and $\sigma_{\mathrm{HR2}}<0.2$, where
$\sigma_{\mathrm{HR1}}$ and $\sigma_{\mathrm{HR2}}$ are the uncertainties in
the measured HR1 and HR2.
i. We prefer unidentified hard X-ray source with $HR3+1.1\times HR2>0$ as XRB.

###  3.2 Multi-Wavelength Cross Identification

There are basically three types of X-ray sources detected in the field:
foreground sources which are mainly stellar sources (single or binary stars)
in the MW, various types of X-ray sources associated with M 31 (SNRs, globular
clusters, and many stellar sources), and distant sources in the background
(AGN, galaxies, and galaxy clusters). The most reliable way to firmly identify
these X-ray sources is often to search for their identified multi-wavelength
counterparts, using the catalogues and cross-match algorithm described in the
above section (§3.1). This is often more reliable than a simple classification
of the sources based on their X-ray or multi-band colors or other multi-
wavelength parameters (§3.3).

####  3.2.1 Stellar X-ray sources in the foreground

Since M 31 is located in the direction off the Galactic plane, most of the
foreground X-ray sources should be relatively old stars, including both single
and binary stars in the MW. Although in principle we can also detect other
types of sources such as SNRs or globular clusters, they could in principle be
easily identified and unlikely to be the dominant population in the direction
of M 31 (in fact, we do not find any SNRs or globular clusters in the MW
toward the direction of M 31 in our catalogue).

We will discuss the classification of binary X-ray sources in §3.3. Here we
only focus on single star X-ray sources. Single stars tend to be individually
faint in X-ray. Typically, K and M stars have $L_{X}\lesssim
10^{29}\rm~{}ergs~{}s^{-1}$ (e.g., Schmitt et al. 1995). O, B stars can be as
luminous as $L_{X}\sim 10^{33}\rm~{}ergs~{}s^{-1}$ (e.g., Sana et al. 2006),
which is marginally detectable at the distance of M 31 with very deep X-ray
observations (the lowest detection limit toward the nuclear region of M 31 in
our NEW-ANGELS project is $L_{\rm 0.2-12~{}keV}\sim
10^{34}\rm~{}ergs~{}s^{-1}$; see Paper II for details). However, these young
stellar populations are not expected to be located far away from the disk of
the MW. Therefore, most of the X-ray emitting single stars cross-matched with
the GAIA catalogue should be within the solar neighbourhood. We have firmly
identified 352 X-ray sources as single stars in the GAIA catalogue, of which,
234 have a reliable distance measurement, and the median value is
$d=434_{-207}^{+555}\rm~{}pc$, confirming their nature as foreground sources.

Cautions should be made here that the GAIA catalogue does not distinguish
single star and close binary stars, but simply call them “single stars” due to
the dominance of single stars in the catalogue (Delchambre et al., 2022). We
find some sources classified as “fg stars” in Table 2 have hard X-ray spectra
(Fig. 4a), which may indicate some of them are actually accreting XRBs.
Nevertheless, we still call fg stars identified in GAIA as “single stars”
throughout the paper.

####  3.2.2 GlCs and SNRs associated with M 31

Most of the discrete X-ray sources associated with M 31 are neutron star or
black hole accreting binaries. Most such binary systems are faint in optical
and IR, so are identified mainly based on their X-ray properties (e.g., Stiele
et al. 2011). Classification of these sources will be further discussed in
§3.3. We herein only cross-identify two types of X-ray sources associated with
M 31, GlC and SNRs, with the corresponding multi-wavelength catalogues.

X-ray emission from GlCs is often contributed by various types of low-
luminosity X-ray sources, [$L_{\rm X}<10^{35}\rm~{}ergs~{}s^{-1}$, including
active binaries (ABs), cataclysmic variables (CVs), and millisecond pulsars
(MSPs), and quiescent LMXBs, etc. (e.g., Heinke et al. 2005; Bahramian et al.
2020] or dominated by accreting binaries. Such sources also tend to show
significant X-ray variabilities (e.g., Heinke et al. 2005; Bahramian et al.
2020). The integrated X-ray spectra of GlCs often comprise both thermal and
non-thermal components, with the former mainly from ABs and CVs while the
latter from MSPs and LMXBs (e.g., Heinke et al. 2005; Zhao & Heinke 2022).
Since GlCs are bright and often well identified in optical, we cross match our
X-ray catalogue with the Revised Bologna Catalog of M 31 clusters (Galleti et
al., 2014), with the criteria described in §3.1 and summarized in Table 2. We
in total identified 35 X-ray bright GlCs in M 31.

SNRs are often characterized with a strong thermal plasma X-ray spectrum,
although some young ones also have a non-thermal hard X-ray tail. There are
$\sim 300$ SNRs identified in the MW (Green, 2019). A large fraction of them
reside in the Galactic plane, so suffer from strong foreground extinction.
Compared to the SNRs in the MW, studying SNRs in an external galaxy has the
advantage of having a typically lower foreground extinction and a more
accurate distance. Until now, there are at least a few hundred SNRs detected
in external galaxies with multi-wavelength observations (e.g., Maggi et al.
2016, 2019; Bozzetto et al. 2017). M 31 is one of the galaxies with the
largest number of SNRs identified (e.g., Sasaki et al. 2012; Lee & Lee 2014),
only after the face-on and star forming galaxy M 33 (e.g., Long et al. 2010;
White et al. 2019) and M 83 (e.g., Blair et al. 2012, 2015). We merge the
optical SNR catalogue of M 31 from Jennings et al. (2014) and Lee & Lee
(2014), resulting in 177 SNR candidates. Since SNRs are extended sources and
the optical/X-ray morphologies are not necessarily well correlated with each
other, in additional to an automatic cross match, we also manually check our
_XMM-Newton_ X-ray and LGGS (Massey et al., 2006) H$\alpha$ image to make sure
there is an X-ray source associated with the SNR. We regard X-ray sources with
a separation of $\Delta\mathrm{pos}<3.44\sigma_{\mathrm{combined}}$ from an
identified SNR as a firmly identified X-ray emitting SNR, while those with
$3.44\sigma_{\mathrm{combined}}\leq\Delta\mathrm{pos}<10^{\prime\prime}$ as an
SNR candidate. We in total identify 27 X-ray emitting SNRs and 4 more
candidates.

####  3.2.3 Background sources

Background X-ray sources are anything in the distant universe, including AGNs,
normal galaxies, and groups/clusters of galaxies, etc. In principle, their
number densities should have a uniform spatial distribution across a small sky
area such as that covered by our New-ANGLES survey. The X-ray emission from a
normal galaxy without an AGN is comprised of both a thermal hot gas and a non-
thermal stellar source component (e.g., Mineo et al. 2012; Li & Wang 2013a).
It is in principle distinguishable from an AGN based on their X-ray hardness
ratios, especially if the hot gas contribution is significant (see §3.3 for
details). Groups of galaxies also have softer spectra compared to AGNs, and
their X-ray emissions often appear as extended sources with the centroid
offset from a galaxy (e.g., Sun et al. 2009). On the other hand, a galaxy
cluster often has stronger X-ray emission from the hot gas than from the AGN,
but the hot gas emission is often significantly harder than that of a galaxy
(due to the higher temperature, e.g., Li & Wang 2013b), so not significantly
distinguishable in X-ray hardness from an AGN. However, the X-ray emission of
a galaxy cluster is usually extended, and the nearby cluster (e.g., $z<0.5$)
is always well identified in optical images. Therefore, it is often not
difficult to distinguish these different types of background sources. There
may be some difficulties in distinguishing AGNs and XBs just based on their
X-ray properties measured with poor counting statistics, but it is quite
straightforward to identify an X-ray AGN if it is already identified in other
ways (e.g., with an optical spectrum; Lyke et al. 2020).

By cross-matching our X-ray catalog with the Milliquas catalogue (Flesch,
2015), we identify 62 confirmed X-ray emitting AGNs and 504 candidates. Since
many of the AGN candidates are identified based on their multi-band colors
instead of the spectral properties, the identification of an X-ray counterpart
makes them a higher chance to be a real AGN. Since our identification of the
X-ray emitting AGN is mostly based on the existing AGN catalogues, many of the
unclassified hard X-ray sources (especially in the North and South region)
could in fact be unidentified AGNs in these catalogues.

By manually checking their multi-wavelength images (e.g. mostly optical and IR
from SDSS, Pan-STARRS, WISE, and HST), we identify 59 X-ray emitting galaxies
without an identified AGN, and three more candidates of galaxies. Some of
these X-ray sources could be associated with multiple galaxies, so may
actually be galaxy groups. Furthermore, we also identify five extended X-ray
sources as GCl candidates, while only one is firmly identified as a galaxy
cluster at $z\sim 0.29$ (2E 171, Kotov et al. 2006). This firmly identified
GCl is projected in the direction of the disk of M 31, and appears as an
extended hard X-ray source.

###  3.3 Classification of X-ray Sources Based on Their Multi-band Properties

In the above section (§3.2), we have firmly identified hundreds of single
stars in the foreground, GlCs and SNRs associated with M 31, as well as AGNs,
galaxies, and GCls in the background in our _XMM-Newton_ X-ray source
catalogue. We have also less firmly identified hundreds of candidates of all
of these types of sources, except for fg stars (will be discussed below). The
cross-identification is mostly based on multi-wavelength cross-match of
different identified source catalogues and is in general reliable and unique.
However, the total number of sources identified this way is only $\lesssim
10^{3}$, or $\sim 20\%$ or the total number of X-ray detected sources. A rough
classification of a larger fraction of the X-ray sources, even if not unique
and less reliable, is critical in the follow-up statistical analysis of
different source populations. In this section, we discuss how to classify the
remaining X-ray sources based on their X-ray and/or multi-band colors, or the
X-ray variability.

Among all 62 AGNs and 504 candidates, 160 have an X-ray flux $F_{\rm
2-4.5~{}keV}>10^{-14}\rm~{}ergs~{}s^{-1}$ in the entire $7.2\rm~{}deg^{2}$
area covered by our NEW-ANGELS survey, leading to a surface density of
$\mathrm{18.3~{}deg^{-2}}$. This is only $\sim 20\%$ of the prediction based
on some cosmological surveys where most of the detected X-ray sources should
be AGN (e.g., Chen et al. 2018). However, when we zoom in to the inner halo
regions (North and South), the number density of all detected sources is
comparable to that of those surveys, the huge difference between the number of
classified and expected AGNs may be caused by the large number of unidentified
AGNs, which may have poorer optical data and not included in the Milliquas
catalogue. Furthermore, most of the stellar X-ray sources, either single or
binary stars, are also not unambiguously identified, unless they are
foreground sources included in the GAIA catalogue. In many cases, the
classifications of these AGNs and stellar X-ray sources may not be unique.

####  3.3.1 Types of stellar X-ray sources

Both single stars and binaries can be X-ray sources. Single stars are often
too faint in X-ray to be individually detected at the distance of M 31, so
have to be foreground sources (§3.2.1). On the other hand, binary X-ray
sources have a broad X-ray luminosity range (e.g., Gilfanov 2004), so could be
either foreground sources or associated with M 31. There are basically two
types of stellar binary X-ray sources: accreting binaries whose X-ray emission
is mainly powered by the accretion of materials from the companion star to the
compact star, and non-accreting binary sources whose X-ray emission is mainly
produced via other mechanisms such as the stellar corona activity.

The X-ray emission from a non-accreting binary could be produced by the
magnetically driven coronal activities (e.g., Güdel 2004). These sources are
often identified as chromospherically active binaries (ABs; e.g., Sazonov et
al. 2006), whose soft X-ray emission shows strong variability in a timescale
of a few hours, and the spectrum is characterized by a thermal plasma at a
typical temperature of $kT\sim 0.5\rm~{}keV$ (sometimes with more complex
temperature distributions; e.g., Revnivtsev et al. 2008; Singh & Pandey 2022).
There are also many individually faint stars (either binary stars or single
stars) with a thermal plasma X-ray spectrum but only individually detectable
with deep X-ray observations within the MW (e.g., Rosner et al. 1985; Schmitt
et al. 1995; Sana et al. 2006; Revnivtsev et al. 2009). Most of these non-
accreting binary X-ray sources cannot be individually detected at the distance
of M 31, but could still collectively contribute to the unresolved X-ray
emissions.

Accreting X-ray binaries include LMXBs, HMXBs, cataclysmic variables (CVs),
and supersoft sources (SSSs), etc., depending on the mass of their donor stars
and the nature of the accreting compact star (black hole, neutron star, and
white dwarf; e.g., Remillard & McClintock 2006; Mukai 2017). Some special
types of X-ray sources, such as ULXs and probably the major X-ray emitting
sources in GlCs, are also accreting X-ray binaries (e.g., Voss & Gilfanov
2007). The X-ray emission from an accreting binary is mainly produced in its
accretion disk and corona, and appears to be a power law with a photon index
typically in the range of $\Gamma\sim 1.5-2.0$ (Irwin et al., 2003; Fabbiano,
2006). On the other hand, because the temperature of accretion disk around a
black hole is expected to fall with the increasing mass of the accreting
compact object (e.g., Miller et al. 2004), the intrinsic X-ray emission tends
to be harder than an accreting SMBH (the photon index of an AGN is typically
$\Gamma\sim 2$; e.g., Brightman et al. 2013; Li et al. 2021a). However, it is
often not straightforward to distinguish an individual X-ray binary either in
the foreground or associated with M 31 from a background AGN only based on
their X-ray spectral slopes, due to the limited number of photons and the
complex intrinsic absorption. Furthermore, there also exist some special types
of accreting X-ray binaries whose X-ray emission is supersoft. These SSSs are
accreting white dwarfs, but different from the CVs, their X-ray emission is
mostly produced by steady nuclear fusion on the white dwarf’s surface, instead
of from the accretion disk (e.g., Greiner 2000).

Accreting X-ray binaries span a large range of X-ray luminosity, with some
most luminous ones could be detected individually in nearby galaxies (e.g.,
Gilfanov 2004). Therefore, it is often not easy to distinguish if a source is
foreground or associated with M 31 only based on its spectral shape and X-ray
brightness, especially if the source is located outside the disk of M 31.
Nevertheless, based on multi-wavelength cross-identifications, there are
various types of accreting X-ray binaries or candidates identified associated
with M 31 in the literature, such as LMXBs (e.g., Stiele et al. 2011; Sasaki
et al. 2018), HMXBs (e.g., Shaw Greening et al. 2009; Williams et al. 2018;
Dalcanton et al. 2012; Williams et al. 2014; Lazzarini et al. 2021), and SSSs
(e.g., Pietsch et al. 2005b, a; Stiele et al. 2011; Sasaki et al. 2018). In
particular, there are also two confirmed ULXs in M 31: CXOM31 J004253.1+411422
($L_{\rm 0.2-10~{}keV}\approx 3.8\times 10^{39}\rm~{}ergs~{}s^{-1}$; Henze et
al. 2009; Kaur et al. 2012) and XMMU J004243.6+412519 ($L_{\rm
0.5-10~{}keV}\approx 2.3\times 10^{39}\rm~{}ergs~{}s^{-1}$; Henze et al. 2012;
Esposito et al. 2013). In the next subsection (§3.3.2), we will introduce a
systematic way to classify these stellar X-ray sources and AGNs.

Figure 4: Color-color diagram of the detected X-ray sources with HR errors
$\sigma_{\mathrm{HR}}<0.2$. Identified fg stars, AGNs and galaxies are plotted
in the top panels (a1, a2 and a3), with the firmly identified ones plotted in
filled circle, while candidates in open circles. Identified globular clusters,
XRBs and SNRs are plotted in the middle panels (b1, b2 and b3). All the
sources detected in the present work are plotted in the bottom panels (c1, c2
and c3). The underlying false-color images are the probability distribution of
the cross-matched sources between 4XMM-DR11s (Traulsen et al., 2020, 2022) and
SIMBAD (top row: AGN in blue, galaxy in green, fg star in red; middle row: XRB
in blue, globular cluster in green, SNR in red). The dotted contours enclose
68% of the cross-matched sources. We also overlay different power-law (in
blue) and APEC (in red) models in the mesh grids. The color of the thick solid
curves denote $N_{\mathrm{H}}$, which changes from 0 to $\rm 3\times
10^{21}~{}\mathrm{cm}^{-2}$, with the three dashed curves mark
$N_{\mathrm{H}}=0$, $5\times 10^{20}$, and $3\times
10^{21}~{}\mathrm{cm}^{-2}$, respectively. The upper limit of $N_{\mathrm{H}}$
is roughly consistent with the peak value in the M 31 disk. When computing the
models, the response files of PN, MOS-1 and MOS-2 are used for the top,
middle, and bottom rows, respectively. The dash-dotted lines show our criteria
to classify different types of objects (SSSs, “hard” and “soft” sources; see
Table 2 for details)

Figure 5: The probability density distribution of different types sources in
Fig 4 at different hardness ratios. The vertical dashed lines mark our
criteria to separate fg star v.s. AGN and XRB. The HR1-HR2 criterion in the
upper panel is used in the source classification as summarized in Table 2.

####  3.3.2 X-ray source classification criteria

We first classify the X-ray sources based solely on their X-ray colors, which
are defined with a few inter-band hardness ratios as defined in §2. Compared
to spectral analysis which is often adopted for bright sources, these hardness
ratios are especially helpful to roughly characterize the spectral shape of
faint sources which have too few counts to extract a spectrum. A few X-ray
color-color diagrams based on different hardness ratios are presented in Fig.
4, where we also overlay the expected locations of a few simple spectral
models (APEC and power law) with different parameters (foreground absorption
column density $N_{\rm H}$, thermal plasma temperature $kT$ of the APEC model,
or photon index $\Gamma$ of the power law model). Three different column
densities in the figure represent typical $N_{\rm H}$ values of no absorption
with $N_{\rm H}=0~{}\mathrm{cm}^{-2}$, Galactic foreground absorption to the
direction of M 31 with $N_{\rm H}\approx 5\times 10^{20}~{}\mathrm{cm}^{-2}$,
and the absorption of M 31 disk with $N_{\rm H}\approx 3\times
10^{21}~{}\mathrm{cm}^{-2}$ which are estimated from HI4PI HI map (HI4PI
Collaboration et al., 2016), respectively. Assuming either a power-law or APEC
model, the absorption would cause X-ray sources to shift along the solid line
shown in the color-color diagram (Fig. 4). Despite M 31’s proximity to the
Galactic plane (with a Galactic latitude of $b=-21.4^{\circ}$), the amount of
Galactic foreground absorption is not substantial enough to cause a
significant shift in its position on the color-color diagram according to Fig.
4. All the data points plotted in Fig. 4 are the detected sources in M 31 with
the detection likelihood EP_DET_ML $\geq 6$, and the uncertainty on the
measured hardness ratios $\sigma_{\rm HR}<0.2$. There are in total $\sim 2000$
sources plotted in Fig. 4. We will only use these sources with a relatively
high detection S/N to discuss the source classification criteria below. The
remaining ones, if not already uniquely classified as fg stars, AGNs, GlCs,
SNRs, galaxies, or GCls, will then be treated as unclassified sources (Table
2).

We first characterize the location of the identified X-ray sources in 4XMM-
DR11s on the color-color diagram, and compare them to our firmly identified
and classified sources around M 31, in order to determine the source
classification criteria. We cross-match the 4XMM-DR11s catalogue (e.g.,
Traulsen et al. 2020, 2022) with the SIMBAD catalogue to identify the X-ray
sources, with a strict criteria of the separation between the sources in the
two catalogues $\Delta\mathrm{pos}<1^{\prime\prime}$. As there are too many
identified sources matched to 4XMM-DR11s (18605 AGNs, 3446 galaxies, 7037
stars, 51 SNRs, 379 XRBs, 154 GlCs), we plot the probability density
distribution, instead of individual data points, of different types of sources
in Fig. 4.

It is clear that different types of sources distribute in distinct areas in
the X-ray color-color diagram (Fig. 4), although some populations are heavily
overlapped. In general, AGNs, XRBs and GlCs are hard in X-ray, while SNRs and
fg stars are soft. These “hard” and “soft” sources are easy to distinguish.
Galaxies have a wide distribution on the color-color diagram, and includes the
area occupied by AGNs, indicating that some of the X-ray sources identified as
galaxies may actually host an unidentified X-ray bright AGN. Most of the fg
stars appear soft in X-ray. These sources are likely single stars or non-
accreting binaries as introduced in §3.2.1 and 3.3.1. However, a significant
fraction of fg stars have a hard X-ray spectrum consistent with that of XRBs.
These sources may thus be unidentified accreting X-ray binaries instead of
single stars (§3.2.1; Delchambre et al. 2022).

The contamination of AGNs and XRBs in the identification of galaxies and fg
stars is more clearly shown in Fig. 5, where we plot the probability
distribution of different types of sources in two X-ray color combinations
obtained from the HR1-HR2 and HR2-HR3 diagrams. The dashed lines in the panels
a and b of Fig. 5 ($HR2-HR1+0.53=0$, $HR3+1.1\times HR2+0.71=0$) are the same
as those in Fig. 4a,b, separating the “hard” and “soft” sources. Notably, the
criterion used in the HR1-HR2 diagram (Fig. 4a) is in line with the effect of
absorption. Even when there is a significant amount of absorption, modifying
the value of $N_{\mathrm{H}}$ would not substantially impact the
classification of X-rays as either “hard’ or “soft”. It is clear that galaxies
have a similar peak position in X-ray colors as AGNs, but a significantly
broader distribution. This similar peak position indicates many galaxies
should indeed host an unidentified AGN. Despite XRBs would dominate the
emission of galaxies, the peak of galaxies shown in Fig. 4b is still in line
with that of AGNs. On the other hand, fg stars, although the peak in the soft
X-ray color domain, have a very asymmetric probability distribution, which is
significantly biased to a harder tail. This hard tail should reflect the
contribution from unidentified binary stars. Meanwhile, as indicated by Fig.
5b, XRBs tend to be harder than AGNs.

In addition to the “hard” and “soft” sources, we also identify some supersoft
sources in Fig. 4. These three category of sources are defined as:

$\bullet$ Hard: $HR1-HR2<0.53$ and $HR2>-0.5$ in the HR1-HR2 diagram;
$HR3+1.1\times HR2>-0.71$ on the HR2-HR3 diagram.

$\bullet$ Soft: $HR1-HR2>0.53$ and $HR1>0$ in the HR1-HR2 diagram;
$HR3+1.1\times HR2<-0.71$ on the HR2-HR3 diagram.

$\bullet$ Supersoft: $HR2<-0.9$ and $HR1<0$ in the HR1-HR2 diagram. If a
source is only detected in the 0.2-0.5 keV band and we cannot calculate HR2,
it is also regarded as a candidate of SSSs (Table 2). Since SSSs are often not
detected in the hard X-ray band, we do not define a criterion to identify them
on the HR2-HR3 diagram.

Most ($\approx 70\%$) fg stars and SNRs are “soft” sources, while most
($\approx 90\%$) AGNs, galaxies, XRBs and GlCs are “hard”. SSSs by definition
are in the supersoft domain. They are often optical novae, or accreting white
dwarfs, which often have a thermal spectrum with a temperature of $kT\lesssim
100\rm~{}eV$ (e.g., Di Stefano et al. 2004; Pietsch et al. 2005a).

Figure 6: The X-ray to infrared flux ratio (X-ray flux calculated in 0.2-12
keV, while IR flux is the WISE 3.4 $\mathrm{\mu m}$ flux) and X-ray
variability of different X-ray source populations. Symbols are the same as in
Fig. 4, except that the firmly identified LMXBs and HMXBs in the literatures
(not limited to M 31; e.g., Binder et al. 2015; Zhang et al. 2011) are plotted
in plus and cross symbols. The vertical dash-dotted line roughly separates fg
stars and AGN, while the horizontal dashed line defines “highly variable”
sources, which is a key criterion to firmly identify XRBs (Table 2).

In addition to the X-ray colors, we also adopt the X-ray variability and the
X-ray to IR flux ratio as two additional criteria to classify different types
of sources. Here we characterize the variability of an X-ray source with the
parameter FLUXVAR, which is the largest flux difference in terms of the
standard deviation $\sigma$ between multiple _XMM-Newton_ observations (Table
D). The $3.4\rm~{}\mu m$ IR flux of an X-ray source is taken from the AllWISE
catalogue (Cutri et al., 2021). As shown in Fig. 6, the most variable X-ray
sources are always XRBs, so we take FLUXVAR$>10$ as an additional criterion
for firmly identified XRBs (Table 2), although many XRBs are indistinguishable
from fg stars and AGNs in X-ray variability. AGNs and fg stars are also
significantly distinguishable in the X-ray-IR color, we then use $\log(F_{\rm
X}/F_{\rm IR})=-1.5$ (the vertical line in Fig. 6) as an auxiliary criterion
to separate fg stars and AGNs. Although this criterion is not directly used in
the classification of the sources, because fg stars and AGNs are often well
separated in X-ray colors, our results are still reaffirmed, since our
identified and classified fg stars and AGNs are also well separated by the
$\log(F_{\rm X}/F_{\rm IR})=-1.5$. So it is only used to place a caveat if the
classification based on the X-ray color is thought to be less reliable, e.g.,
in case the source has a low S/N, or the two criteria based on the X-ray color
and the X-ray-to-IR ratio are clearly conflict with each other.

####  3.3.3 Procedure to classify unidentified sources

Based on the above discussions, our final procedure to classify the
_unidentified_ X-ray sources (stellar sources and AGNs) in our NEW-ANGELS
survey is summarized below (also see a summary in Table 2):

$\bullet$ We first cross-identify confirmed fg stars, confirmed or candidate
AGNs, GlCs, SNRs, galaxies, GCls, based on their multi-wavelength counterparts
(§3.2). The _XMM-Newton_ data of some of these sources may not have high
enough S/N to compute their X-ray colors with small uncertainties.

$\bullet$ For sources not identified in the above way, we calculate their
X-ray colors HR1 and HR2. Sources with the uncertainties on HR1 and HR2
$\sigma_{\rm HR1}\geq 0.2$ or $\sigma_{\rm HR2}\geq 0.2$ typically have low
S/N, so are often regarded as unclassified, although we sometimes give them a
preferred classification. Sources only detected in 0.2-0.5 keV are taken as
candidates of SSSs.

$\bullet$ For relatively bright unclassified sources with $\sigma_{\rm
HR1}<0.2$ and $\sigma_{\rm HR2}<0.2$, we first classify them into “hard”,
“soft”, and “supersoft” sources, based on their X-ray colors defined in
§3.3.2. “Supersoft” sources are directly regarded as confirmed SSSs. “Soft”
sources are directly taken as candidates of fg stars. The remaining “hard”
sources are regarded as unclassified.

$\bullet$ For the “hard” unclassified sources, we further give them some
preferred but non-unique classifications based on some additional multi-
wavelength criteria. If the optical counterpart source is blue, they can be
either HMXBs or AGNs, with their X-ray color defined with HR2 and HR3 being an
additional criterion to assign the preferred classification. If the source is
red in optical, or has no confirmed optical counterpart, they can be either
LMXBs or AGNs, with the same X-ray color criterion to assign the preferred
classification. We do not expect to match low-mass main sequence stars in M
31, but OB-type or giant stars are possible. Additionally, the possibility
that the detected XRBs are foreground sources is not ruled out. Therefore, if
no counterpart is found, the XRB is considered a LMXB. However, if a possible
counterpart is found, the XRB is then classified as a HMXB or LMXB based on
the color of the counterpart. Despite the potential for a false positive match
due to the limited apparent magnitude of the actual donor star, a match can
still offer insights into the environment of the XRB, such as the presence of
a star-forming region.

$\bullet$ The above classification of some types of sources, e.g., the X-ray
soft fg star candidates, could be largely uncertain. We then use some
auxiliary criteria to add some caveats to their classification, such as the
X-ray-to-IR flux ratio.

###  3.4 Noted sources of interest

In this section, we summarize a few noted X-ray sources which may be
especially interesting in some aspects. This is only a very incomplete
summary. We include some additional brief notes on many other sources in the
final catalogue as will be described in §4.

Figure 7: False-color image of the newly discovered superbubble candidate
J004436.8+412514. It is composed of $\mathrm{H{\alpha}}$ (red), [O III]
$\lambda 5007\rm\AA$ (green), and the X-ray (blue, $0.2-1.0$ keV image which
is smoothed with a 20 arcsec Gaussian kernel. A dashed circle with a diameter
of $30^{\prime\prime}$ ($\sim 110$ pc at a distance of 761 kpc) has been
superimposed on the location of the super bubble candidate.

We discovered a $\sim 110\rm~{}pc$ diameter superbubble candidate
J004436.8+412514 in the eastern disk of M 31 (Fig. 7). The extended soft X-ray
emission is apparently enclosed by a few shells and filaments bright in
optical emission lines such as H$\alpha$ (optical images obtained from the
LGGS project; Local Group Galaxies Survey, Massey et al. 2006). The
overlapping location of the extended X-ray source and the $\rm H\alpha$ shell
structure suggests the possible existence of a hot super bubble. The _XMM-
Newton_ spectra extracted from the entire bubble could be well fitted with an
absorbed thermal plasma model (APEC, with $N_{\mathrm{H}}=2.4\times
10^{21}~{}\mathrm{cm^{-2}}$, $kT=0.2~{}\mathrm{keV}$), the absorption
corrected luminosity between 0.2-10 keV is $1.1\times
10^{37}~{}\mathrm{erg~{}s^{-1}}$.

Figure 8: The stacked pn, mos1 and mos2 spectrum of AGN candidate
J004442.8+415340 are shown in black, red and green respectively. Also shown
are the corresponding best-fit absorbed power-law model and the residuals.

We detect a very hard point source J004442.8+415340 in the eastern disk
direction of M 31, with a $HR3=0.96\pm 0.02$. The flux below 2 keV is
negligible. The spectrum, as shown in Fig. 8, can be well modeled using an
absorbed power-law with $N_{\mathrm{H}}={1.7\pm 0.2}\times
10^{23}~{}\mathrm{cm^{-2}}$ and $\Gamma=1.9\pm 0.3$. The uncertainty is
defined in the 90% confidence region. The measured flux (and unabsorbed flux)
between 2-8 keV is $\rm 1.2\times 10^{-13}~{}ergs~{}s^{-1}~{}cm^{-2}$ ($\rm
3.0\times 10^{-13}~{}ergs~{}s^{-1}~{}cm^{-2}$). Our analysis suggests that the
source is likely a moderately obscured AGN.

Figure 9: The X-ray contour and optical image of 8 extended galaxies. The
contours are the 2 sigma (background uncertainty) and above of the 0.5-4.5 keV
X-ray count rate images smoothed with 5 arcsec Gaussian kernel. The
$\mathrm{1\times 1~{}arcmin^{2}}$ optical images are from Pan-STARRS g, r and
z band.

In this work, we detect eight extended X-ray sources associated with galaxies
(see Fig. 9). Two of them (a,b) have unique single galaxy counterparts. The
remaining six (c-h) have multiple galaxy counterparts and have potential to be
galaxy groups. Four sources’ counterparts (a-d) have measured redshift and are
therefore confirmed to be background sources. The extended X-ray source
J004133.4+422036 (a) has an apparent soft X-ray luminosity of $2.06\times
10^{41}~{}\mathrm{erg~{}s^{-1}}$ at the distance of its counterpart
2MASXJ00413355+4220359 ($z=0.093$, Caldwell et al. 2009). J003621.8+412836,
associated with 2MASXJ00362166+4128333 at $z=0.064$ (Bilicki et al., 2014),
has an apparent luminosity of ${3.7\times 10^{40}~{}\rm erg~{}s^{-1}}$. For
J004355.8+405854, the apparent luminosity of the detected extended source is
$\mathrm{3.49\times 10^{40}~{}erg~{}s^{-1}}$ at a distance of $z=0.121$
(Caldwell et al., 2009), based on the redshift record of its counterpart NAME
[G2012b]C039. J004253.1+414921 has an apparent luminosity of $4.9\times
10^{40}~{}\rm erg~{}s^{-1}$ at a distance of the counterpart
2MASXJ00414697+4138094 with $z=0.106$ (Galleti et al., 2007). This source also
shows potential AGN activity based on its radio counterpart WSTB 37W145. In
spite of the measured redshift, the limited luminosity of these sources
excludes their possibilities as galaxy clusters. For the rest four extended
X-ray source (e-h), the lack of measured redshift of the counterparts prevents
estimation of their luminosity. These extended X-ray sources are still
classified as galaxy in the catalogue, while we will note that they are
extended and have one or more galaxy counterparts.

##  4 X-ray Source Catalog

In this paper, we present the most complete catalogue of 4506 X-ray sources
detected from an area of $\sim 7.2\rm~{}deg^{2}$ around M 31 (Fig. 3). All
reported sources have a limiting detection likelihood EP_DET_ML$>$6, which
leads to a false detection rate of $<0.5\%$ (e.g., Ni et al. 2021).

Stiele et al. (2011) detected 1948 X-ray sources in a comprehensive analysis
of the archival XMM-Newton data covering the entire disk of M 31. By
incorporating 31 additional observations pointing slightly offset the disk of
M 31, we detect 2776 sources in the same region, including 1014 newly
discovered X-ray sources. About 200 sources in Stiele et al. (2011)’s
catalogue are rejected due to their low detection likelihood (e.g., $<30$).
The archival Chandra data of M 31 has a better angular resolution, but covers
a small portion of the disk. We also include the information of the cross-
matched Chandra sources (from the Chandra Source Catalog Release 2.0; Evans &
Civano 2018) in our catalogue for comparison.

For each source, the reported parameters can be classified into three
categories. We first summarize the basic detection information, including the
position, the detection likelihood, and the involved observations where the
source is detected. The second is the physical parameters of the source, count
rate, flux, hardness ratio, extent etc. These parameters are not only reported
for combined result from all involved exposures, but also for individual
observation, instruments (all-EPIC, pn, MOS1, and MOS2), and energy bands
(0.2-12.0 keV, 0.2-0.5 keV, 0.5-1.0 keV, 1.0-2.0 keV, 2.0-4.5 keV, and
4.5-12.0 keV). The last is the classification, we list our preferred
identification or classification of the source based on either the multi-
wavelength cross-identification (§3.2) or the brief multi-color classification
(§3.3). We describe the catalogue of the source parameters in Appendix D. A
machine-readable format of the table is provided online only.

Results of the classification in our X-ray source catalogue are also
summarized in Table 2. Based on the multi-wavelength cross-identifications, in
our X-ray source catalogue, we identify 352 single stars in the foreground (fg
stars; all regarded as firmly identified), 35 firmly identified GlCs and 31
SNRs (27 firmly identified, 4 as candidates) associated with M 31, as well as
567 AGNs (62 firmly identified, 505 as candidates), 62 galaxies (59 firmly
identified, 3 as candidates), and 6 GCls (1 firmly identified, 5 as
candidates) in the background. We uniquely classify 236 fg star and 17 SSS
candidates based on their X-ray colors. Since the LMXBs, HMXBs, and AGNs are
not explicitly separated just based on their X-ray and optical colors, we
often give them a preferred but not confirmed classification based on multiple
criteria (based on the X-ray colors, X-ray-to-optical colors, and X-ray
variability). The exceptions are some highly variable X-ray sources which are
regarded as firmly identified XRBs. 83 of them are identified as LMXBs, and 1
of them is taken as HMXBs. The remaining 3116 X-ray sources either have too
low S/N to calculate their X-ray colors or have not unique classification, so
are regarded as unclassified.

We do not perform standard astrometry correction to individual observations
before conducting source detection. This is partially because the astrometry
correction, typically calculated based on cross-matching the X-ray and optical
sources, could be largely uncertain, especially in the halo of M 31 where only
a few sources can be identified in optical. Instead, we directly apply the
astrometry correction result for each observations after detecting the
sources, using the suggested offset values from the 4XMM-DR12s catalogue
(Traulsen et al., 2020). For sources detected in overlapping observations, we
weight the offset of different observations by the number of counts of the
detected sources in the corresponding observations. We also list the updated
source position (ast_RA and ast_DEC) considering the astrometry correction in
the catalogue. Besides the original identification and classification result
(type), the sources with an updated astrometry correction has a slightly
different multi-wavelength cross-matching result. We also list this updated
identification and classification result (ast_type) in the catalogue for
reference, but caution that this is based on a simple geometric correction,
without updating the source detection parameters.

We publish the full source catalogue with the X-ray/multi-wavelength
properties of the sources and their classifications as an online only table
(§D,§E, and Table A.2). This source catalogue is unique for the study of the
X-ray source populations, as well as quantitatively estimating the
contribution of X-ray sources in the unresolved X-ray emissions of an external
galaxy. These topics will be discussed in the follow-up papers. We also
summarize our X-ray source classification criteria in Table 2, which are
potentially applicable to other galaxies.

## Acknowledgements

The authors would like to thank Prof. Junjie Mao (Tsinghua University) and
Prof. B. Luo (Nanjing University) for helpful discussions. This work was
supported in part by the Ministry of Science and Technology of China through
Grant 2018YFA0404502 and the National Natural Science Foundation of China
through Grants E3GJ251110 and 11821303. RH acknowledges support from the China
Scholarship Council. GP acknowledges funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 865637) and from ”Bando per il Finanziamento
della Ricerca Fondamentale 2022 dell’Istituto Nazionale di Astrofisica (INAF):
Canale: GO Large program”

This publication makes use of data products from the Wide-field Infrared
Survey Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration. This work has
made use of data from the European Space Agency (ESA) mission Gaia
(www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis
Consortium (DPAC, www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for
the DPAC has been provided by national institutions, in particular the
institutions participating in the Gaia Multilateral Agreement. This research
has made use of the VizieR catalog access tool, CDS, Strasbourg, France (DOI :
10.26093/cds/vizier). The original description of the VizieR service was
published in 2000, A&AS 143, 23

Data Availability: The X-ray source catalogue is published online in machine-
readable format. The original _XMM-Newton_ data used in the presented paper is
available on the _XMM-Newton_ data archive. The reduced data could be shared
by reasonable request to the corresponding author.

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##  Appendix A XMM-Newton Data Used in the NEW-ANGELS Program

Table A.1:  The _XMM-Newton_ observations used in the New-ANGELS program. The
total good time interval (GTI) of the mos1, mos2 and PN cameras are in unit of
ks. M and T1 in the filter columns refer to the median and thin1 filter. Begin
of Table
---
ObsID | RA | DEC | Start Date |  PI |  $t_{\mathrm{M1}}$ (GTI) |  $t_{\mathrm{M2}}$ (GTI) |  $t_{\mathrm{PN}}$(GTI) |  filterM1 |  filterM2 |  filterPN
0109270101 | 00 42 42.9 | +41 15 46.0 | 2001-06-29 |  Mason |  50.8 (28.4) |  50.8 (30.8) |  45.5 (25.1) |  M |  M |  M
0109270301 | 00 45 20.0 | +41 56 09.0 | 2002-01-26 |  Mason |  55.6 (26.6) |  55.9 (26.9) |  27.5 (25.4) |  M |  M |  M
0109270401 | 00 46 38.0 | +42 16 20.0 | 2002-06-29 |  Mason |  53.3 (48.9) |  53.9 (50.1) |  91.6 (64.2) |  M |  M |  M
0109270701 | 00 44 00.9 | +41 35 57.0 | 2002-01-05 |  Mason |  57.4 (56.8) |  57.4 (57.0) |  54.9 (54.5) |  M |  M |  M
0112570101 | 00 42 42.9 | +41 15 46.0 | 2002-01-06 |  Watson |  62.5 (59.6) |  63.7 (59.9) |  53.2 (50.1) |  T1 |  T1 |  T1
0112570201 | 00 41 24.9 | +40 55 35.0 | 2002-01-12 |  Watson |  66.5 (55.5) |  66.5 (55.3) |  59.6 (51.3) |  T1 |  T1 |  T1
0112570301 | 00 40 06.0 | +40 35 24.0 | 2002-01-24 |  Watson |  53.1 (28.5) |  53.3 (30.3) |  45.4 (21.5) |  T1 |  T1 |  T1
0112570401 | 00 42 42.9 | +41 15 46.0 | 2000-06-25 |  Watson |  30.0 (29.9) |  30.0 (29.5) |  26.3 (26.1) |  M |  M |  M
0151580201 | 00 43 11.9 | +39 47 60.0 | 2003-02-03 |  Di Stefano |  |  flared |  |  |  |
0151580301 | 00 45 59.0 | +40 42 36.0 | 2003-02-03 |  Di Stefano |  |  flared |  |  |  |
0151580401 | 00 46 06.9 | +41 20 58.0 | 2003-02-06 |  Di Stefano |  13.2 (12.8) |  13.2 (12.8) |  11.5 (11.1) |  M |  M |  M
0151581201 | 00 43 11.9 | +39 47 60.0 | 2003-07-01 |  Di Stefano |  |  flared |  |  |  |
0151581301 | 00 45 59.0 | +40 42 36.0 | 2003-07-01 |  Di Stefano |  6.4(2.2) |  6.4(2.3) |  |  M |  M |
0202230301 | 00 42 38.5 | +41 16 03.8 | 2004-07-17 |  Barnard |  |  flared |  |  |  |
0204790401 | 00 40 22.2 | +41 41 09.0 | 2004-01-02 |  Di Stefano |  |  flared |  |  |  |
0300910201 | 00 41 53.3 | +40 21 18.0 | 2005-08-01 |  Piconcelli |  |  flared |  |  |  |
0402560101 | 00 38 52.8 | +40 15 00.0 | 2006-06-28 |  Pietsch |  42.1 (6.1) |  9.1 (3.6) |  42.1 (6.7) |  M |  M |  T1
0402560201 | 00 43 28.8 | +40 55 12.0 | 2006-06-30 |  Pietsch |  |  flared |  |  |  |
0402560301 | 00 40 43.2 | +41 17 60.0 | 2006-07-01 |  Pietsch |  61.4 (48.0) |  61.4 (49.4) |  57.6 (39.0) |  M |  M |  T1
0402560401 | 00 42 16.8 | +40 37 12.0 | 2006-07-08 |  Pietsch |  |  flared |  |  |  |
0402560501 | 00 39 40.7 | +40 58 48.0 | 2006-07-20 |  Pietsch |  58.7 (54.8) |  58.7 (56.3) |  47.6 (28.6) |  M |  M |  T1
0402560601 | 00 40 45.6 | +40 21 05.1 | 2006-07-28 |  Pietsch |  49.4 (32.4) |  49.2 (32.2) |  42.6 (25.1) |  M |  M |  T1
0402560701 | 00 39 02.4 | +40 37 48.0 | 2006-07-23 |  Pietsch |  61.1 (26.0) |  61.7 (30.7) |  51.2 (18.3) |  M |  M |  T1
0402560801 | 00 40 06.0 | +40 35 24.0 | 2006-12-25 |  Pietsch |  52.1 (49.8) |  52.1 (49.0) |  50.8 (44.1) |  M |  M |  T1
0402560901 | 00 41 52.7 | +41 36 36.0 | 2006-12-26 |  Pietsch |  49.0 (45.6) |  49.0 (45.3) |  44.6 (40.8) |  M |  M |  T1
0402561001 | 00 44 38.4 | +41 12 01.0 | 2006-12-30 |  Pietsch |  54.8 (52.0) |  54.7 (53.3) |  45.8 (42.2) |  M |  M |  T1
0402561101 | 00 43 09.6 | +41 55 12.0 | 2007-01-01 |  Pietsch |  57.8 (47.7) |  57.9 (47.1) |  57.6 (42.5) |  M |  M |  T1
0402561201 | 00 45 43.1 | +41 31 48.0 | 2007-01-02 |  Pietsch |  54.4 (41.4) |  54.4 (40.7) |  53.0 (35.7) |  M |  M |  T1
0402561301 | 00 44 45.5 | +42 09 36.0 | 2007-01-03 |  Pietsch |  54.3 (36.4) |  54.3 (36.0) |  40.3 (29.6) |  M |  M |  T1
0402561401 | 00 46 38.4 | +41 53 60.0 | 2007-01-04 |  Pietsch |  52.4 (46.1) |  52.4 (46.5) |  51.0 (43.4) |  M |  M |  T1
0402561501 | 00 45 20.0 | +41 56 09.0 | 2007-01-05 |  Pietsch |  45.4 (43.8) |  45.4 (43.8) |  43.0 (37.9) |  M |  M |  T1
0404060201 | 00 45 19.5 | +40 57 47.0 | 2006-07-03 |  Bregman |  35.3 (21.1) |  35.3 (22.3) |  33.6 (16.1) |  T1 |  T1 |  T1
0405320501 | 00 42 44.3 | +41 16 09.4 | 2006-07-02 |  Pietsch |  21.4 (13.4) |  21.7 (15.1) |  13.3 (9.5) |  M |  M |  T1
0405320601 | 00 42 44.3 | +41 16 09.4 | 2006-08-09 |  Pietsch |  |  flared |  |  |  |
0405320801 | 00 42 44.3 | +41 16 09.4 | 2007-01-16 |  Pietsch |  |  flared |  |  |  |
0405320901 | 00 42 44.3 | +41 16 09.4 | 2007-02-05 |  Pietsch |  16.4 (16.0) |  16.6 (16.3) |  15.0 (13.2) |  |  |
0410582001 | 00 40 59.1 | +41 15 51.2 | 2007-07-25 |  Schartel |  15.9 (14.9) |  15.9 (15.5) |  13.4 (10.5) |  M |  M |  T1
0505720201 | 00 42 44.3 | +41 16 09.4 | 2007-12-29 |  Pietsch |  27.2 (26.9) |  27.2 (27.1) |  25.7 (25.6) |  M |  M |  T1
0505720301 | 00 42 44.3 | +41 16 09.4 | 2008-01-08 |  Pietsch |  26.9 (26.4) |  26.9 (26.3) |  24.4 (22.8) |  M |  M |  T1
0505720401 | 00 42 44.3 | +41 16 09.4 | 2008-01-18 |  Pietsch |  22.4 (21.6) |  22.4 (21.5) |  20.8 (17.2) |  M |  M |  T1
0505720501 | 00 42 44.3 | +41 16 09.4 | 2008-01-27 |  Pietsch |  21.5 (14.2) |  21.5 (15.0) |  15.0 (7.8) |  M |  M |  T1
0505720601 | 00 42 44.3 | +41 16 09.4 | 2008-02-07 |  Pietsch |  |  flared |  |  |  |
0505760101 | 00 38 52.8 | +40 15 00.0 | 2007-07-24 |  Pietsch |  35.5 (27.6) |  55.7 (29.7) |  34.8 (17.8) |  M |  M |  T1
0505760201 | 00 43 28.8 | +40 55 12.0 | 2007-07-22 |  Pietsch |  57.5 (42.4) |  57.5 (47.1) |  34.6 (23.8) |  M |  M |  T1
0505760301 | 00 42 16.8 | +40 37 12.0 | 2007-12-28 |  Pietsch |  44.2 (42.7) |  44.4 (44.0) |  40.1 (39.5) |  M |  M |  T1
0505760401 | 00 40 45.6 | +40 21 05.1 | 2007-12-25 |  Pietsch |  28.6 (28.5) |  28.6 (28.4) |  27.1 (26.3) |  M |  M |  T1
0505760501 | 00 39 02.4 | +40 37 48.0 | 2007-12-31 |  Pietsch |  38.6 (34.5) |  38.6 (35.1) |  37.0 (25.8) |  M |  M |  T1
0505900101 | 00 38 19.5 | +41 47 15.0 | 2007-07-21 |  Tanvir |  |  flared |  |  |  |
0505900301 | 00 38 04.5 | +40 44 39.0 | 2007-12-27 |  Tanvir |  |  flared |  |  |  |
0505900801 | 00 38 04.5 | +40 44 39.0 | 2008-02-09 |  Tanvir |  |  flared |  |  |  |
0511380101 | 00 38 52.8 | +40 15 00.0 | 2008-01-02 |  Pietsch |  45.6 (45.4) |  45.6 (45.4) |  44.0 (41.4) |  M |  M |  T1
0511380201 | 00 43 28.8 | +40 55 12.0 | 2008-01-05 |  Pietsch |  |  flared |  |  |  |
0511380301 | 00 39 40.7 | +40 58 48.0 | 2008-01-06 |  Pietsch |  35.4 (33.1) |  35.4 (33.0) |  33.9 (27.4) |  M |  M |  T1
0511380601 | 00 43 28.8 | +40 55 12.0 | 2008-02-09 |  Pietsch |  |  flared |  |  |  |
0551690201 | 00 42 44.3 | +41 16 09.4 | 2008-12-30 |  Pietsch |  |  flared |  |  |  |
0551690301 | 00 42 44.3 | +41 16 09.4 | 2009-01-09 |  Pietsch |  21.6 (20.8) |  21.6 (20.6) |  20.0 (18.3) |  M |  M |  T1
0551690401 | 00 42 44.3 | +41 16 09.4 | 2009-01-15 |  Pietsch |  17.1 (5.3) |  11.4 (5.1) |  9.4 (3.5) |  M |  M |  T1
0551690501 | 00 42 44.3 | +41 16 09.4 | 2009-01-27 |  Pietsch |  |  flared |  |  |  |
0551690601 | 00 42 44.3 | +41 16 09.4 | 2009-02-04 |  Pietsch |  |  flared |  |  |  |
0560180101 | 00 43 19.9 | +41 13 46.6 | 2008-07-18 |  Schartel |  21.1 (9.2) |  19.9 (8.8) |  16.5 (4.4) |  M |  M |  T1
0600660201 | 00 42 44.3 | +41 16 09.4 | 2009-12-28 |  Pietsch |  18.5 (18.1) |  18.5 (17.8) |  16.9 (16.1) |  |  |
0600660301 | 00 42 44.3 | +41 16 09.4 | 2010-01-07 |  Pietsch |  17.0 (16.9) |  17.0 (16.9) |  15.4 (14.8) |  |  |
0600660401 | 00 42 44.3 | +41 16 09.4 | 2010-01-15 |  Pietsch |  16.8 (16.7) |  16.5 (16.4) |  12.7 (7.7) |  |  |
0600660501 | 00 42 44.3 | +41 16 09.4 | 2010-01-25 |  Pietsch |  19.3 (13.7) |  19.4 (16.1) |  17.8 (17.8) |  |  |
0600660601 | 00 42 44.3 | +41 16 09.4 | 2010-02-02 |  Pietsch |  17.0 (16.0) |  17.0 (16.2) |  15.4 (10.2) |  |  |
0650560201 | 00 42 44.3 | +41 16 09.4 | 2010-12-26 |  Pietsch |  |  flared |  |  |  |
0650560301 | 00 42 44.3 | +41 16 09.4 | 2011-01-04 |  Pietsch |  33.1 (28.6) |  33.1 (30.9) |  30.6 (17.9) |  M |  M |  T1
0650560401 | 00 42 44.3 | +41 16 09.4 | 2011-01-14 |  Pietsch |  21.8 (13.1) |  22.1 (15.4) |  21.5 (10.1) |  M |  M |  T1
0650560501 | 00 42 44.3 | +41 16 09.4 | 2011-01-25 |  Pietsch |  23.6 (22.8) |  23.6 (22.8) |  9.2 (5.5) |  M |  M |  T1
0650560601 | 00 42 44.3 | +41 16 09.4 | 2011-02-03 |  Pietsch |  23.3 (22.0) |  23.3 (22.5) |  18.7 (11.0) |  M |  M |  T1
0652500101 | 00 46 55.0 | +40 31 00.0 | 2011-02-01 |  Di Stefano |  |  flared |  |  |  |
0652500201 | 00 49 05.0 | +40 17 32.0 | 2011-02-01 |  Di Stefano |  21.6 (12.1) |  21.6 (12.2) |  20.0 (8.3) |  T1 |  T1 |  T1
0652500301 | 00 53 27.9 | +39 49 46.0 | 2011-02-03 |  Di Stefano |  |  flared |  |  |  |
0655620301 | 00 43 45.5 | +41 07 54.7 | 2011-08-01 |  Henze |  |  flared |  |  |  |
0655620401 | 00 44 01.7 | +41 04 23.8 | 2012-01-21 |  Henze |  20.5 (12.5) |  20.6 (12.8) |  9.1 (8.7) |  M |  M |  T1
0672130101 | 00 42 41.8 | +40 51 54.6 | 2011-06-27 |  Wang |  100.5 (85.9) |  100.6 (90.8) |  97.8 (53.3) |  T1 |  T1 |  T1
0672130501 | 00 42 41.8 | +40 51 54.6 | 2011-07-13 |  Wang |  49.4 (27.1) |  49.4 (29.6) |  47.6 (12.8) |  T1 |  T1 |  T1
0672130601 | 00 42 41.8 | +40 51 54.6 | 2011-07-05 |  Wang |  95.9 (74.5) |  92.4 (78.9) |  95.4 (58.8) |  T1 |  T1 |  T1
0672130701 | 00 42 41.8 | +40 51 54.6 | 2011-07-07 |  Wang |  85.7 (78.4) |  90.8 (80.1) |  82.0 (62.4) |  T1 |  T1 |  T1
0674210201 | 00 42 44.3 | +41 16 09.4 | 2011-12-28 |  Pietsch |  20.6 (20.6) |  20.6 (20.6) |  18.9 (18.5) |  M |  M |  T1
0674210601 | 00 42 44.3 | +41 16 09.4 | 2012-01-31 |  Pietsch |  |  flared |  |  |  |
0690600401 | 00 42 52.0 | +41 31 07.8 | 2012-06-26 |  Barnard |  114.3 (89.8) |  114.4 (96.6) |  103.5 (57.0) |  T1 |  T1 |  T1
0700380501 | 00 42 43.7 | +41 25 18.5 | 2012-07-28 |  Schartel |  11.6 (11.6) |  11.6 (11.6) |  10.0 (9.9) |  M |  M |  T1
0700380601 | 00 42 43.7 | +41 25 18.5 | 2012-08-08 |  Schartel |  20.8 (20.1) |  20.2 (19.2) |  19.6 (18.3) |  M |  M |  T1
0701981201 | 00 44 02.0 | +41 25 44.4 | 2013-02-08 |  Schartel |  23.6 (19.8) |  23.6 (19.8) |  21.9 (17.0) |  T1 |  T1 |  T1
0727960401 | 00 42 52.4 | +41 16 31.2 | 2013-07-06 |  Schartel |  10.6 (10.3) |  10.6 (10.4) |  9.0 (9.0) |  |  |
0744350301 | 00 43 26.7 | +41 23 33.3 | 2014-08-09 |  Henze |  23.4 (23.2) |  23.4 (23.0) |  21.8 (21.0) |  M |  M |  T1
0744350901 | 00 43 26.7 | +41 23 33.3 | 2015-02-01 |  Henze |  11.3 (7.9) |  11.3 (8.2) |  9.9 (9.8) |  M |  M |  T1
0761970101 | 00 43 37.9 | +41 19 19.0 | 2015-06-27 |  Hornschemeier |  |  flared |  |  |  |
0763120101 | 00 44 21.9 | +41 31 16.6 | 2015-06-28 |  Sasaki |  96.7 (95.1) |  96.6 (95.2) |  94.7 (85.0) |  M |  M |  T1
0763120201 | 00 44 21.9 | +41 31 16.6 | 2016-01-21 |  Sasaki |  21.2 (8.5) |  80.9 (52.5) |  21.4 (10.3) |  M |  M |  T1
0763120301 | 00 44 49.3 | +41 49 31.1 | 2015-08-11 |  Sasaki |  101.3 (100.7) |  101.6 (100.9) |  99.9 (96.9) |  M |  M |  T1
0763120401 | 00 44 54.3 | +41 49 12.7 | 2016-01-01 |  Sasaki |  98.9 (69.6) |  99.0 (73.2) |  97.4 (50.8) |  M |  M |  T1
0764030301 | 00 42 57.7 | +41 08 12.3 | 2016-01-16 |  Henze |  |  flared |  |  |  |
0764030401 | 00 42 57.7 | +41 08 12.3 | 2016-02-09 |  Henze |  11.1 (10.6) |  11.6 (11.4) |  7.0 (5.6) |  T1 |  T1 |  T1
0784000101 | 00 45 28.8 | +41 54 09.9 | 2016-12-26 |  Henze |  40.5 (13.6) |  40.5 (14.5) |  36.1 (6.4) |  T1 |  T1 |  T1
0784000201 | 00 45 28.8 | +41 54 09.9 | 2016-12-28 |  Henze |  57.5 (40.0) |  58.3 (40.9) |  56.0 (35.4) |  T1 |  T1 |  T1
0790830101 | 00 43 31.9 | +41 13 14.3 | 2017-01-21 |  Yukita |  58.7 (39.2) |  58.6 (39.5) |  57.0 (36.4) |  M |  M |  M
0800730101 | 00 37 02.3 | +43 13 20.9 | 2017-06-28 |  Li |  18.1 (15.6) |  22.8 (18.5) |  14.3 (6.6) |  T1 |  T1 |  T1
0800730201 | 00 35 39.4 | +42 52 34.0 | 2017-07-25 |  Li |  15.6 (15.6) |  15.6 (15.5) |  11.7 (11.4) |  T1 |  T1 |  T1
0800730301 | 00 34 06.2 | +42 34 03.8 | 2017-07-14 |  Li |  23.7 (20.4) |  24.6 (23.7) |  13.8 (11.5) |  T1 |  T1 |  T1
0800730401 | 00 35 05.4 | +42 11 46.9 | 2017-07-27 |  Li |  15.6 (15.3) |  15.6 (15.6) |  11.7 (11.7) |  T1 |  T1 |  T1
0800730501 | 00 36 27.1 | +42 28 34.6 | 2017-07-28 |  Li |  24.5 (17.7) |  24.5 (18.6) |  14.1 (11.5) |  T1 |  T1 |  T1
0800730601 | 00 37 41.8 | +42 48 47.7 | 2017-08-12 |  Li |  15.6 (13.5) |  15.6 (13.3) |  11.1 (7.7) |  T1 |  T1 |  T1
0800730701 | 00 38 31.0 | +42 25 33.8 | 2017-08-12 |  Li |  15.5 (15.4) |  15.6 (15.4) |  10.8 (10.8) |  T1 |  T1 |  T1
0800730801 | 00 37 14.0 | +42 09 03.0 | 2017-08-10 |  Li |  15.7 (15.6) |  15.7 (15.7) |  11.8 (11.8) |  T1 |  T1 |  T1
0800730901 | 00 35 55.5 | +41 53 21.6 | 2018-01-07 |  Li |  19.7 (19.6) |  19.7 (19.6) |  15.8 (14.8) |  T1 |  T1 |  T1
0800731001 | 00 36 43.7 | +41 33 24.1 | 2017-08-10 |  Li |  15.6 (15.4) |  15.6 (15.5) |  11.7 (11.7) |  T1 |  T1 |  T1
0800731101 | 00 39 10.6 | +42 01 39.4 | 2018-01-07 |  Li |  20.9 (20.7) |  20.9 (20.8) |  17.3 (16.5) |  T1 |  T1 |  T1
0800731201 | 00 40 13.9 | +42 22 05.6 | 2018-01-10 |  Li |  17.6 (6.3) |  17.6 (8.0) |  4.4 (3.7) |  T1 |  T1 |  T1
0800731301 | 00 42 27.3 | +42 13 16.8 | 2018-01-11 |  Li |  11.4 (10.9) |  11.4 (11.1) |  7.5 (6.6) |  T1 |  T1 |  T1
0800731401 | 00 41 08.2 | +41 58 34.9 | 2018-01-11 |  Li |  15.2 (7.0) |  15.1 (7.3) |  11.7 (4.5) |  T1 |  T1 |  T1
0800731501 | 00 38 58.6 | +41 29 21.5 | 2017-08-12 |  Li |  15.6 (15.5) |  15.6 (15.4) |  11.7 (11.4) |  T1 |  T1 |  T1
0800731601 | 00 37 48.6 | +41 12 46.3 | 2017-08-02 |  Li |  21.5 (21.4) |  21.5 (21.5) |  17.6 (16.2) |  T1 |  T1 |  T1
0800731701 | 00 43 24.4 | +40 18 50.8 | 2018-01-11 |  Li |  |  flared |  |  |  |
0800731801 | 00 45 00.6 | +40 36 11.2 | 2018-01-12 |  Li |  17.6 (3.8) |  17.6 (5.4) |  8.9 (0.7) |  T1 |  T1 |  T1
0800731901 | 00 46 32.3 | +40 56 27.6 | 2018-01-13 |  Li |  17.6 (17.5) |  17.6 (17.6) |  13.7 (13.7) |  T1 |  T1 |  T1
0800732001 | 00 47 44.2 | +41 19 12.1 | 2018-01-13 |  Li |  17.6 (17.6) |  17.6 (17.5) |  13.6 (13.5) |  T1 |  T1 |  T1
0800732101 | 00 48 44.9 | +41 00 00.0 | 2018-01-13 |  Li |  19.2 (15.7) |  21.1 (16.9) |  16.8 (11.2) |  T1 |  T1 |  T1
0800732201 | 00 48 06.0 | +40 44 34.9 | 2018-01-14 |  Li |  15.6 (10.0) |  15.6 (10.2) |  11.7 (5.6) |  T1 |  T1 |  T1
0800732301 | 00 45 23.1 | +40 10 48.9 | 2018-01-15 |  Li |  15.6 (11.7) |  15.6 (12.7) |  11.7 (7.4) |  T1 |  T1 |  T1
0800732401 | 00 47 03.6 | +40 04 29.5 | 2018-01-15 |  Li |  15.3 (6.0) |  15.3 (6.4) |  11.2 (1.8) |  T1 |  T1 |  T1
0800732501 | 00 49 41.6 | +40 42 43.4 | 2018-01-15 |  Li |  16.9 (11.9) |  16.9 (12.3) |  12.9 (7.6) |  T1 |  T1 |  T1
0800732601 | 00 50 32.4 | +40 24 05.7 | 2018-01-16 |  Li |  8.7 (6.4) |  9.1 (7.9) |  5.6 (3.5) |  T1 |  T1 |  T1
0800732701 | 00 49 03.6 | +40 00 34.6 | 2018-01-17 |  Li |  15.6 (10.1) |  15.6 (11.0) |  11.6 (4.8) |  T1 |  T1 |  T1
0800732801 | 00 48 17.8 | +39 42 55.5 | 2018-01-17 |  Li |  15.6 (12.3) |  15.6 (12.2) |  11.6 (6.7) |  T1 |  T1 |  T1
0800732901 | 00 50 11.8 | +39 49 41.7 | 2018-01-19 |  Li |  15.3 (12.5) |  15.3 (13.2) |  11.7 (7.6) |  T1 |  T1 |  T1
0800733001 | 00 51 23.6 | +40 05 56.9 | 2018-01-19 |  Li |  11.8 (11.5) |  11.8 (11.8) |  11.4 (11.2) |  T1 |  T1 |  T1
0800733101 | 00 38 31.0 | +42 25 33.8 | 2018-01-03 |  Li |  |  flared |  |  |  |
total |  |  |  |  |  3082.9 (2491.6) |  3133.9 (2602.0) |  2710.2 (1927.4) |  |  |
End of Table

##  Appendix B Astrometric Accuracy

Figure 10: Left: The probability density function (PDF) of the offset
$\Delta\mathrm{pos}$ between _XMM-Newton_ X-ray sources and GAIA optical
sources at the different ranges of the position statistical uncertainty
$\sigma_{\mathrm{pos}}$ of the X-ray sources. The corresponding best-fit
models are shown in dashed lines. The distribution have been shifted
vertically for the ease of comparison. Right: Total position uncertainty
$\sigma_{\mathrm{combined}}$ as the function of $\sigma_{\mathrm{pos}}$. The
$\sigma_{\mathrm{combined}}$ is the $\sigma$ of Rayleigh distribution. The
measured $\sigma_{\mathrm{combined}}$ is in black dot, while the red dashed
line is the best-fit model and the black dotted line represent the uncorrected
$\sigma_{\mathrm{pos}}$.

We initially use a $\Delta\mathrm{pos}<3.44~{}\sigma_{\mathrm{pos}}$ criterion
to match X-ray sources, but this approach proved inadequate for exceptionally
bright sources. This is due to the fact that the statistical position
uncertainty, $\sigma_{\mathrm{pos}}$, underestimated the actual uncertainty
for these sources, resulting in failed matches. To address this issue, we
match the 4XMM-DR11s serendipitous source catalogue from stacks (Traulsen et
al., 2020, 2022) with GAIA DR3 catalogue (Gaia Collaboration, 2022) to apply a
correction to the position uncertainty. We filter the GAIA DR3 catalogue with
Gmag$<$18 and PSS$>$0.9, which excludes optical faint sources and limits our
selection to fg stars, as some fg stars are particularly bright in X-ray
observations. In Fig. 10, we clearly see the evolution of the distribution of
the offset $\Delta\mathrm{pos}$ between the X-ray sources and GAIA sources
with the position uncertainty $\sigma_{\mathrm{pos}}$. The distribution can be
modeled using a Rayleigh function and a proportional function. The Rayleigh
function represents true counterparts, while the proportional function
accounts for the false positive matches. We take the fitted $\sigma$ of
Rayleigh function as the $\sigma_{\mathrm{combined}}$. The relation between
the $\sigma_{\mathrm{combined}}$ and the statistical position uncertainty
$\sigma_{\mathrm{pos}}$ is shown in the right panel of Fig. 10. At low
$\sigma_{\mathrm{pos}}$, which is often the case for bright X-ray sources, the
deviation of $\sigma_{\mathrm{combined}}$ from $\sigma_{\mathrm{pos}}$ is
evident. However, at the large $\sigma_{\mathrm{pos}}$ end,
$\sigma_{\mathrm{combined}}$ is almost unchanged.

We fit the measured $\sigma_{\mathrm{combined}}$, and get the best fit model
(Equation. 1)

$\sigma_{\mathrm{combined}}=\sqrt{0.89\times\sigma_{\mathrm{pos}}^{2}+0.42^{2}}$

Then we modify the matching criterion based on distance as
$\Delta\mathrm{pos}<3.44~{}\sigma_{\mathrm{combined}}$. Since we use the same
source detection tool edetect_stack in this work as in 4XMM-DR11s, the
empirical relation of the $\sigma_{\mathrm{combined}}$ can be adopted in this
work.

##  Appendix C Cross-matching with NWAY

Figure 11: The probability density of GAIA Gmag, $F_{\mathrm{X/G}}$(flux ratio
between 0.5-2.0 keV to GAIA G band), and $HR2$ for secure matches and non-
matches based on distance. Also shown are the corresponding ratio of the
kernel density of these parameters. Figure 12: a. The fraction of matched
sources and matches of shifted X-ray sources as the function of p_any (the
probability of matching defined in NWAY) based on the distance; b. The
fraction of the matched sources as the function of the fraction of the matches
of shifted sources; c. The estimated number of secure matches as the function
of the fraction of false positive matches. In b and c, we demonstrate the
comparison of matching performance between different priors: no prior
(distance only), Gmag, $F_{\mathrm{X/G}}$, and $F_{\mathrm{X/G}}$ with $HR2$.

In our study, we utilize NWAY (Salvato et al., 2018), a Bayesian cross-
matching algorithm, to match fg stars with our X-ray source list. Since it is
possible for one X-ray source to match with multiple stars within the distance
criterion due to the numerous stars in GAIA catalogue. NWAY takes into account
positional uncertainties and assigns probabilities to potential matches based
on source properties and positional agreement. The priors of these properties
can be automatically assigned based on the sources of secure matches and non-
matches in the field. Compared to distance-based matching algorithms, NWAY can
handle complex fields and provides more reliable and informative matches.

To select reference star catalogues, we filter GAIA sources with PSS $>$ 0.9.
Initially, we match GAIA sources based solely on distance and compare the GAIA
parameter distributions of the matched sources with those of non-matched
sources. Fig. 11 shows the parameter distributions and highlights a
significant trend where counterpart stars are optically bright, have a
relatively small flux ratio between 0.5-2.0 keV and GAIA G band
($F_{\mathrm{X/G}}$), and the matched X-ray source are soft.

Next, we consider $Gmag$, $F_{\mathrm{X/G}}$, and $HR2$ as prior parameters
and re-run the NWAY algorithm. To test the reliability of our method, we
randomly shift our X-ray source list and perform matching with the same prior
parameters. In Fig. 12a, we present the fraction of matched sources
($N_{\mathrm{match}}/N_{\mathrm{total}}$) and matches to shifted X-ray sources
($N_{\mathrm{shift~{}match}}/N_{\mathrm{total}}$) as a function of p_any.
$N_{\mathrm{total}}$ is the total number of the X-ray sources to be matched.
p_any is the posterior probability of the X-ray source having any correct
counterparts defined by NWAY. In Fig. 12b, We present the function of the
fraction of matched sources as the fraction of matches to shifted sources by
varying p_any. The different priors, including no prior (distance only),
$Gmag$, $F_{\mathrm{X/G}}$, and $F_{\mathrm{X/G}}+HR2$, are compared. We
estimate the true counterpart as the function of the false match fraction in
Fig. 12c. Increasing the range of p_any can include more true counterparts but
comes at the cost of a higher fraction of false matches. However, there is
still an upper limit to the number of true sources. The introduction of other
parameters has resulted in a noticeable improvement in matches. We can clearly
observe the improvement in the matches after introducing other parameters. As
Gmag and $F_{\mathrm{X/G}}$ are correlated, we ultimately choose to use
$F_{\mathrm{X/G}}$ for its better performance. Additionally, despite HR2 not
resulting in a significant improvement in the final matching performance, we
still took it into consideration since it represents the X-ray color
preference of stars. Ultimately, we selected p_any$>$0.9 to identify
foreground stars in X-ray sources, which corresponded to only 5% of false
matches.

##  Appendix D Description of the New-ANGELS catalogue columns

  1. 1.

Column 1, SRCID: Source identifier.

  2. 2.

Column 2, OBS_ID: Identification pf XMM-Newton observation.

  3. 3.

Column 3, N_OBS: Number of observations involved in the stack.

  4. 4.

Column 4, N_CONTRIB: Number of observations in which the source was fitted.

  5. 5.

Column 5, N_EXP: Number of instruments in which the source was fitted.

  6. 6.

Column 6-8, RA, DEC and RADEC_ERR: Right ascension and Declination (J2000, in
degree) and square root of squared sum of their 1-sigma uncertaintys (in
arcsec).

  7. 7.

Column 9-10, ast_RA and ast_DEC: Astrometry corrected Right ascension and
Declination (J2000, in degree).

  8. 8.

Column 11-12, RAOFFSET and DECOFFSET: RA and DEC offset of the observation
preferred in 4XMM-DR12s.

  9. 9.

Column 13-14, LII and BII: Galactic longitude and latitude (in degree).

  10. 10.

Column 15, DIST_NN: Distance (in arcsec) to the nearest neighbouring detected
source.

  11. 11.

Column 16, N_BLEND: Number of neighbouring sources being fit simultaneously.

  12. 12.

Column 17-18, 29-30, 41-42, 53-54, EP_FLUX, PN_FLUX, M1_FLUX, M2_FLUX,
EP_FLUX_ERR, PN_FLUX_ERR, M1_FLUX_ERR and M2_FLUX_ERR: Total flux
($\mathrm{erg~{}cm^{-2}~{}s^{-2}}$) of all-EPIC, pn, MOS1, and MOS2 and their
1-sigma uncertainty in the energy range of 0.2-12.0 keV. The flux and flux
uncertainty are derived from counts rates and errors according to energy
conversion factors. ($\rm{ECF=\frac{count~{}rate}{flux}}$, in units of
$10^{11}\rm~{}cts~{}cm^{-2}/erg$). The factor for each detector and energy
band is different depend on the detector, pattern selection and filter used
during the observation. So the ECFs (fluxes and energy conversion factors)
were derived with XSPEC using on-axis response matrices assuming a power law
model with photon index $\Gamma=1.7$ and the Galactic foreground absorption of
$N_{H}=7\times 10^{20}\mathrm{cm^{-2}}$ (Stark et al. 1992, see also PFH2005)
to be the universal source spectrum for the ECF calculation.

  13. 13.

Column 19-28, 31-40, 43-52, 55-64, EP_n_FLUX, PN_n_FLUX, M1_n_FLUX, M2_n_FLUX,
EP_n_FLUX_ERR, PN_n_FLUX_ERR, M1_n_FLUX_ERR and M2_n_FLUX_ERR: The flux
($\mathrm{erg~{}cm^{-2}s^{-}1)}$) of all-EPIC, pn, MOS1, and MOS2 in energy
band n and their 1-sigma uncertainty. Energy band 1, 2, 3, 4, and 5 cover
0.2-0.5 keV, 0.5-1.0 keV, 1.0-2.0 keV, 2.0-4.5 keV, and 4.5-12.0 keV
respectively. The flux and the flux uncertainty of all-EPIC are weighted from
that of pn, MOS1, and MOS2.

$\displaystyle\rm EP\\_n\\_FLUX=$
$\displaystyle\rm\frac{PN\\_n\\_FLUX\times(PN\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}}$
(D1)
$\displaystyle\rm+\frac{M1\\_n\\_FLUX\times(M1\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}}$
$\displaystyle\rm+\frac{M2\\_n\\_FLUX\times(M2\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}}$

$\displaystyle\rm EP\\_n\\_FLUX\\_ERR=$
$\displaystyle\rm((\frac{PN\\_n\\_FLUX\\_ERR\times(PN\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}})^{2}$
(D2)
$\displaystyle\rm+(\frac{M1\\_n\\_FLUX\\_ERR\times(M1\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}})^{2}$
$\displaystyle\rm+(\frac{M2\\_n\\_FLUX\\_ERR\times(M2\\_n\\_FLUX\\_ERR)^{-2}}{(PN\\_n\\_FLUX\\_ERR)^{-2}+(M1\\_n\\_FLUX\\_ERR)^{-2}+(M2\\_n\\_FLUX\\_ERR)^{-2}})^{2})^{-2}$

  14. 14.

Column 65-68, 79-80, 91-92, EP_RATE, PN_RATE, M1_RATE, M2_RATE, EP_RATE_ERR,
PN_RATE_ERR, M1_RATE_ERR and M2_RATE_ERR: Count rate
($\mathrm{counts~{}s^{-1}}$) of all-EPIC, pn, mos1 and mos2 detectors and
their 1-sigma uncertainty.

  15. 15.

Column 69-78, 81-90, 93-102 PN_n_RATE, M1_n_RATE, M2_n_RATE, PN_n_RATE_ERR,
M1_n_RATE_ERR and M2_n_RATE_ERR: Count rate ($\mathrm{counts~{}s^{-1}}$) of
pn, mos1 and mos2 detectors in energy band n and their 1-sigma uncertainty.

  16. 16.

Column 103-110, EP_CTS, PN_CTS, M1_CTS, M2_CTS, EP_CTS_ERR, PN_CTS_ERR,
M1_CTS_ERR and M2_CTS_ERR: Number of counts ($\mathrm{counts}$) of all-EPIC,
pn, mos1 and mos2 detectors and their 1-sigma uncertainty.

  17. 17.

Column 111, 117, 123, 129 EP_DET_ML, PN_DET_ML, M1_DET_ML and M2_DET_ML:
Equivalent maximum detection likelihood of all-EPIC, pn, mos1 and mos2
detectors. The likelihood is calculated as

$\mathrm{DET\\_ML}=-\ln(1-\Gamma(\frac{\nu}{2},\sum_{i=1}^{n}\frac{\Delta
C_{i}}{2}))\\\ $ (D3)

where $C$ is C-statistic (Cash 1979). $n$ is the number of images used for the
detection of the same source. $\nu$ is the degree of freedom, $\nu=n+2$ for
point source, $\nu=n+3$ for the extend source. While combining the detection
from different instrument or observations, $\Delta C$ are summed up in
equation D3. In principal, the detection likelihood also follows $L=-\ln(p)$,
where the p is the probability of resulting in at least the observed counts by
Poissonian random fluctuation. The probability $p$ is calculated from
incomplete Gamma function $P(a,b)$, where a is the raw source counts and b is
the raw background counts in the detection cell. (For more detail of detection
likelihood, see Watson et al. 2009, Traulsen et al. 2019)

  18. 18.

Column 112-116, 118-122, 124-128, 130-134 EP_n_DET_ML, PN_n_DET_ML,
M1_n_DET_ML and M2_n_DET_ML: Equivalent maximum detection likelihood ($n=1$ in
equation D3) of all-EPIC, pn, MOS1 and MOS2 detectors in energy band n, n=1,
2, 3, 4 and 5.

  19. 19.

Column 135-136, EXTENT and EXTENT_ERR: Extent radius ($\mathrm{arcsec}$) ans
its 1-sigma uncertainty. The parameters are obtained when fitting the extended
source with a convolution of the instrumental PSF and an extent model ($\beta$
model with fixed $\beta=2/3$). ($\nu=n+3$ in equation D3).

  20. 20.

Column 137, EXTENT_ML: Likelihood of the detection being extended when fitting
with a convolution of the instrumental PSF and an extent model ($\beta$ model
with fixed $\beta=2/3$). ($\nu=n+3$ in equation D3).

  21. 21.

Column 138-169, EP_HRn, PN_HRn, M1_HRn, M2_HRn, EP_HRn_ERR, PN_HRn_ERR,
M1_HRn_ERR and M2_HRn_ERR: Hardness ratio and corresponding 1-sigma
uncertainty of all-EPIC, pn, mos1, and mos2 detectors between energy band n
and n+1, n=1, 2, 3 and 4. The hardness ratios are defined
as:${HR}_{n}=\frac{B_{n+1}-B_{n}}{B_{n+1}+B_{n}}$, $B_{n}$ is the count rate
in energy band n. After computing the hardness ratios, we can plot the
hardness ratio diagram to classify the spectra.

  22. 22.

Column 170, 176, 182, PN_EXP, M1_EXP and M2_EXP: PSF-weighted exposure time
($\mathrm{second}$) of the detection in pn, mos1 and mos2.

  23. 23.

Column 171-175, 177-181, 183-187, PN_n_EXP, M1_n_EXP and M2_n_EXP: PSF-
weighted exposure ($\mathrm{second}$) of the detection in energy band n of pn,
mos1, and mos2.

  24. 24.

Column 188, 194, 100, PN_BG, M1_BG and M2_BG: Background map
($\mathrm{counts~{}pixel^{-1}}$) at detection position on pn, mos1 and mos2.

  25. 25.

Column 189-193, 195-199, 201-205, PN_n_BG, M1_n_BG and M2_n_BG: Background map
($\mathrm{counts~{}pixel^{-1}}$) in energy band n of pn, mos1 and mos2 at the
detection position.

  26. 26.

Column 206-209, EP_ONTIME, PN_ONTIME, M1_ONTIME and M2_ONTIME: Total good
exposure time ($\mathrm{second}$) of all-EPIC, pn, mos1 and mos2 detectors.

  27. 27.

Column 210-212, PN_PILEUP, M1_PILEUP and M2_PILEUP: Estimate of the pile-up
level in pn, mos1 and mos2. It is calculated in terms of source count rate and
instrument readout. For point-like sources, it is defined as the source count
rate times the frame time, divided by an instrument-specific pile-up
threshold. For extended sources, it is derived from the source counts per
instrument pixel times the frame time, divided by the number of instrument
pixels covered by an image pixel and by a pile-up threshold.

  28. 28.

Column 213-215, PN_MASKFRAC, M1_MASKFRAC and M2_MASKFRAC: PSF-weighted
detector coverage in pn, mos1 and mos2.

  29. 29.

Column 216, DIST_REF: Distance (arcmin) to the reference coordinates of the
field.

  30. 30.

Column 217-220, EP_OFFAX, PN_OFFAX, M1_OFFAX and M2_OFFAX: Offaxis angle
(arcmin) between source position and aim point all-EPIC, pn, mos1, and mos2
detectors.

  31. 31.

Column 221-235, PN_n_VIG, M1_n_VIG and M2_n_VIG: Vignetting factor in energy
band n of pn, mos1 and mos2 detectors for the detection.

  32. 32.

Column 236, STACK_FLAG: Integer representation of the stack detection flags.

  33. 33.

Column 237, OVERLAP: True, if N_CONTRIB$\geq 2$ at the source position.

  34. 34.

Column 238, VAR_CHI2: Reduced chi square of all-EPIC inter-observation
variability.
VAR_CHI2=$\frac{1}{n-1}\sum_{k=1}^{n}\left(\frac{F_{k}-F_{\mathrm{EPIC}}}{\sigma_{k}}\right)^{2}$,
$F_{k}$ is EP_FLUX for each observation, $\sigma_{k}$ is EP_FLUX_ERR.
$F_{EPIC}$ is the mean EP_FLUX for all detections.

  35. 35.

Column 239-243, VAR_CHI2_n: Reduced chi square of all-EPIC band n inter-
observation variability.

  36. 36.

Column 244, VAR_PROB: Probability that the all-EPIC flux variability is
consistent with zero. VAR_PROB
$=\int_{\chi^{2}}^{\infty}\frac{x^{v/2-1}e^{-x/2}}{2^{v/2}\Gamma(v/2)}dx$,
$\chi^{2}$ is VAR_CHI2 at $\nu=n-1$ degrees of freedom. The high VAR_PROB
means that the flux of the source is almost constant throughout the
observations.

  37. 37.

Column 245-249, VAR_PROB_n: Probability that the all-EPIC band n flux
variability is consistent with zero.

  38. 38.

Column 250, FRATIO and FRATIO_ERR: The ratio and corresponding 1-sigma
uncertainty between the highest and the lowest (non-zero, non-null) mean EPIC
flux. FRATIO $=F_{\max}/F_{\min}$, $F_{\max}$ and $F_{\min}$ are the maximum
and minimum of EP_FLUX in detections.

  39. 39.

Column 252-261, FRATIO_n and FRATIO_n_ERR: The ratio and corresponding 1-sigma
uncertainty between the highest and the lowest (non-zero, non-null) mean EPIC
flux in energy band n.

  40. 40.

Column 262, FLUXVAR: The Largest all-EPIC flux difference in terms of sigma.
FLUXVAR$=\max_{k,l\in[1,n]}\frac{\left|F_{k}-F_{l}\right|}{\sqrt{\sigma_{k}^{2}+\sigma_{l}^{2}}}$,
$F_{k}$ is EP_RATE, $\sigma_{k}$ is EP_RATE_ERR.

  41. 41.

Column 263-267, FLUXVAR_n: The Largest all-EPIC band n flux difference in
energy band n in terms of sigma.

  42. 42.

Column 269-270, MJD_FIRST and MJD_LAST: Modified Julian Date JD-2400000.5 (in
days) when starting and ending the observation.

  43. 43.

Column 270, REVOLUT: XMM-Newton revolution number (in orbit) of the
observation.

  44. 44.

Column 271, PA_PNT: Mean position angle (degree) of the spacecraft.

  45. 45.

Column 272-274, PN_SUBMODE, M1_SUBMODE and M2_SUBMODE: instrument submode of
pn, mos1 and mos2 used for the observation.

  46. 46.

Column 275-277, PN_FILTER, M1_FILTER and M2_FILTER: Filter used for the pn,
mos1 and mos2.

  47. 47.

Column 278, type: The identification or classification type assigned to each
source. The classification types include fg star, AGN, galaxy, GlC, GCl, SNR,
HMXB, LMXB, and SSS. The classification of each candidate source is enclosed
within angle brackets ($<>$) for easy identification.

  48. 48.

Column 279, ast_type: The same as type, but the source is matched with new
source position (ast_RA and ast_DEC).

  49. 49.

Column 280, note: additional comments.

  50. 50.

Column 281, XMMLPt: the source number of matched sources in Stiele et al.
(2011).

  51. 51.

Column 282, CSC_name: The name of the matched source in the Chandra Source
Catalog Release 2.0 (Evans & Civano, 2018).

##  Appendix E An example of the source catalogue table

Table A.2: An example of the source catalogue table that contains only one
source covered by two observations. Each column has three rows for this
source. The first row is the summary row which contains the parameters
obtained based on all of the related observations. The second and third rows
contain the results based on two individual observations. Begin of Table
---
SRCID | OBS_ID | N_OBS | N_CONTRIB | N_EXP | RA | DEC | ast_RA | ast_DEC | RAOFFSET
23010927070100304 |  | 31 | 8 | 20 | 11.15348030 | 41.42053952 | 11.09348034 | 42.28709875 | 0.05999996
23010927070100304 | 0109270701 | – | – | 3 | 11.15348030 | 41.42053952 | – | – | 0.0
23010927070100304 | 0402561001 | – | – | 3 | 11.15348030 | 41.42053952 | – | – | 0.0
DECOFFSET | RADEC_ERR | LII | BII | DIST_NN | N_BLEND | EP_FLUX | EP_FLUX_ERR | EP_1_FLUX | EP_1_FLUX_ERR
-0.86655923 | 1.1616716 | 121.5576631 | -21.43299982 | 28.409655 | 1 | 9.7772e-14 | 3.1135e-14 | 4.7373e-15 | 5.0262e-16
0.0 | 1.1616716 | 121.5576631 | -21.43299982 | 28.409655 | 1 | 7.9128e-14 | 4.4409e-14 | 7.7186e-15 | 2.1086e-15
0.0 | 1.1616716 | 121.5576631 | -21.43299982 | 28.409655 | 1 | 1.8289e-13 | 1.0293e-13 | 5.4740e-15 | 1.4772e-15
PN_FLUX | PN_FLUX_ERR | PN_1_FLUX | PN_1_FLUX_ERR | M1_FLUX | M1_FLUX_ERR | M1_1_FLUX | M1_1_FLUX_ERR | M2_FLUX | M2_FLUX_ERR
9.1766e-14 | 4.2648e-14 | 4.3386e-15 | 5.5695e-16 | 1.1074e-13 | 6.4199e-14 | 6.5578e-15 | 1.9507e-15 | 1.1598e-13 | 6.8233e-14
5.7552e-14 | 6.3138e-14 | 6.1542e-15 | 3.1553e-15 | 9.7584e-14 | 8.6648e-14 | 1.0393e-14 | 4.2934e-15 | 1.4657e-13 | 9.3396e-14
2.1863e-13 | 1.5237e-13 | 5.9267e-15 | 1.7166e-15 | 1.5368e-13 | 1.3875e-13 | 3.8231e-15 | 3.9790e-15 | 1.6361e-14 | 7.6997e-15
M2_1_FLUX | M2_1_FLUX_ERR | EP_RATE | EP_RATE_ERR | PN_RATE | PN_RATE_ERR | PN_1_RATE | PN_1_RATE_ERR | M1_RATE | M1_RATE_ERR
6.4477e-15 | 1.4557e-15 | 0.03645468 | 0.00219558 | 0.02337551 | 0.00186468 | 0.00409002 | 0.00052355 | 0.00643091 | 0.00096972
7.8904e-15 | 3.7736e-15 | 0.04422306 | 0.00716647 | 0.02952519 | 0.00663382 | 0.00515083 | 0.00264084 | 0.00602423 | 0.00186651
4.5875e-15 | 4.2368e-15 | 0.04965767 | 0.01016562 | 0.03871836 | 0.00946021 | 0.00564509 | 0.00163499 | 0.00815423 | 0.00262398
M1_1_RATE | M1_1_RATE_ERR | M2_RATE | M2_RATE_ERR | M2_1_RATE | M2_1_RATE_ERR | EP_CTS | EP_CTS_ERR | PN_CTS | PN_CTS_ERR
0.00100714 | 0.00030009 | 0.00664825 | 0.00063500 | 0.00099870 | 0.00022413 | 3891.196 | 205.65431 | 2536.822 | 179.87935
0.00158575 | 0.00065509 | 0.00867364 | 0.00196641 | 0.00120115 | 0.00057445 | 501.36707 | 64.01653 | 193.49692 | 39.751995
0.00058333 | 0.00060712 | 0.00278509 | 0.00263800 | 0.00069836 | 0.00064496 | 618.26685 | 91.57865 | 439.2531 | 78.04734
M1_CTS | M1_CTS_ERR | M2_CTS | M2_CTS_ERR | EP_DET_ML | EP_1_DET_ML | PN_DET_ML | PN_1_DET_ML | M1_DET_ML | M1_1_DET_ML
467.70544 | 62.865623 | 886.6685 | 77.36295 | 519.283 | 40.153515 | 378.32312 | 32.29504 | 28.289425 | 2.6725852
119.68079 | 33.35646 | 188.18935 | 37.486553 | 38.77565 | – | 15.839467 | 2.4071922 | 4.0498304 | 4.0510645
131.51355 | 35.5845 | 47.50021 | 32.078136 | 51.64108 | – | 42.96344 | 7.913733 | 12.368129 | 0.53715014
M2_DET_ML | M2_1_DET_ML | EXTENT | EXTENT_ERR | EXTENT_ML | EP_HR1 | EP_HR1_ERR | PN_HR1 | PN_HR1_ERR | M1_HR1
126.46535 | 6.2184834 | 27.585667 | 1.0059265 | 335.00296 | 0.59011996 | 0.03774169 | 0.57942075 | 0.04802216 | 0.48118436
19.935226 | 2.939534 | 27.585667 | 1.0059265 | 335.00296 | 0.43357438 | 0.15567033 | 0.5555008 | 0.24856497 | -0.15709119
0.41799778 | 0.6974814 | 27.585667 | 1.0059265 | 335.00296 | 0.5311424 | 0.14330031 | 0.488368 | 0.16499938 | 0.76985604
M1_HR1_ERR | M2_HR1 | PN_EXP | PN_1_EXP | M1_EXP | M1_1_EXP | M2_EXP | M2_1_EXP | PN_BG | PN_1_BG
0.12708639 | 0.6452527 | 519375.5 | 109760.27 | 349907.03 | 76494.08 | 632365.75 | 133364.56 | 12.555466 | 1.3695921
0.35245 | 0.5969048 | 30627.36 | 6542.403 | 98723.5 | 21758.725 | 106946.56 | 23466.432 | 5e-05 | 1e-05
0.34081677 | 0.38698247 | 58203.832 | 12877.205 | 80653.89 | 17832.574 | 77865.1 | 17235.486 | 1.4581821 | 0.13973232
M1_BG | M1_1_BG | M2_BG | M2_1_BG | EP_ONTIME | PN_ONTIME | M1_ONTIME | M2_ONTIME | PN_PILEUP | M1_PILEUP
2.2322547 | 0.23470314 | 3.3413908 | 0.37062544 | 341184.5 | 271198.94 | 200632.45 | 275560.44 | 0.00924482 | 0.00125283
0.5171118 | 0.06214709 | 0.5573624 | 0.06325618 | 56904.203 | 54506.547 | 56576.934 | 56904.203 | 1.0634e-07 | 0.00057253
0.6422717 | 0.05786567 | 0.69377303 | 0.05424231 | 53185.09 | 42057.21 | 51987.848 | 53185.09 | 0.00096860 | 0.00075341
M2_PILEUP | PN_MASKFRAC | M1_MASKFRAC | M2_MASKFRAC | DIST_REF | EP_OFFAX | PN_OFFAX | M1_OFFAX | M2_OFFAX | PN_1_VIG
0.00110123 | 0.915966 | 0.91859525 | 0.91738135 | 22.996138 | – | – | – | – | –
0.00074969 | 0.2550554 | 0.91859525 | 0.91738135 | 22.996138 | 11.488442 | 12.455518 | 12.512937 | 11.488442 | 0.41582617
0.00061821 | 0.8852963 | 0.8975847 | 0.874431 | 22.996138 | 13.433759 | 14.05184 | 13.433759 | 14.252835 | 0.35662016
M1_1_VIG | M2_1_VIG | OVERLAP | STACK_FLAG | VAR_CHI2 | VAR_PROB | FRATIO | FRATIO_ERR | FLUXVAR | MJD_FIRST
– | – | True | -1 | 1.2860699 | 0.25247739 | 8.347179 | 25.2418 | 1.2803135 | 52279.30103
0.39645877 | 0.44362473 | True | -1 | – | – | – | – | – | 52279.30103
0.35751617 | 0.33471233 | True | -1 | – | – | – | – | – | 54099.81458
MJD_LAST | REVOLUT | PA_PNT | PN_SUBMODE | M1_SUBMODE | M2_SUBMODE | PN_FILTER | M1_FILTER | M2_FILTER | type
57409.95817 | – | – |  |  |  |  |  |  | superbubble
52279.93645 | 380 | 251.26717 | PrimeFullWindow | PrimeFullWindow | PrimeFullWindow | Medium | Medium | Medium | –
54100.55166 | 1293 | 252.63655 | PrimeFullWindow | PrimeFullWindow | PrimeFullWindow | Thin1 | Medium | Medium | –
ast_type | note | XMMLPt | CSC_name |  |  |  |  |  |
superbubble | superbubble | – | – |  |  |  |  |  |
– | – | – | – |  |  |  |  |  |
– | – | – | – |  |  |  |  |  |