#  The XMM-SERVS survey: new XMM-Newton point-source catalog for the XMM-LSS
field

C.-T.J. Chen(陳建廷)1,2, W.N. Brandt1,2,3, B. Luo4,5, P. Ranalli6, G. Yang1,2,
D.M. Alexander7, F.E. Bauer8,9,10, D.D. Kelson11, M. Lacy12, K. Nyland12, P.
Tozzi13, F. Vito1,2, M. Cirasuolo14, R. Gilli15, M.J. Jarvis16,17, B.D.
Lehmer18, M. Paolillo19, D.P. Schneider1,2, O. Shemmer20, I. Smail7, M.
Sun21,22 M. Tanaka23, M. Vaccari17,24, C. Vignali25,15, Y.Q. Xue21,22, M.
Banerji26, K.E. Chow27, B. Häußler28, R.P. Norris29,27, J.D. Silverman30, and
J.R. Trump31
1Department of Astronomy & Astrophysics, 525 Davey Lab, The Pennsylvania State
University, University Park, PA 16802, USA
2Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
3Department of Physics, The Pennsylvania State University, University Park, PA
16802, USA
4School of Astronomy and Space Science, Nanjing University, Nanjing 210093,
China
5Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University),
Ministry of Education, Nanjing, Jiangsu 210093, China E-mail<EMAIL_ADDRESS>
(Accepted for publication in MNRAS)

###### \par\LTX@newpageAbstract

We present an X-ray point-source catalog from the XMM-Large Scale Structure
survey region (XMM-LSS), one of the XMM-Spitzer Extragalactic Representative
Volume Survey (XMM-SERVS) fields. We target the XMM-LSS region with $1.3$ Ms
of new XMM-Newton AO-15 observations, transforming the archival X-ray coverage
in this region into a 5.3 deg2 contiguous field with uniform X-ray coverage
totaling $2.7$ Ms of flare-filtered exposure, with a $46$ ks median PN
exposure time. We provide an X-ray catalog of 5242 sources detected in the
soft (0.5–2 keV), hard (2–10 keV), and/or full (0.5–10 keV) bands with a 1%
expected spurious fraction determined from simulations. A total of 2381 new
X-ray sources are detected compared to previous source catalogs in the same
area. Our survey has flux limits of $1.7\times 10^{-15}$, $1.3\times
10^{-14}$, and $6.5\times 10^{-15}$ erg cm-2 s-1 over 90% of its area in the
soft, hard, and full bands, respectively, which is comparable to those of the
XMM-COSMOS survey. We identify multiwavelength counterpart candidates for
99.9% of the X-ray sources, of which 93% are considered as reliable based on
their matching likelihood ratios. The reliabilities of these high-likelihood-
ratio counterparts are further confirmed to be $\approx 97\%$ reliable based
on deep Chandra coverage over $\approx 5\%$ of the XMM-LSS region. Results of
multiwavelength identifications are also included in the source catalog, along
with basic optical-to-infrared photometry and spectroscopic redshifts from
publicly available surveys. We compute photometric redshifts for X-ray sources
in 4.5 deg2 of our field where forced-aperture multi-band photometry is
available; $>70$% of the X-ray sources in this subfield have either
spectroscopic or high-quality photometric redshifts.

###### keywords:

catalogues – surveys – galaxies:active – X-rays:galaxies – quasars: general

††pubyear: 2018††pagerange: The XMM-SERVS survey: new XMM-Newton point-source
catalog for the XMM-LSS field–The XMM-SERVS survey: new XMM-Newton point-
source catalog for the XMM-LSS field00footnotetext:
6Lund Observatory, Box 43, 22100 Lund, Sweden
7Centre for Extragalactic Astronomy, Department of Physics, Durham University,
South Road, Durham, DH1 3LE, UK
8Instituto de Astrofísica and Centro de Astroingeniería, Facultad de Física,
Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
9Millennium Institute of Astrophysics (MAS), Chile
10Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, Colorado
80301, USA
11The Observatories, The Carnegie Institution for Science, 813 Santa Barbara
St., Pasadena, CA 91101
12National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA
22903, USA
13INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125,
Firenze, Italy
14European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching b.
München, Germany
15INAF – Osservatorio Astronomico di Bologna, Via Gobetti 93/3, 40129 Bologna,
Italy
16Oxford Astrophysics, Denys Wilkinson Building, University of Oxford, Keble
Road, Oxford OX1 3RH, UK
17Department of Physics, University of the Western Cape, Bellville 7535, South
Africa
18Department of Physics, University of Arkansas, 226 Physics Building, 825
West Dickson Street, Fayetteville, AR 72701, USA
19Dip.di Fisica Ettore Pancini, Università di Napoli Federico II, via Cintia,
80126, Napoli, Italy
20Department of Physics, University of North Texas, Denton, TX 76203, USA
21CAS Key Laboratory for Research in Galaxies and Cosmology, Department of
Astronomy, University of Science and Technology of China, Hefei 230026, China
22School of Astronomy and Space Science, University of Science and Technology
of China, Hefei 230026, China
23National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
24INAF – Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy
25Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, Via
Gobetti 93/2, 40129 Bologna, Italy
26Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge
CB3 0HA, United Kingdom
27CSIRO Astronomy and Space Science, PO Pox 76, Epping, NSW, 1710, Australia
28European Southern Observatory, Alonso de Cordova 3107, Vitacura, Santiago,
Chile
29Western Sydney University, Locked Bag 1797, Penrith South, NSW 1797,
Australia
30Kavli Institute for the Physics and Mathematics of the Universe, The
University of Tokyo, Kashiwa, Japan 277-8583 (Kavli IPMU, WPI)
31Department of Physics, University of Connecticut, 2152 Hillside Road,
Storrs, CT 06269, USA

##  1 Introduction

Table 1:  Current and scheduled 1–10 deg2 multiwavelength coverage of the XMM-SERVS fields. References: [a] Franzen et al. (2015); [b] Jarvis et al. (2017); [c] Oliver et al. (2012); [d] Lonsdale et al. (2003); [e] Mauduit et al. (2012). Note that SERVS has recently been expanded to cover the full LSST deep drilling fields (Spitzer Program ID 11086). [f] Jarvis et al. (2012); [g] http://www.ast.cam.ac.uk/~mbanerji/VEILS/veils_index.html; [h] http://euclid2017.london/slides/Monday/Session3/SurveyStatus-Scaramella.pdf; [i] Diehl et al. (2014); [j] Aihara et al. (2018); [k] Tonry et al. (2012); [l] Vaccari et al. (2016); [m] http://www.lsst.org/News/enews/deep-drilling-201202.html; [n] Kelson et al. (2014); Patel et al. (2015); [o] Coil et al. (2011); [p] https://devilsurvey.org/wp/; [q] http://www.roe.ac.uk/~ciras/MOONS/VLT-MOONS.html; [r] Takada et al. (2014); [s] http://www.galex.caltech.edu/researcher/techdoc-ch2.html. [t] http://personal.psu.edu/wnb3/xmmservs/xmmservs.html.  Band | Survey Name | Coverage (XMM-LSS, W-CDF-S, ELAIS-S1); Notes
---|---|---
Radio |  Australia Telescope Large Area Survey (ATLAS)a |  –, 3.7, 2.7 deg2; 15 $\mu$Jy rms depth at 1.4 GHz
|  MIGHTEE Survey (Starting Soon)b |  4.5, 3, 4.5 deg2; 1 $\mu$Jy rms depth at 1.4 GHz
FIR |  Herschel Multi-tiered Extragal. Surv. (HerMES)c |  0.6–18 deg2; 5–60 mJy depth at 100–500 $\mu$m
MIR |  Spitzer Wide-area IR Extragal. Survey (SWIRE)d |  9.4, 8.2, 7.0 deg2; 0.04–30 mJy depth at 3.6–160 $\mu$m
NIR |  Spitzer Extragal. Rep. Vol. Survey (SERVS)e |  4.5, 3, 4.5 deg2; 2 $\mu$Jy depth at 3.6 and 4.5 $\mu$m
|  VISTA Deep Extragal. Obs. Survey (VIDEO)f |  4.5, 3, 4.5 deg2; $ZYJHK_{s}$ to $m_{\rm AB}\approx 23.8$–25.7
|  VISTA Extragal. Infr. Legacy Survey (VEILS)g |  3, 3, 3 deg2; $JK_{s}$ to $m_{\rm AB}\approx 24.5$–25.5
|  Euclid Deep Fieldh |  –, 10, – deg2; $YJH$ to $m_{\rm AB}\approx 26$, VIS to $m_{\rm AB}\approx 26.5$
Optical |  Dark Energy Survey (DES)i |  9, 6, 9 deg2; Multi-epoch $griz$, $m_{\rm AB}\approx 27$ co-added
Photometry |  Hyper Suprime-Cam (HSC) Deep Surveyj |  5.3, –, – deg2; $grizy$ to $m_{\rm AB}\approx 25.3$–27.5
|  Pan-STARRS1 Medium-Deep Survey (PS1MD)k |  8, –, 8 deg2; Multi-epoch $grizy$, $m_{\rm AB}\approx 26$ co-added
|  VST Opt. Imaging of CDF-S and ES1 (VOICE)l |  –, 4.5, 3 deg2; Multi-epoch $ugri$, $m_{\rm AB}\approx 26$ co-added
|  SWIRE optical imagingd |  8, 7, 6 deg2; $u^{\prime}g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ to $m_{\rm AB}\approx 24$–26
|  LSST deep-drilling field (Planned)m |  10, 10, 10 deg2; $ugrizy$, $\gtrsim 10\,000$ visits per field
Optical/NIR |  Carnegie-Spitzer-IMACS Survey (CSI)n |  6.9, 4.8, 3.6 deg2; $140\,000$ redshifts, 3.6 $\mu$m selected
Spectroscopy |  PRIsm MUlti-object Survey (PRIMUS)o |  2.9, 2.0, 0.9 deg2; 77 000 redshifts to $i_{\rm AB}\approx 23.5$
|  AAT Deep Extragal. Legacy Survey (DEVILS)p |  3.0, 1.5, – deg2; 43 500 redshifts to $Y=21.2$
|  VLT MOONS Survey (Scheduled)q |  4.5, 3, 4.5 deg2; $210\,000$ redshifts to $H_{\rm AB}\approx 23.5$
|  Subaru PFS survey (Planned)r |  5.3, –, – deg2; $J\approx 23.4$ for HSC deep fields.
UV |  GALEX Deep Imaging Surveys |  8, 7, 7 deg2; Depth $m_{\rm AB}\approx 25$
X-ray | XMM-SERVSt |  5.3, 4.5, 3 deg2; 4.7 Ms XMM-Newton time, $\approx 50$ ks depth

Due to the penetrating nature of X-ray emission and its ubiquity from
accreting supermassive black holes (SMBHs), extragalactic X-ray surveys have
provided an effective census of active galactic nuclei (AGNs), including
obscured systems, in the distant universe. Over at least the past three
decades, the overall design of cosmic X-ray surveys has followed a “wedding
cake” strategy. At the extremes of this strategy, some surveys have ultra-deep
X-ray coverage and a narrow “pencil-beam” survey area ($\lesssim 1$ deg2),
while others have shallow X-ray coverage over a wide survey area ($\approx$
10–104 deg2). The wealth of data from cosmic X-ray surveys (and their co-
located multiwavelength surveys) have provided a primary source of information
in shaping understanding of how SMBHs grow through cosmic time, where deep
surveys generally sample high-redshift, moderately luminous AGNs, and wide-
field surveys generally probe the high-luminosity, rare objects that are
missed by surveys covering smaller volumes. However, narrow-field surveys lack
the contiguous volume to encompass a wide range of cosmic large-scale
structures, and wide-field surveys generally lack the X-ray sensitivity to
track the bulk of the AGN population through the era of massive galaxy
assembly (see Brandt & Alexander 2015 for a recent review).

Among extragalactic X-ray surveys, the medium-deep COSMOS survey over $\approx
2$ deg2 has the necessary sensitivity-area combination to begin to track how a
large fraction of distant SMBH growth relates to cosmic large-scale structures
(e.g., Hasinger et al., 2007; Civano et al., 2016). However, even COSMOS
cannot sample the full range of cosmic environments. The largest structures
found in cold dark matter simulations are already as large as the angular
extent of COSMOS at $z\approx 1$ (80–100 Mpc in comoving size, which covers
2–3 deg2; e.g., see Klypin et al. 2016). Clustering analyses also demonstrate
that COSMOS-sized fields are still subject to significant cosmic variance
(e.g., Meneux et al., 2009; de la Torre et al., 2010; Skibba et al., 2014).

Therefore, to study SMBH growth across the full range of cosmic environments
and minimize cosmic variance, it is necessary to obtain multiple medium-deep
X-ray surveys in distinct sky regions (e.g., Driver & Robotham, 2010; Moster
et al., 2011) with multiwavelength data comparable to those of COSMOS. In this
work, we present a catalog of 5242 XMM-Newton sources detected over 5.3 deg2
in one of the well-studied Spitzer Extragalactic Representative Volume Survey
(SERVS, Mauduit et al., 2012) fields, the XMM-Large Scale Structure (XMM-LSS)
region. This is the first field of the broader XMM-SERVS survey which aims to
expand the parameter space of X-ray surveys with three $>3$ deg2 surveys
reaching XMM-COSMOS-like depths, including XMM-LSS, Wide Chandra Deep Field-
South (W-CDF-S), and ELAIS-S1.111XMM-Newton observations of W-CDF-S and
ELAIS-S1 have been allocated via the AO-17 XMM-Newton Multi-year Heritage
Program. These three extragalactic fields have been chosen based on their
excellent multiwavelength coverage and superior legacy value. We list the
current and scheduled multiwavelength coverage of XMM-SERVS in Table 1.

The X-ray source catalog presented here has been generated using a total of
1.3 Ms of XMM-Newton AO-15 observations in the XMM-LSS field (specifically the
region covered by SERVS), plus all archival XMM-Newton data in this same
region. Our AO-15 observations target the central part of XMM-LSS adjacent to
(and partly including) the Subaru XMM-Newton Deep Survey (SXDS, Ueda et al.,
2008), transforming the complex archival XMM-Newton coverage in this region
into a contiguous 5.3 deg2 field with relatively uniform X-ray coverage. The
median clean exposure time with the PN instrument is $\approx 46$ ks, reaching
survey depths comparable to those of XMM-COSMOS (e.g., Cappelluti et al.,
2009) and SXDS. We also present multiwavelength counterparts, basic
photometric properties, and spectroscopic redshifts obtained from the
literature. Photometric redshifts are derived over a 4.5 deg2 region using the
forced-photometry catalog of Nyland et al. 2018 (in preparation). The
excellent multiwavelength coverage in the XMM-SERVS XMM-LSS field will provide
the necessary data for studying the general galaxy population and tracing
large-scale structures. The combination of these multiwavelength data and the
new X-ray source catalog (along with similar data for COSMOS and the other
XMM-SERVS fields) will enable potent studies of SMBH growth across the full
range of cosmic environments, from voids to massive clusters, while minimizing
cosmic variance effects. The XMM-Newton source catalog and several associated
data products are being made publicly available along with this
paper.222http://personal.psu.edu/wnb3/xmmservs/xmmservs.html.

This paper is organized as follows: in §2 we present the details of the new
and archival observations, and the procedures for data reduction. In §3 we
describe the X-ray source-searching strategies and the details of the
production of the X-ray point-source catalog. We also outline the reliability
assessment of the X-ray catalog using simulated X-ray observations. The survey
sensitivity and the number counts are also presented here. In §4, we describe
the multiwavelength counterpart identification methods and reliability
assessments. In §5, we describe the spectroscopic and photometric redshifts of
the X-ray sources. The basic multiwavelength properties and the source
classifications are presented in §6. A summary is given in §7. The source
catalog, including the properties of the multiwavelength counterparts
identified with likelihood-ratio matching methods, and the descriptions of
columns are included in Appendix A. Multiwavelength matching results using the
Bayesian matching code NWAY are included in Appendix B. In addition to the
X-ray sources, we also present the photometric redshifts for the galaxies in
our survey region in Appendix C. Throughout the paper, we assume a
$\Lambda$CDM cosmology with $H_{0}=70$ km s-1 Mpc-1, $\Omega_{m}=0.3$, and
$\Omega_{\Lambda}=0.7$. We adopt a Galactic column density $N_{\rm
H}=3.57\times 10^{20}$ cm-2 along the line of sight to the center of the
source-detection region at RA$=35.6625^{\circ}$, DEC$=-4.795^{\circ}$ (e.g.,
Stark et al., 1992).333Derived using the colden task included in the CIAO
software package. AB magnitudes are used unless noted otherwise.

Figure 1:  Illustration of the survey regions of XMM-XXL-North (XXL-N, Pierre
et al. 2016, orange dashed line), the Subaru XMM-Newton Deep Survey (SXDS,
Ueda et al. 2008, blue dotted circle), and the XMM-SERVS survey of XMM-LSS
presented in this work (black box). The Spitzer SERVS coverage of XMM-LSS is
also shown as the red polygon.

##  2 XMM-Newton Observations in the XMM-LSS region and data reduction

Table 2:  The XMM-Newton data used to create the source catalog include 155
pointings with a total of 2.7 Ms of flare-filtered exposure time, of which 1.1
Ms is from the new AO-15 observations.a Columns from left to right: target
field, XMM-Newton revolution, XMM-Newton ObsID, observation starting
date/time, Right Ascension and Declination of the pointing center (J2000,
degrees), cleaned exposure time for PN, MOS1, and MOS2 in each pointing. This
table is available in its entirety online.

Field | Revolution | ObsID | Date | R.A. | Decl. | GTI (PN) | GTI (MOS1) | GTI (MOS2)
---|---|---|---|---|---|---|---|---
|  |  | (UT) |  |  | (ks) | (ks) | (ks)
AO-15 | 3054 | 0780450101 | 2016-08-13T01:34:06 | 35.81072 | $-5.15989$ | 20.91 | 23.61 | 23.61
XMM-LSS | 1205 | 0404965101 | 2006-07-09T08:08:08 | 35.80953 | $-5.48532$ | 3.44 | 10.36 | 9.91
XMDS | 287 | 0111110401 | 2001-07-03T14:01:54 | 35.97582 | $-5.15253$ | 21.40 | 27.20 | 27.40
SXDS | 118 | 0112370101 | 2000-07-31T21:57:54 | 34.47819 | $-4.98115$ | 39.13 | 42.70 | 42.83
XMM-XXL-North | 2137 | 0677580101 | 2011-08-10T01:53:35 | 37.16867 | $-4.49993$ | 4.94 | 5.93 | 5.52
XMM-XXL-North | 2137 | 0677580101 | 2011-08-10T01:53:35 | 37.33404 | $-4.49993$ | 2.01 | 6.47 | 6.67
XLSSJ022404.0–041328 | 0928 | 0210490101 | 2005-01-01T19:08:30 | 36.03267 | $-4.20230$ | 80.28 | 87.98 | 87.98

a: MOS only (MOS1 and MOS2 have the same exposure time). For PN, the total
flare-filtered time is 2.3 Ms, of which 0.9 Ms is from the new AO-15
observations.

###  2.1 XMM-Newton and Chandra data in the XMM-LSS region

The XMM-LSS field has been targeted by a number of XMM-Newton surveys of
different sensitivities (e.g., see Fig. 3 of Brandt & Alexander 2015 and Fig.
1 of Xue 2017). The original XMM-LSS survey was an $\approx 11$ deg2 field
typically covered by XMM-Newton observations of $\approx 10$ ks exposure time
per pointing (Pacaud et al., 2006; Pierre et al., 2016). Within the 11 deg2
field, $\approx 4$ deg2 were observed by the XMM-Newton Medium Deep Survey
(XMDS, $20-25$ ks exposure depth, Chiappetti et al., 2005). In addition, the
Subaru XMM-Newton Deep Survey (SXDS, Ueda et al., 2008), adjacent to the XMDS
field, covers a 1.14 deg2 area and reaches a nominal $\approx 50$ ks exposure
per pointing (Ueda et al., 2008). Moreover, the XMM-LSS field recently became
a part of the 25 deg2 XMM-XXL-North field (Pierre et al., 2016), which has
similar XMM-Newton coverage as the original XMM-LSS survey (i.e., $\approx 10$
ks depth).

Figure 2: Locations of the XMM-Newton observations used in this work. The
AO-15 observations are marked as the blue-filled circles with solid
boundaries. The archival observations are marked as dashed circles. Circles
with green, orange, blue, and cyan colors are for XMM-LSS, SXDS, XMDS, and
XMM-XXL observations, respectively. The RA/DEC range of our catalog selection
area is indicated by the black rectangle, and the Spitzer SERVS footprint is
marked as the dark-red polygon. Our AO-15 observations do not cover the
entirety of the SERVS region, because the existing data from SXDS (bottom-
right corner, orange circles) and from deep X-ray cluster observations (top-
middle and top-right, the red circles) reached the desired depth.

In addition to the XMM-Newton data, the XMM-LSS region has extensive
multiwavelength coverage (see Table 1 for a summary, also see Vaccari 2016).
In particular, the central $\approx 5$ deg2 area of the XMM-XXL-North field
(i.e., the combination of the XMDS and SXDS fields, see Fig. 1 for an
illustration of the relative positions of different surveys.) was selected to
be one of the SERVS fields. This sky region is covered uniformly by multiple
photometric and spectroscopic surveys (see Sec. 4 for more details), and it is
one of the deep drilling fields of the Dark Energy Survey (Diehl et al., 2014)
and the upcoming Large Synoptic Survey Telescope (LSST) surveys (see Table 1).
However, compared to the relatively uniform multiwavelength data, archival
XMM-Newton observations covering this sky region span a wide range of exposure
time (see Table 2). In order to advance studies of accreting SMBHs and their
environments, deep X-ray observations with similar areal coverage are required
in addition to the rich multiwavelength data in this field. To this end, we
obtained XMM-Newton AO-15 observations taken between July 2016 and February
2017 with a total of 1.3 Ms exposure time. The relative sky coverage of our
survey region, XMM-XXL-North, and SXDS are displayed in Fig 1. Our AO-15 data
include 67 XMM-Newton observations. All of these 67 observations were carried
out with a THIN filter for the EPIC cameras. The choice of the THIN filter
maximizes the signal-to-noise ratio. Since the XMM-LSS field is far from the
Galactic plane and thus the number of bright stars is small, the optical
loading effects are negligible for almost all detected X-ray sources. Even for
the brightest star in XMM-LSS, HD 14417, the optical loading effects are only
limited to a few pixels at its position. In addition to the new data, we made
use of all the overlapping archival XMM-Newton observations to create a
uniform, sensitive XMM-Newton survey contiguously covering most of the SERVS
data in the XMM-LSS region. After excluding observations that were completely
lost due to flaring background (see §2.2), the archival data used here include
51 observations culled from the $10$ ks XMM-LSS survey, 18 observations from
XMDS with $20-25$ ks exposures, four mosaic-mode observations444Each mosaic-
mode observation is comprised of a number of 10 ks exposures, see https://xmm-
tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/mosaic.html.
obtained as part of the XMM-XXL survey (Pierre et al., 2016), four archival
XMM-Newton observations targeting galaxy clusters identified in the XMM-XXL-
North and XMM-LSS surveys ($\approx 30-100$ ks), and the ten $50$ ks
observations from SXDS. We present the details of each observation in Table 2,
and show the positions of each XMM-Newton observation used in this work in
Fig. 2.

Our AO-15 observations were separated into two epochs to minimize the effects
of background flaring. We first observed the XMM-LSS sky region in the SERVS
footprint with $\approx 1$ Ms of XMM-Newton exposure time during July–August
2016. These first observations were screened for flaring backgrounds (§2.2);
we then re-observed the background-contaminated sky regions using the
remaining 0.3 Ms. We also observed the SXDS region in which one of the SXDS
observations carried out in 2002 was severely affected by background flares.
In this work, we present an X-ray source catalog obtained from a 5.3 deg2 sky-
region with $34.2^{\circ}\leq\alpha_{\rm J2000}\leq 37.125^{\circ}$ and
$-5.72^{\circ}\leq\delta_{\rm J2000}\leq-3.87^{\circ}$555This is equivalent to
the Galactic coordinates $170.25184^{\circ}<l<172.07153^{\circ}$,
$-60.49169^{\circ}<b<-57.17011^{\circ}$.  (black rectangle in Fig 1 and Fig
2). The sky region is primarily selected by the footprint of our AO-15
observations, with additional SXDS data within the SERVS footprint in the
south-west corner. A total of $3.0$ Ms of raw XMM-Newton observations are used
for generating the X-ray source catalog.

In addition to the XMM-Newton data, there are also a number of Chandra
observations in our source-search region, including 18 observations of 10–90
ks exposure depth following up X-ray galaxy clusters identified in the XMM-LSS
and XMM-XXL surveys (PIs: Andreon, S.; Jones, L.; Mantz, A.; Maughan, B.;
Murray, S.; Pierre, M.); these observations occupy a wide RA/DEC range in our
catalog region. In §4.1 and §4.2, we make use of the Chandra sources in these
observations culled from the Chandra Source Catalog 2.0 (CSC 2.0; Evans et
al., 2010).666We use the CSC Preliminary Detections List
http://cxc.harvard.edu/csc2/pd2/. There are a total of 328 Chandra sources
from CSC 2.0 in our survey region. Note that the source-flux information is
not yet available for the CSC 2.0 Preliminary Detections List. Of these 328
Chandra sources, 201 of them are in CSC 1.1 (Evans et al., 2010). Their 0.5–7
keV band fluxes range from $3\times 10^{-16}-1.7\times 10^{-13}$ erg cm-2 s-1,
with a median value of $9.7\times 10^{-15}$ erg cm-2 s-1. We use these Chandra
sources as a means to improve and assess the multiwavelength counterpart
identification reliabilities, since Chandra has better angular resolution and
astrometric accuracy than those of XMM-Newton.

###  2.2 Data preparation and background-flare filtering

Figure 3:  Left – Full-band survey effective exposure map (PN + MOS). The 5.3
deg2 survey region from which the X-ray source catalog is constructed is
marked as the cyan rectangular box. Except for several regions with deep XMM-
Newton follow-up observations of galaxy clusters, the XMM-Newton coverage in
our survey region is generally uniform. Right – The black solid line shows the
cumulative survey solid angle as a function of full-band effective (i.e.,
vignetted) PN+MOS exposure for observations used in this work. Distributions
for individual instruments are indicated as the dashed line (PN), dash-dotted
line (MOS1), and dotted line (MOS2). For comparison, the cumulative survey
solid angle for the archival XMM-Newton data in our survey region, in XMM-
COSMOS, and in SXDS are shown as the thin purple line, thick orange line, and
thick green line, respectively. The dashed vertical line marks exposure time
$=100$ ks.

We use the XMM-Newton Science Analysis System (SAS)
16.1.0777https://www.cosmos.esa.int/web/xmm-newton/sas-release-notes-1610. and
HEASOFT
6.21888https://heasarc.gsfc.nasa.gov/FTP/software/ftools/release/archive/Release_Notes_6.21.
for our data analysis. The XMM-Newton Observation Data Files (ODFs) were
processed with the SAS tasks epicproc (epproc and emproc for PN and MOS,
respectively) to create MOS1, MOS2, PN, and PN out-of-time (OOT) event files
for each ObsID. For observations taken in mosaic mode or with unexpected
interruptions due to strong background flares, we use the SAS task
emosaic_prep to separate the event files into individual pseudo-exposures and
assign pseudo-exposure IDs. For the mosaic-mode observations, we also
determine the sky coordinates of each pseudo-exposure using the AHFRA and
AHFDEC values in the attitude files created using the SAS task atthkgen.

For each event file, we create single-event light curves in time bins of 100 s
for high (10–12 keV) and low (0.3–10 keV) energies using evselect to search
for time intervals without significant background flares (the “good time
intervals”, GTIs). We first remove time intervals with 10–12 keV count rates
exceeding $3\sigma$ above the mean, and then repeat the $3\sigma$ clipping
procedure for the low-energy light curves. Since background flares usually
manifest themselves as a high-count-rate tail in addition to the Gaussian-
shape count-rate histogram, adopting the $3\sigma$ clipping rule can
effectively remove the high-count-rate tail while retaining useful scientific
data. For a small number of event files with intense background flares, we
filter the event files using the nominal count-rate thresholds suggested by
the XMM-Newton Science Operations
Centre.999https://www.cosmos.esa.int/web/xmm-newton/sas-thread-epic-
filterbackground We exclude 12 pointings with GTI $<$ $2$ ks from our
analysis. A total of 2.7 Ms (2.3 Ms) of MOS (PN) exposure remains after flare
filtering, including 1.1 Ms (0.9 Ms) from AO–15 and 1.6 Ms (1.4 Ms) from the
archival data. The flare-filtered median PN exposure time of the full 5.3 deg2
survey region is $\approx 45.8$ ks. For the central $\approx 4.5$ deg2 region
covered by SERVS, the median PN exposure time is $48.5$ ks. These values were
not corrected for vignetting.

After screening for background flares, we further exclude events in energy
ranges that overlap with the instrumental background lines (Al K$\alpha$ lines
at 1.45–1.54 keV for MOS and PN, which usually accounts for $\approx 10\%$ of
the mean counts101010https://xmm-
tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/epicintbkgd.html.;
Cu lines at 7.2–7.6 keV and 7.8–8.2 keV for PN, which accounts for 30% of the
2–10 keV counts111111Ranalli et al. (2015).).

From the flare-filtered, instrumental-line-removed event files, we construct
images with a commonly adopted $4^{\prime\prime}$ pixel size using evselect in
the following bands: 0.5–2 keV (soft), 2–10 keV (hard), and 0.5–10 keV (full).
For each image, we generate exposure maps with and without vignetting
corrections using the SAS task eexpmap. We set usefastpixelization=0 and
attrebin=0.5 in order to obtain more accurate exposure maps. The exposure maps
without vignetting-corrections are only used for generating maps of the
instrumental background, which is not affected by vignetting (see §3).
Detector masks were also generated using the SAS task emask. The distribution
of vignetting-corrected exposure values across the XMM-LSS field and the
PN+MOS1+MOS2 exposure map are presented in Fig. 3.

Figure 4:  Left: Distribution of the number of X-ray sources used for finding
the required angular offset. The median value is marked as the dashed line.
Right: Distributions of optical-to-X-ray separations in RA for the matched
X-ray sources in ObsID 0037982201 after the astrometric corrections. The
results based on our iterative method are shown as the blue histogram, and the
results based on the eposcorr task are shown as the orange histogram. For the
vast majority of the ObsIDs, the difference is small, but some have non-
negligible differences and we choose the required astrometric correction based
on comparing angular-offset distributions similar to the one shown here.

##  3 The Main X-ray Source Catalog

###  3.1 First-pass source detection and astrometric correction

The astrometric accuracy of XMM-Newton observations can be affected by the
pointing uncertainties of XMM-Newton. This uncertainty is usually smaller than
a few arcsec, but can be as large as $\approx 10^{\prime\prime}$ (e.g.,
Cappelluti et al., 2007; Watson et al., 2008; Rosen et al., 2016). To achieve
better astrometric accuracy and to minimize any systematic offsets between
different XMM-Newton observations, we run an initial pass of source detection
for each observation and then use the first-pass source list to register the
XMM-Newton observations onto a common WCS frame. The first-pass source
detection methods are outlined below:

  1. (i)

For the exposures taken by each of the three instruments for each observation,
we generate a temporary source list using the SAS task ewavelet with a low
likelihood threshold (threshold=4). ewavelet is a wavelet-based algorithm that
runs on the count-rate image generated using the image and vignetting-
corrected exposure map extracted as described in §2.2.

Figure 5: Spatial distribution of the 5242 sources detected in this work. We
have identified reliable multiwavelength counterparts (see Sec. 4.1 and Sec.
4.2 for details) for 93% of the XMM-Newton sources (blue dots), while the
remaining 7% of sources are marked as open red circles. Some of the
multiwavelength coverage of the XMM-LSS field is also shown as labeled (see §4
for details).

  2. (ii)

We use the temporary source list as an input to generate background images
using the SAS task esplinemap with method=model. This option fits the source-
excised image with two templates: the vignetted exposure map, and the un-
vignetted exposure map. The former represents the cosmic X-ray background with
an astrophysical origin, while the latter represents the intrinsic
instrumental noise. esplinemap then finds the best-fit linear combination of
the two templates and generates a background map. The details of this method
are described in Cappelluti et al. (2007). The background maps are used for
the PSF-fitting based source detection task described in Step (iv).

  3. (iii)

We run ewavelet again for each observation. This time the source list is
generated by running ewavelet on the exposure map and image coadded across the
PN, MOS1, and MOS2 exposures (when available) with the default likelihood
threshold (threshold=5).

  4. (iv)

For each ewavelet source list, we use the SAS task emldetect to re-assess the
detection likelihood and determine the best-fit X-ray positions. emldetect is
a PSF-fitting tool which performs maximum-likelihood fits to the input source
considering the XMM-Newton PSF, exposure values, and background levels of the
input source on each image. emldetect also convolves the PSF with a
$\beta$-model brightness profile121212http://xmm-
tools.cosmos.esa.int/external/sas/current/doc/emldetect/node3.html. for
clusters and uses the result to determine if the input source is extended.
Instead of running on the co-added image, emldetect takes the image, exposure
map, background map, and detector mask of each input observation into account.
We use a stringent likelihood threshold (likmin$=10.8$) to ensure that
astrometric corrections are calculated based on real detections, and we only
keep the point sources.

  5. (v)

For the mosaic-mode observations (see Footnote 2), the multiple pointings
under the same ObsID were already registered on the same WCS frame of the
ObsID. Therefore, we do not correct the astrometry for each pseudo-exposure
but only consider the astrometric offsets on an ObsID-by-ObsID basis. The
source lists for the mosaic-mode observations were generated using the SAS
task emosaic_proc, which is a mosaic-mode wrapper for procedures similar to
(i)-(iv) described above.

For steps (iv) and (v), the source searching was conducted simultaneously on
the images of the three EPIC cameras as the astrometric offsets between PN,
MOS1, and MOS2 are negligible. For each ObsID, we cross-correlate the high-
confidence emldetect list of point sources (with the emldetect flag EXT$=0$)
with the optical source catalog culled from the Hyper Suprime-Cam Subaru
Strategic Program Public Data Release 1 (HSC-SSP; Aihara et al., 2018), which
is an ultra-deep optical photometric catalog with sub-arcsec angular
resolution. The astrometry of HSC-SSP is calibrated to the Pan-STARRS1 $3\pi$
survey and has a $\lesssim 0.05^{\prime\prime}$ astrometric uncertainty. More
details of the HSC-SSP catalog can be found in Aihara et al. (2018), and it is
also briefly discussed in §4. For astrometric corrections, we limit the
optical catalog to HSC sources with $i=18-23$ to minimize possible spurious
matches due to large faint source densities at $i>23$ and matches to bright
stars that might have proper motions or parallaxes.

The offset between each ObsID and the HSC catalog is calculated based on a
maximum-likelihood algorithm similar to the SAS task eposcorr. The major
difference between our approach and eposcorr is that we use an iterative
optimization approach compared to the grid-searching algorithm adopted by
eposcorr. During each iteration, we cross-correlate the optical catalog with
the X-ray catalog using a $10^{\prime\prime}$ search radius and exclude all
matches with multiple counterparts (less than $5\%$ of our X-ray sources have
more than one optical counterpart in the bright HSC-SSP catalog). The
$10^{\prime\prime}$ search radius is motivated by both the positional accuracy
and PSF size of XMM-Newton, and the largest separations between the XMM-Newton
and Chandra positions of the sources in the Chandra COSMOS Legacy Survey
(Marchesi et al., 2016). We then calculate the required astrometric
corrections that maximize the cross-correlation likelihood. After each
iteration, we apply the best-fit astrometric offsets to the source list and
next repeat the catalog cross-correlation steps and re-calculate the required
additional corrections for the source list. The required astrometric
corrections usually converge after 1–2 iterations. For the purpose of frame
correction, we adopt the X-ray positional uncertainties calculated based on
the PSF-fitting likelihood ratios provided by emldetect ($\sigma_{eml}$
hereafter). The positional uncertainty information is necessary because the
required astrometric corrections should be weighted toward X-ray sources with
better positions within each observation. To avoid over-weighting sources with
extremely small $\sigma_{eml}$, we also include a constant
$0.5^{\prime\prime}$ systematic uncertainty when calculating the best-fit
values for frame-correction.131313We assume the systematic uncertainties to be
$0.5^{\prime\prime}$ as suggested by Watson et al. (2008). The median number
of X-ray sources in an ObsID with only one HSC counterpart within
$3^{\prime\prime}$ is 28. See Fig. 4-left for a histogram of the number of
X-ray sources used for determining the required angular offsets.

The required frame-correction offsets calculated using our approach are less
than $3^{\prime\prime}$ in both RA and DEC and are generally consistent with
the results calculated using eposcorr, with a median difference of
$0.1^{\prime\prime}$. For demonstration purposes, we show the difference
between our RA offsets and the eposcorr RA offsets for ObsID 0037982201 in Fig
4-right. For two ObsIDs the difference between our offsets and the eposcorr
offsets are non-negligible ($>0.5^{\prime\prime}$). We visually inspect the
X-ray to optical angular offsets similar to the one shown in Fig 4-right of
these ObsIDs and conclude that our approach does improve the alignments
between the optical and corrected X-ray images. The event files and the
attitude file for each ObsID are then projected onto the WCS frame of the HSC
catalog by updating the relevant keywords using a modified version of
Chandra’s align_evt routine (Ranalli et al., 2013). Since the sky coordinates
for the event files of the mosaic-mode pseudo-pointings are derived based on
the reference point centered at the nominal RA and DEC positions of the
mosaic-mode ObsIDs, we also recalculate the sky coordinates for these event
files with the SAS task attcalc using the true pointing positions as the
reference point, which is necessary for using regular SAS tasks for mosaic-
mode pseudo-exposures.

###  3.2 Second-pass source detection

We re-create images, exposure maps, detector masks, and background maps using
the frame-corrected event files and attitude files. We then run source-
detection tasks for the second time considering all XMM-Newton observations
listed in Table 2. Similar to the approach used for the XMM-H-ATLAS survey
(Ranalli et al., 2015), we divide the XMM-LSS field into a grid when running
the second-pass source detection because the number of images that can be
processed by a single emldetect thread is limited. We use a custom-built
wrapper of relevant SAS tasks to carry out the second-pass source detection,
which is similar to the griddetect141414https://github.com/piero-
ranalli/griddetect. tool built for the XMM-H-ATLAS survey (Ranalli et al.,
2015).

The cell sizes of the grid are determined by the number of ewavelet sources.
For each cell in the grid, we co-add the images and exposure maps for all
observations with footprint inside the cell and run ewavelet with a low
detection threshold151515threshold=4. on the co-added image and exposure map.
For each cell, we only keep ewavelet sources within the RA/DEC range of the
cell plus 1′ “padding” on each side of the cell. We then use the ewavelet list
as an input for emldetect to assess the detection likelihood. The emldetect
point-source list of the full XMM-LSS region is constructed from the union of
the sources from all cells after removing duplicates due to the “padding”. We
search for sources in three different bands: 0.5–2 keV (soft), 2–10 keV
(hard), and 0.5–10 keV (full). For each source, emldetect computes a detection
likelihood det_ml, which is defined as det_ml$=-\ln P$, where $P$ is the
probability of a detected source being a random Poisson fluctuation of the
background. In practice, the spurious fractions of a source catalog derived
based on simulations are known to differ from the values obtained with the
simple det_ml$=-\ln P$ equation (e.g., Cappelluti et al., 2007, 2009; Ueda et
al., 2008; Watson et al., 2008; LaMassa et al., 2016). Since the source
catalog is constructed based on a complex multi-stage source-detection
approach, the relation between det_ml and the true spurious fraction may not
be as straightforward as the simple det_ml$=-\ln P$ equation, especially in
the low source count regime where even this simple relation fails.161616See
http://xmm-tools.cosmos.esa.int/external/sas/current/doc/emldetect.pdf.
Therefore, we do not adopt a single det_ml value for our source catalog.
Instead, we use the det_ml value corresponding to the 1% spurious fraction
determined by simulations for each band (see the next subsection, §3.3, for
details). The det_ml thresholds with 1% spurious fraction are 4.8, 7.8, and
6.2 for the soft, hard, and full bands, respectively. A total of 5242 sources
satisfy this criterion in at least one of the three bands (see §3.5). We show
the spatial distribution of the 5242 detected sources in Fig. 5.

###  3.3 Monte Carlo simulations

Figure 6:  Left: The fraction of spurious sources detected at different det_ml
based on simulations. The detection threshold relevant to our catalog is
marked as the horizontal dashed line. Right: The minimum source counts for the
detected sources (the median of all 20 simulations) with det_ml values above a
given det_ml threshold. As expected, higher det_ml thresholds can only detect
sources with higher numbers of counts. The det_ml values corresponding to the
$1\%$ spurious fraction are marked as the open circles.

To assess our survey sensitivity and catalog reliability, we perform Monte
Carlo simulations of X-ray observations. For each simulation, we generate a
list of mock X-ray sources by sampling from the $\log N-\log S$ relations
reported in the XMM-COSMOS survey (Cappelluti et al., 2009, for the 0.5–2 keV
and 2–10 keV bands) and the Chandra Multiwavelength Project survey (ChaMP; Kim
et al., 2007, for the 0.5–10 keV band). The maximum flux of the mock X-ray
catalogs is set at $10^{-11}$ erg cm-2 s-1. The minimum flux of the mock X-ray
sources at each energy band is set as 0.5 dex lower than the minimum detected
flux (e.g., LaMassa et al., 2016). We randomly place the mock X-ray sources in
the RA/DEC range covered by the XMM-Newton observations used in this work. We
then use a modified version of the simulator written for the XMM-Newton survey
of the CDF-S (Ranalli et al., 2013), CDFS-SIM,171717 https://github.com/piero-
ranalli/cdfs-sim to create mock event files. CDFS-SIM converts X-ray fluxes to
PN and MOS count rates with the same model used for deriving the ECFs, and it
then randomly places X-ray events around the source location according to the
count rates, the XMM-Newton PSFs at the given off-axis angle, and the real
exposure maps. We extract images from the simulated event files using the same
methods described in §3. For each observation, the simulated image is combined
with a simulated background, which is created by re-sampling the original
background map according to Poisson distributions to create simulated images
that mimic the real observations. For each energy band, a total of 20
simulations are created. We run the same two-stage source-detection procedures
described in §3.2 on the simulated data products. For each simulation, we
match the detected sources to the input sources within a $10^{\prime\prime}$
cut-off radius by minimizing the quantity $R^{2}$ (Eq. 4 of Cappelluti et al.,
2009):

$R^{2}=\big{(}\frac{\Delta{\rm RA}}{\sigma_{\rm
RA}}\big{)}^{2}+\big{(}\frac{\Delta{\rm DEC}}{\sigma_{\rm
DEC}}\big{)}^{2}+\big{(}\frac{\Delta{\rm RATE}}{\sigma_{\rm
RATE}}\big{)}^{2}.$ (1)

Here $\Delta{\rm RA}$ and $\Delta{\rm DEC}$ are the differences between the
simulated RA/DEC positions and the RA/DEC positions obtained by running source
detection on the simulated images. $\Delta{\rm RATE}$ is the difference
between the simulated count rates and the detected count rates. $\sigma_{\rm
RA}$, $\sigma_{\rm DEC}$, and $\sigma_{\rm RATE}$ are the uncertainties of RA,
DEC, and count rates of the detected sources. Minimizing $R^{2}$ takes into
account the flux and positional differences between the input catalog and the
sources detected in the simulated images (e.g., Cappelluti et al., 2007;
Ranalli et al., 2015). Detected sources without any input sources within the
$10^{\prime\prime}$ radius are considered to be spurious detections.

Fig. 6-left presents the spurious fraction ($f_{\rm spurious}$) as a function
of det_ml for the soft, hard, and full bands. For our catalog, we consider
sources with $f_{\rm spurious}$ less than 1% to be reliably detected. At this
threshold, the corresponding det_ml values are 4.8, 7.8, and 6.2 for the soft,
hard, and full bands, respectively. The difference between the det_ml
thresholds in the three bands are likely due to their different background
levels. For the full X-ray source catalog of 5242 sources, the $f_{\rm
spurious}=1\%$ criterion translates to $\approx 52$ spurious detections. For
each source, we have also calculated a detection reliability parameter
(defined as $1-f_{\rm spurious}$) for each band using the simulation results
presented in Fig. 6-left, which can be used for selecting sources with a
desired reliability. We also display the minimum detected source counts (the
median values of all 20 simulations) as a function of the det_ml threshold in
Fig.6-right. We test for source confusion following the methods described in
Hasinger et al. (1998) and Cappelluti et al. (2007). For all the simulated
sources that are detected (i.e., having det_ml values greater than the 1%
thresholds), we consider sources with observed fluxes ($S_{\rm out}$) that are
larger than the simulated fluxes ($S_{\rm in}$) by the following threshold to
be “confused” sources: $S_{\rm out}/(S_{\rm in}+3\times S_{\rm out}^{\rm
Err})>1.5$. Here $S_{\rm out}^{\rm Err}$ is the statistical fluctuation of the
observed fluxes. The source confusion fractions are 0.14%, 0.16%, and 0.43% in
the soft, hard, and full bands, respectively. For the 5242 X-ray sources in
this catalog, these fractions translate to $\approx 7-22$ sources with
confusion.

###  3.4 Astrometric accuracy

Figure 7:  Histogram of the normalized full-band positional offsets, a
dimensionless quantity defined as the positional offsets normalized by the
empirically derived positional uncertainty, and comparison with the expected
Rayleigh distribution, the solid red curve. The kernel-density estimation of
the normalized positional offset distribution is shown as the solid blue
curve. The excellent agreement between the two distributions suggests that our
empirically derived $\sigma_{x}$ values are reliable indicators of the true
positional uncertainties.

We investigate the positional accuracy of the XMM-Newton sources by comparing
the second-pass X-ray catalog with the HSC-SSP catalog. Similar to the frame-
correction procedures described in §3.1, we search for unique optical
counterparts around the X-ray positions using a $3^{\prime\prime}$ search
radius. For the 5199 X-ray sources detected in the full-band during the
second-pass source-searching process, a total of 2434 X-ray sources are found
to have only one $i=18-23$ HSC counterpart within $3^{\prime\prime}$. We use
the separations between the optical and X-ray positions of this subsample as a
means to determine empirical X-ray positional uncertainties, which is a
commonly adopted practice in X-ray surveys (e.g. Watson et al., 2008; Luo et
al., 2010; Xue et al., 2011, 2016; Luo et al., 2017).

The X-ray positional accuracy is determined by how well the PSF-centroid
location can be measured, which usually depends on the number of counts of the
detected source and the PSF size of the instrument (primarily dependent on the
off-axis angle). For the vast majority of the X-ray sources presented in this
work, the detected photons are from at least three different observations, and
hence the dynamical range of effective off-axis angle for each source detected
on the coadded image is relatively small. Thus, the X-ray positional
uncertainty is mostly dependent on the number of counts available for detected
sources. Using the angular separations between the 2434 X-ray sources and
their unique optical counterparts, we derive an empirical relation between the
number of X-ray counts, $C$,181818An upper limit of 2000 is set on $C$ because
the improvement of positional accuracy is not significant for larger source
counts (e.g., Luo et al., 2017). and the 68% positional-uncertainty radius
($r_{68\%}$) for the full-band-detected X-ray sources,
$\log_{10}r_{68\%}=-0.31^{+0.02}_{-0.01}\times\log_{10}C+0.85$. The parameters
are chosen such that $68\%$ of the sources have positional offsets smaller
than the empirical relation.

For this work, we define the X-ray positional uncertainty, $\sigma_{x}$, to be
the same as the uncertainties in RA and DEC where $\sigma_{\rm RA}=\sigma_{\rm
DEC}=\sigma_{x}$. Under this definition, $\sigma_{x}$ is $r_{68\%}$ divided by
a factor of $1.515$ (e.g., Eq. 21 and §4.2 of Pineau et al., 2017). The factor
1.515 is determined by integrating the Rayleigh distribution until the
cumulative probability reaches 0.68. For reference, 90%, 95%, and 99.73%
uncertainties correspond to $2.146\sigma_{x}$, $2.448\sigma_{x}$, and
$3.439\sigma_{x}$, respectively. Because the separations in both RA and DEC
behave as a univariate normal distribution with $\sigma_{\rm RA}$ and
$\sigma_{\rm DEC}$, respectively,191919Here we consider the positional
uncertainties of the HSC-SSP catalog to be negligible compared to the XMM-
Newton positional uncertainties. the angular separation should therefore
follow the joint probability distribution function of the uncertainties in the
RA and DEC directions. Since we assume $\sigma_{\rm RA}=\sigma_{\rm DEC}$, the
angular separation between an optical source and an X-ray source should follow
the univariate Rayleigh distribution with the scaling parameter $\sigma_{x}$,
where $\sigma_{x}=\sigma_{\rm RA}=\sigma_{\rm DEC}$ (see §4 of Pineau et al.,
2017, for details).

For each energy band, we repeat the same process to find the best-fit relation
for $\sigma_{x}$ using the following equation:

$\log_{10}\sigma_{x}=\alpha\times\log_{10}C+\beta.$ (2)

Given the PSF size and positional accuracy of XMM-Newton, it is possible for
X-ray sources to have angular separation from optical sources larger than
$3^{\prime\prime}$, and the positional uncertainties derived based on
counterparts found within the $3^{\prime\prime}$ search radius can be
underestimated. Therefore, we adopt an iterative process. For each iteration,
we use the derived $\sigma_{x}$ to identify reliable matches using the
likelihood-ratio matching method described in §4.1. We then re-derive Eq. 2
using the reliable matches, and the updated astrometric uncertainties are used
for running likelihood-ratio matching again. This is a stable process, as the
parameters converge after 2–3 iterations. The average positional uncertainties
($\sigma_{x}$) for our soft-band, hard-band, and full-band X-ray catalogs are
1$\aas@@fstack{\prime\prime}$35, 1$\aas@@fstack{\prime\prime}$37, and
1$\aas@@fstack{\prime\prime}$31, respectively. The standard deviations of the
positional uncertainties are 0$\aas@@fstack{\prime\prime}$37,
0$\aas@@fstack{\prime\prime}$25, and 0$\aas@@fstack{\prime\prime}$30 for the
soft, hard, and full bands, respectively. Fig. 7 presents a comparison of the
normalized separation (Separation/$\sigma$) between the full-band X-ray
sources and their bright optical counterparts with $\sigma$ derived using Eq.
2, $\sigma_{x}$. The agreement between the Rayleigh distribution and the
Separation/$\sigma_{x}$ distribution of our sample demonstrates that our
empirically derived $\sigma_{x}$ values are reliable indicators of the true
positional uncertainties. As for $\sigma_{eml}$, previous studies have
reported that some on-axis sources with large numbers of counts can have
unrealistically low $\sigma_{eml}$ values, therefore an irreducible systematic
uncertainty should be added to $\sigma_{eml}$ for the normalized separation to
follow a Rayleigh distribution (e.g., Watson et al., 2008), but the nature of
this systematic uncertainty remains unclear. For this work, we use
$\sigma_{x}$ as the positional uncertainties of our X-ray catalog, but
$\sigma_{eml}$ is also included in the final catalog for completeness.

###  3.5 The main X-ray source catalog

Figure 8:  Left – Source-count distributions for the sources detected in the
soft (red), hard (blue), and full (gray) bands. Right – Flux distributions of
the sources detected in the three bands. Colors are the same as in the left
panel.

We detect 3988, 2618, and 5199 point sources with $f_{\rm spurious}\leq 1\%$
in the 0.5–2 keV, 2–10 keV, and 0.5–10 keV bands, respectively. The details of
the main X-ray source catalog are reported in Table F of Appendix A. The
extended sources (identified by the EXT > 0 flag of emldetect) are not
included, as the properties of the extended X-ray emission are beyond the
scope of this work.202020There are 68, 11, and 77 sources identified as EXT
$>$ 0 by emldetect in the 0.5–2 keV, 2–10 keV, and 0.5–10 keV bands,
respectively. The properties of the extended sources will be reported in a
separate work.  We combine catalogs from the three energy bands using a
similar approach to that adopted by the XMM-Newton Serendipitous Source
Catalogue. We consider two sources from different catalogs to be the same if
their angular separation is smaller than any of the following quantities: (1)
10′′, (2) distance to the nearest-neighbor in each catalog, or (3) quadratic
sum of the $99.73\%$ positional uncertainties from both bands. The final
source catalog is the union of the sources detected in the three energy bands.
We check for potential duplicate sources by visually inspecting all sources
with distance to the nearest-neighbor (DIST_NN) less than 10′′, and only one
set of sources is found to be duplicated, resulting in a total of 5242 unique
sources. There are 2967 sources with more than 100 PN+MOS counts in the full-
band, and 126 sources with more than 1000 X-ray counts. A unique X-ray source
ID is assigned to each of the 5242 sources at this stage. Visual inspection of
the image in each band suggests that no apparent sources were missed by our
detection algorithm.

We also derive the count rate (vignetting-corrected) to flux energy conversion
factors (ECFs) assuming a power-law spectrum with photon index $\Gamma=1.7$,
which is typical for distant X-ray AGNs found in XMM-Newton surveys with
comparable sensitivities (e.g., XMM-COSMOS, Mainieri et al. 2007 and XMM-H-
ATLAS, Ranalli et al. 2015) and Galactic absorption, $N_{\rm H}=3.57\times
10^{20}$ cm-2. The energy ranges are those where the removed instrumental
lines are excluded when deriving the ECFs. Since the archival observations and
the AO-15 observations were carried out in different epochs between 2000–2017,
we compute the ECFs by taking the slight temporal variations in the EPIC
instrumental calibrations into account. In detail, we make use of the “canned”
response files of 14 different epochs for MOS and 3 different epochs for PN
available at the XMM-Newton SOC website.212121
https://www.cosmos.esa.int/web/xmm-newton/epic-response-files. The effective
ECF for each detected source is the exposure-time-weighed average of all
relevant observations. For all X-ray sources, the mean conversion factors for
(PN, MOS1, MOS2) are $(6.23,1.78,1.76)$, $(1.15,0.43,0.43)$, and
$(2.84,0.88,0.87)$ counts s${}^{-1}/10^{-11}$erg cm-2 s-1, in the 0.5–2 keV,
2–10 keV, and 0.5–10 keV bands, respectively. We note that temporal variations
in the ECFs are $<1\%$ for all three bands (e.g., Mateos et al., 2009; Rosen
et al., 2016). For each source detected by emldetect, the flux from each EPIC
camera is calculated separately using the corresponding ECF. The final flux of
the source is the error-weighted mean of the fluxes from the three EPIC
cameras, when available. The median fluxes for the soft, hard, and full bands
are $2.9\times 10^{-15}$, $1.5\times 10^{-14}$, and $9.4\times 10^{-15}$ erg
cm-2 s-1, respectively. The source-count and flux distributions of the sources
detected in the three energy bands are displayed in Fig. 8.

Figure 9:  Comparison of the soft-band X-ray fluxes of our X-ray sources and
those of the XMM-Newton counterparts identified in the XMM-XXL-North source
catalogs (Liu et al., 2016) within a 10′′ radius. As expected, almost all of
the XMM-XXL-North X-ray sources in our catalog region can be matched to a
counterpart in our X-ray source catalog with comparable flux.

For sources that are detected in fewer than three bands, we calculate the
source-count upper limits using the mosaicked background map of the band in
which the source is not detected. The mosaicked background map of each band is
generated by summing the background maps from all individual observations (see
§3.1). According to the Poisson probability set by the emldetect detection
likelihood threshold ($P_{\rm Random}$, the probability of the detected source
being a random Poisson fluctuation due to the background), we can calculate
the minimum required total counts ($m$ in the following equation) required to
exceed the expected number of background counts, $B$, using the regularized
upper incomplete $\Gamma$ function (which is equivalent to Eq. 2 of Civano et
al. 2016 if $m$ is a positive integer):

$P_{\rm Random}=\frac{1}{\Gamma(m)}\int_{B}^{\infty}t^{m-1}e^{-t}dt$ (3)

The upper limits are those corresponding to the det_ml values with a 1%
spurious fraction: $P_{\rm Random}=8.2\times 10^{-3}$ for the soft band,
$P_{\rm Random}=4.1\times 10^{-4}$ for the hard band, and $P_{\rm
Random}=2.0\times 10^{-3}$ for the full band. For each non-detected source in
each band, we determine the background counts by summing the background map
within the circle with 70% encircled energy fraction (EEF). We then calculate
$m$ by solving Eq. 3 using the Scipy function
scipy.special.gammainccinv.222222This quantity is the inverse function of Eq.
2. Since $m$ is the required total counts to exceed random background
fluctuations at the given probability, the flux upper limit is calculated
based on the following equation, which is similar to Equation 2 of Cappelluti
et al. (2009) and Equation 2 of Civano et al. (2016):

$S=\frac{m-B}{t_{\rm exp}\times{\rm EEF}\times{\rm ECF}}.$ (4)

Here EEF corrects for PSF loss and is 0.7, and $t_{\rm exp}$ is the median
exposure time within the 70% EEF circle. The flux upper limits are calculated
as the exposure-time-weighted mean of the three EPIC detectors.

For each source detected in either the soft or the hard band (or both), we
calculate its hardness ratio (HR), defined as $(H-S)/(H+S)$, where $H$ and $S$
are the source counts weighted by the effective exposure times in the hard and
the soft bands, respectively. The source counts are the default output of
emldetect, which is the sum of the counts from all three EPIC detectors.232323
Not all sources have data from all three EPIC detectors because one of the
chips of MOS1 is permanently damaged, and some sources happen to fall on the
chip gaps in one of the detectors. The exposure times for these sources are
set to $-$99 in Table F for the relevant detector.  The three EPIC detectors
have different energy responses, and the hardness ratios reported here did not
take these into account. We report this value in our catalog for direct
comparison with previous XMM-Newton studies. The uncertainties on HR are
calculated based on the count uncertainties from the output of emldetect using
the error-propagation method described in §1.7.3 of Lyons (1991). For sources
not detected in either the soft or the hard band, we calculate the limits of
their HRs assuming each non-detection has net counts $=m-B$, where $m$ is the
count upper limits calculated using Eq. 3 and $B$ is the background counts.
The HR uncertainties for these sources are set to $-$99.

We also report the hardness ratios independently for PN, MOS1, and MOS2,
calculated using the Bayesian Estimation of Hardness Ratios (BEHR) code (Park
et al., 2006) assuming the recommended indices for the $\Gamma$-function
priors (softidx$=1$ and hardidx$=1$). BEHR is designed to determine HRs for
low-count sources in the regime of Poisson distributions. It also computes
uncertainties using Markov chain Monte Carlo methods for sources including
those with non-detections in either the soft or hard band. Since our sources
are usually detected over multiple exposures, we scale the HRs by setting the
softeff and hardeff parameters in BEHR to account for the effective exposure
times using Eq. (6) of Georgakakis & Nandra (2011). Qualitatively, the BEHR
hardness ratios for sources that are detected in both the soft and hard bands
are consistent with those calculated using the simple approach described in
the previous paragraph. For the sources with non-detections in either the soft
or hard band, we quote the default 68% upper or lower bounds calculated with
BEHR. As expected, these limits are almost always weaker than the HR limits
obtained by assuming the non-detections have 99% source count upper limits
given by Eq. 3.

Figure 10: Top – Background-subtracted, smoothed, and coadded PN+MOS image in
the 0.5–10 keV band for a $0.8\times 0.6$ deg2 region centered at
RA$=35.580^{\circ}$, DEC=$-4.965^{\circ}$. This image is created using both
archival data and the new AO-15 data, and a total of 869 sources are detected
in this region. Bottom – Same as the top image, but only the archival data are
included. The two images are matched in color scale. In the Liu et al. (2016)
catalog, only 581 sources can be found in this region. The typical vignetting-
corrected exposure times are shown at the bottom of both panels. The exposure
time of the full survey region is shown in Fig. 3.

As a comparison, a total of 2861 X-ray sources from XMM-XXL-North (Liu et al.,
2016) are found to have a counterpart within the 10′′ radius in our X-ray
catalog.242424The 10′′ search radius is approximately 3 times the quadratic
sum of the largest positional uncertainties in both catalogs. For these
matched sources, we show a comparison between the soft-band X-ray fluxes
reported in the XMM-XXL-North catalog and those in our catalog in Fig. 9. As
expected, the majority of the archival sources detected in our catalog have
archival soft-band fluxes consistent with those in our catalog. The small
scatter in the measured fluxes is expected as the XMM-XXL-North catalog adopts
a different source-detection method, background-subtraction approach, and
energy conversion factors. Since the SXDS observations were also used for
constructing the XXL-North (Liu et al., 2016) catalog, the 2861 sources
matched to the XMM-XXL-North catalogs are considered to be matched to all
available archival sources, and we conclude that the other 2381 X-ray sources
in our catalogs are new sources. We include the IDs from the Liu et al. (2016)
catalog for these matched sources in our catalog (Table F).

In our source-detection region, 172 sources from the original Liu et al.
(2016) catalog do not have a counterpart in our point-source catalog. Of these
172 sources, 150 can be associated with extended sources or sources deemed
unreliable based on our det_ml criteria (see §3.3). The remaining sources
comprise $<1\%$ of the XMM-XXL-North catalog in our source-detection region.
Visual inspection suggests that the vast majority of these sources might be
spurious detections, but we cannot rule out the possibility that some sources
are missed in our catalog due to X-ray variability (e.g., Yang et al., 2016;
Falocco et al., 2017; Paolillo et al., 2017; Zheng et al., 2017). Also, the
XMM-XXL-North catalog adopted a different source-detection approach (see §2 of
Liu et al. 2016 for details). The properties of sources that exhibit strong
X-ray variability will be presented in a separate work. Fig. 10 shows the
background-subtracted, 0.5–10 keV PN+MOS image (see §3 for the details of the
data analysis) from a $\approx 0.5$ deg2 region in XMM-LSS generated using the
combined AO-15 and archival data. An image produced using only the archival
data is also displayed for comparison, demonstrating the improved source
counts with the additional AO-15 observations.

Table 3:  Sensitivity curves. Column 1: Soft-band flux. Column 2: Soft-band survey solid angle. Columns 3–4: Similar to Columns 1–2 but for the hard band. Columns 5–6: Similar to Columns 1–2 but for the full band. This table is available in its entirety online.  $\log S_{\rm 0.5-2keV}$ | $\Omega_{\rm 0.5-2keV}$ | $\log S_{\rm 2-10keV}$ | $\Omega_{\rm 2-10keV}$ | $\log S_{\rm 0.5-10keV}$ | $\Omega_{\rm 0.5-10keV}$
---|---|---|---|---|---
(cgs) |  (deg2) | (cgs) |  (deg2) | (cgs) |  (deg2)
(1) | (2) | (3) | (4) | (5) | (6)
$-$14.78 | 4.828 |  $-$13.93 | 4.652 |  $-$14.38 | 3.421
$-$14.77 | 4.862 |  $-$13.92 | 4.694 |  $-$14.37 | 3.583
$-$14.76 | 4.898 |  $-$13.91 | 4.737 |  $-$14.36 | 3.727
$-$14.75 | 4.931 |  $-$13.90 | 4.778 |  $-$14.35 | 3.855
$-$14.74 | 4.960 |  $-$13.89 | 4.815 |  $-$14.34 | 3.976
$-$14.73 | 4.991 |  $-$13.88 | 4.852 |  $-$14.33 | 4.081
$-$14.72 | 5.016 |  $-$13.87 | 4.885 |  $-$14.32 | 4.182
$-$14.71 | 5.044 |  $-$13.86 | 4.918 |  $-$14.31 | 4.262
… | … | … | … | … | …

###  3.6 Survey sensitivity, sky coverage, and $\log N-\log S$

Figure 11:  Left – Soft-band sensitivity map of the source-detection region
(the same as the cyan box shown in Fig. 3). Right – Comparison of the full-
band sky coverages between this work (solid line) and the archival XMM-Newton
observations (dashed line), demonstrating the improved and more uniform
sensitivity across the wide field enabled by the new data.  Figure 12:  Sky
coverage in the soft, hard, and full bands of our X-ray survey in XMM-LSS. The
sensitivity curves were calculated with det_ml$=4.8$, 7.8, and 6.2 for the
soft, hard, and full bands. These det_ml values correspond to $1\%$ spurious
fraction based on extensive simulations (see §3.3.)

We create sensitivity maps of our survey region in different bands using the
background and exposure maps generated as described in §2.2. The mosaicked
background and exposure maps are binned to $5\times 5$ pixels
($20^{\prime\prime}\times 20^{\prime\prime}$). For each pixel of the binned,
mosaicked background map, the minimum required source counts to exceed the
random background fluctuations are calculated using Eq. 3. The sensitivity is
then calculated using Eq. 4 with the corresponding EEF and ECF values.
According the sensitivity maps, our survey has flux limits of $1.7\times
10^{-15}$, $1.3\times 10^{-14}$, and $6.5\times 10^{-15}$ erg cm-2 s-1 over
90% of its area in the soft, hard, and full bands, respectively, reaching the
desired depth-area combination. We also compared the sensitivity maps with the
detected sources, and find that the spatial distribution of the fluxes of our
sources largely obey the sensitivity maps. The soft-band sensitivity map is
presented in Fig. 11-left. We also generated a soft-band sensitivity map using
only the archival data. To visualize the improvement upon the archival data,
we compare the full-band sky coverage obtained from all available XMM-Newton
data in our survey region with the sky coverage obtained using only the
archival data. Fig. 11-right demonstrates the improved survey depth and
uniformity with the new XMM-Newton observations. The sensitivity curves
corresponding to the det_ml thresholds in the soft, hard, and full bands are
shown in Fig. 12 and presented in Table 3.

Figure 13:  The $\log N-\log S$ relations for our catalog in the soft band
(left), hard band (middle), and full band (right). For comparison, a few $\log
N-\log S$ relations from surveys spanning a wide range of area and sensitivity
are also shown (XMM-COSMOS, Cappelluti et al. 2009; Stripe-82X, LaMassa et al.
2016; COSMOS-Legacy, Civano et al. 2016; and CDF-S 7Ms, Luo et al. 2017; the
energy range and power-law photon index differences have been corrected). The
$\log N-\log S$ relations of our survey are generally consistent with those of
previous studies.

We calculate the $\log N-\log S$ relations of our survey using the sky
coverage curves described above and the following equation:

$N(>S)=\sum\limits_{i=1}^{N_{s}}\frac{1}{\Omega_{i}}.$ (5)

Here $N(>S)$ represents the total number of detected sources with fluxes
larger than $S$, and $\Omega_{i}$ is the sky coverage associated with the flux
of the $i$th source. The $\log N-\log S$ relations of our survey are shown in
Fig. 13, along with the $\log N-\log S$ relations for a selection of surveys
spanning a wide range of area and sensitivity (CDF-S 7Ms, Luo et al. 2017;
XMM-COSMOS, Cappelluti et al. 2009; COSMOS-Legacy, Civano et al. 2016; and
Stripe 82X, LaMassa et al. 2016). The flux differences caused by different
choices of power-law indices and/or slight differences in energy ranges have
been corrected assuming a $\Gamma=1.7$ power-law spectrum adopted in this
work. Considering factors such as different spectral models and/or methods of
generating survey sensitivity curves, our $\log N-\log S$ relations are
consistent with the relations reported in the literature within the
measurement uncertainties.

##  4 Multiwavelength counterpart identifications

The XMM-LSS region is one of the most extensively observed extragalactic
fields. The publicly available multiwavelength observations in the XMM-LSS
region utilized in this work are SERVS (Mauduit et al., 2012), SWIRE (Lonsdale
et al., 2003), VIDEO (Jarvis et al., 2012), the CFHTLS-wide survey (Hudelot et
al., 2012), and the HSC-SSP survey (Aihara et al., 2018).

We focus on identifying the correct counterparts for our X-ray sources in four
deep optical-to-near-IR (OIR) catalogs: SERVS, VIDEO, CFHTLS, and HSC-SSP.
SERVS is a post-cryogenic Spitzer IRAC survey in the near-IR 3.6 and 4.5
$\mu$m bands with $\approx 2\mu$Jy survey sensitivity limits and $\approx 5$
deg2 solid-angle coverage in the XMM-LSS region. We make use of the highly
reliable two-band SERVS catalog built using SExtractor, obtained from the
Spitzer Data Fusion catalog (Vaccari, 2015), which has $\approx 4\times
10^{5}$ sources. The Spitzer Data Fusion catalog has already integrated data
from SWIRE, which include photometry in all four IRAC bands and the photometry
in MIPS 24, 70, and 160 $\mu$m. A total of $82\%$ of the X-ray sources have at
least one SERVS counterpart candidate within their 99.73% positional-
uncertainty radius ($r_{99\%}$ hereafter, which is equivalent to
3.44$\sigma_{x}$), which is calculated based on the quadratic sum of the
99.73% X-ray positional uncertainties and the corresponding OIR positional
uncertainties.

VIDEO is a deep survey in the near-infrared Z, Y, J, H, and $K_{s}$ bands with
$\approx 80\%$ completeness at $K_{s}<23.8$. In the XMM-LSS region, VIDEO
covers a $4.5$ deg2 area ($\approx 85\%$ of our X-ray survey region) with a
total of $\approx 5.7\times 10^{5}$ sources; $79\%$ of the X-ray sources have
at least one VIDEO counterpart candidate within $r_{99\%}$.

The CFHTLS-W1 survey covers the entirety of our X-ray data, with an $80\%$
completeness limit of $i^{\prime}=24.8$. We select the CFHTLS sources in the
RA/DEC ranges marginally larger (1′) than our source-detection region. We
limit the CFHTLS sources to those with $SNR>5$ in the $i^{\prime}$-band. The
total number of sources in the $i^{\prime}$-band selected catalog is $\approx
8.1\times 10^{5}$. A total of 90% of the X-ray sources in our catalog have at
least one CFHTLS counterpart candidate within $r_{99\%}$.

The XMM-LSS field is entirely encompassed by the 108 deg2 HSC-SSP wide survey.
The limiting magnitude in the i-band for the wide HSC-SSP survey is 26.4.
Inside the XMM-LSS field, HSC-SSP also has “ultra-deep” ($\approx 1.77$ deg2)
and “deep” ($\approx 5$ deg2) surveys, which overlap with the SXDS and XMDS
regions, respectively. We focus only on the wide survey because in the
currently available data release it is only 0.1 mag shallower than the deep
survey in the i-band, and the uniform coverage is important for determining
the background source density when matching to the X-ray catalog (see §4.1).
We select the i-band detected HSC-SSP sources in the RA/DEC ranges slightly
larger than our source-detection region.252525We select sources with the
detect_is_primary and idetected_notjunk flags set as True, and
centroid_sdss_flags set as False. According to the HSC-SSP example script for
selecting “clean objects”, we also exclude the HSC sources with
flags_pixel_edge, flags_pixel_saturated_center, flags_pixel_cr_center,
flags_pixel_bad  flags in the i-band to avoid unreliable i-band sources. The
total number of HSC-SSP sources in our source-detection region is $\approx
3.1\times 10^{6}$, and $\approx 93\%$ of the X-ray sources in our main catalog
have at least one HSC-SSP counterpart candidate within $r_{99\%}$.

Although CFHTLS is not as deep as HSC-SSP in the g, r, i, and z bands, it has
complementary u∗-band photometry. Including photometry from both optical
surveys also ensures that we will minimize the risk of missing an optical
counterpart due to bad photometry caused by artifacts such as satellite tracks
in either survey.

Since there are small systematic offsets in the astrometry of each catalog, we
match SERVS, VIDEO, and CFHTLS to the HSC-wide catalog, and correct for the
small offsets between each catalog to the HSC-wide catalog to maximize the
counterpart matching accuracy. In the RA direction, the adopted corrections
are 0$\aas@@fstack{\prime\prime}$020, 0$\aas@@fstack{\prime\prime}$027, and
0$\aas@@fstack{\prime\prime}$026 for SERVS, VIDEO, and CFHTLS, respectively.
For DEC, the adopted corrections are $-$0$\aas@@fstack{\prime\prime}$009,
$-$0$\aas@@fstack{\prime\prime}$006, $-$0$\aas@@fstack{\prime\prime}$008 for
SERVS, VIDEO, and CFHTLS, respectively.

###  4.1 The likelihood-ratio matching method

Figure 14:  Kernel-density estimations of the magnitude distributions (solid
lines) for the expected counterparts in SERVS (top-left), VIDEO (top-right),
CFTHLS (bottom-left), and HSC-SSP (bottom-right). We show the distributions
obtained using the full XMM-Newton catalog ($q(m)_{\it XMM-Newton}$), and the
distributions obtained using the Chandra sources in the XMM-LSS field
($q(m)_{\it Chandra}$). The magnitude distributions of the background,
unrelated sources are also displayed in each panel as the dashed curves. This
figure demonstrates that $q(m)_{\it Chandra}$ significantly improves upon the
background-dominated $q(m)_{\it XMM-Newton}$ for the deep OIR catalogs in the
bottom panels (in particular, the most-probable magnitude values).

To match reliably the X-ray sources to the OIR catalogs with much higher
source densities, we employ the likelihood-ratio method (LR hereafter) similar
to previous X-ray surveys, (e.g., Brusa et al., 2007; Luo et al., 2010; Xue et
al., 2011, 2016; Luo et al., 2017). The likelihood ratio is defined as the
ratio between the probability that the source is the correct counterpart, and
the probability that the source is an unrelated background object (Sutherland
& Saunders, 1992):

$LR=\frac{q(m)f(r)}{n(m)}.$ (6)

Here $q(m)$ is the magnitude distribution of the expected counterparts in each
OIR catalog, $f(r)$ is the probability distribution function of the angular
separation between X-ray and OIR sources, and $n(m)$ is the magnitude
distribution of the background sources in each OIR catalog.

We calculate the background source magnitude distributions using OIR sources
between 10′′ and 50′′ from any sources in our X-ray catalog.

As discussed in §3.4, the probability distribution function of the angular
separation should follow the Rayleigh distribution:

$f(r)=\frac{r}{\sigma_{x}^{2}}\exp^{\frac{-r^{2}}{2\sigma_{x}^{2}}}.$ (7)

Note that Eq. 7 is different from the two-dimensional Gaussian distribution
function that maximizes at $r=0$, and thus the $LR$ values calculated in this
work are not directly comparable to previous works that adopted a Gaussian
$f(r)$.

In practice, for an X-ray source with a total of $Nc$ counterpart candidates
within the search radius, the matching reliability for the $i$-th counterpart
candidate $MR_{i}$, can be determined using the following equation:

$MR_{i}=\frac{LR_{i}}{\sum_{k=0}^{N_{c}}LR_{k}+(1-Q)}$ (8)

Here $Q$ is the completeness factor, which is defined as
$Q=\int_{-\infty}^{m_{\rm lim}}q(m)$, where $m_{\rm lim}$ is the limiting
magnitude of the OIR catalog being used for matching. For each counterpart
candidate, $MR$ is equivalent to the relative matching probability among all
possible counterpart candidates. See Eq. 5 of Sutherland & Saunders (1992) and
§2.2 of Luo et al. (2010) for details.

Figure 15: Left: Distribution of the OIR-to-X-ray positional offsets in the RA
vs. DEC plane for the 4858 XMM-Newton sources with reliably matched OIR
counterparts. The contours represent the isodensity levels of the points. The
mean positional offsets are $<$ 0.1′′ in both the RA and DEC directions (the
red cross). Right: Histograms of positional offsets for the 4858 reliably
matched sources, divided into four bins based on their positional
uncertainties. In each panel, we also mark the median 68% positional offset
value ($r_{\rm 68\%}$) as the vertical dashed line.

Due to the relatively large positional uncertainties of XMM-Newton and the
high source densities of the OIR catalogs, deriving an accurate magnitude
distribution of the expected counterparts, $q(m)$, using XMM-Newton data is
challenging. Therefore, we obtain $q(m)$ for our X-ray sources by first
matching our XMM-Newton catalog to the Chandra Source Catalog 2.0 (CSC 2.0;
Evans et al., 2010) to take advantage of the higher angular resolution and
positional accuracy of Chandra. We derive the positional uncertainties of the
Chandra sources in our survey region using the same empirical approach
described in Xue et al. (2011) by selecting CSC sources in the RA/DEC range of
our catalog, and matching them onto HSC-SSP using a $1.5^{\prime\prime}$
radius. We select CSC sources that are uniquely matched to our X-ray catalogs
within the $95\%$ uncertainties (Chandra and XMM-Newton positional
uncertainties are added in quadrature). A total of 223 sources in our XMM-
Newton catalog are matched to a unique Chandra source in the CSC. We match
these Chandra sources to the four OIR catalogs using Eq. 6, with $q(m)$
derived using the iterative approach described in Luo et al. (2010), which
determines the $LR$ threshold by optimizing the matching reliability and
completeness. The $q(m)$ derived from the CSC sources, $q(m)_{\it Chandra}$,
is then used as the expected magnitude distribution for OIR counterparts of
our XMM-Newton sources. The X-ray flux distributions in the soft, hard, and
full bands of the Chandra-matched subsample are similar to those of our entire
XMM-Newton catalog, and therefore $q(m)_{\it Chandra}$ should be consistent
with the intrinsic magnitude distributions of the real OIR counterparts of our
full X-ray catalog. The counterpart-matching processes are run on four
different OIR catalogs: SERVS, VIDEO, CFHTLS, and HSC-SSP. The details of the
filters and apertures of the photometry in each OIR catalog can be found in
Appendix A, where we give the descriptions of the columns reported in the
source catalog (Columns 128–187 of Table F). For illustration, Fig. 14 shows
the magnitude distributions of the background sources and the distributions of
the expected counterparts derived using CSC sources.

For comparison, we also obtain $q(m)$ for the full XMM-Newton catalog without
using the Chandra positions, $q(m)_{\it XMM-Newton}$. We again use the Luo et
al. (2010) iterative method, but with a $3^{\prime\prime}$ initial search
radius. $q(m)_{\it XMM-Newton}$ is also plotted in Fig. 14. It is evident that
for ultra-deep OIR catalogs such as HSC-SSP and CFHTLS, $q(m)_{\it XMM-
Newton}$ is skewed toward the faint background sources compared to the
Chandra-matched subsample. For the other catalogs, we find no qualitative
difference between $q(m)_{\it Chandra}$ and $q(m)_{\it XMM-Newton}$, but we
still use $q(m)_{\it Chandra}$ for consistency.

We next compute the $LR$ values for all OIR sources within a 10′′ radius
(i.e., the counterpart “candidates”) of the X-ray sources using Eq. 6. For
each OIR catalog, we choose the $LR$ thresholds ($LR_{\rm th}$) such that the
reliability and completeness parameters are maximized (see Eq. 5 of Luo et al.
2010 for details). Counterparts with $LR>LR_{\rm th}$ are considered to be
reliably matched. A summary of the results is reported in Table 4. For each
OIR catalog, we list the number of all X-ray sources with at least one OIR
counterpart candidate within $r_{99\%}$ of the X-ray sources, $N_{\rm All}$,
and the number of X-ray sources with at least one reliably matched source with
$LR>LR_{\rm th}$, $N_{\rm Reliable}$.

Table 4:  Summary of $LR$ counterpart-matching results for each OIR catalog, with an additional summary row for the combined results from all OIR catalogs considered. The columns in the summary row are the same as those for individual OIR catalogs except for Column 7). Column 1: Catalog name. Column 2: Survey magnitude limit for each catalog in AB. Column 3: Survey area. Column 4: Positional uncertainty for each OIR catalog. Column 5: $LR$ threshold. Column 6: Total number of X-ray sources with at least one counterpart within the 10″ search radius in each catalog. Column 7: Average number of OIR sources within $r_{99\%}$ of the X-ray sources (if the X-ray source is within the coverage of the OIR catalog). Here the summary row shows the total number of X-ray sources with at least one OIR counterpart within $r_{99\%}$. Column 8: Total number of X-ray sources with at least one counterpart with $LR>LR_{\rm th}$. The summary row displays the number of all X-ray sources with at least one $LR>LR_{\rm th}$ counterpart from any of the four OIR catalogs, plus the 23 sources with only one unique counterpart within $r_{99\%}$ from all OIR catalogs considered (see §4.1 for details). X-ray sources having only one unique OIR counterpart in all OIR catalogs considered within $r_{99\%}$, but the $LR$ values do not exceed the reliability thresholds in all OIR catalogs. Columns 9–11: See §4.2 for details. Column 9: The fraction of X-ray sources in the “associated population” based on the results of Monte Carlo simulations. Column 10: False-matching rates determined using Monte Carlo simulations. Column 11: Fraction of the X-ray sources having identical reliable counterparts found based on their Chandra and XMM-Newton positions. Based on sources in regions where there is overlapping XMM-Newton and Chandra coverage. For the summary row, Columns 9–11 are calculated as the weighed sum (based on the number of primary counterparts from each catalog) of the results from all four OIR catalogs.  Catalog | Limiting Magnitude | Area | $\sigma$ | $LR_{\rm th}$ | $N_{\rm All}$ | $\overline{N_{99\%}}$ | $N_{\rm Reliable}$ | $f_{\rm AP}$ | False Rate | Identical Fraction
---|---|---|---|---|---|---|---|---|---|---
|  |  deg2 |  |  |  |  |  |  | (Simulation) |  (Chandra)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
SERVS |  $3.6\mu$m $<23.1$ | 5.0 | 0.5″ | 0.32 | 4689 | 1.0 | 3948 | 96.8% | 4.2% | 97.3%
VIDEO | $Ks<23.8$ | 4.5 | 0.3″ | 0.25 | 4380 | 1.3 | 3827 | 86.3% | 8.0% | 94.4%
CFHTLS-wide | $i<24.8$ | 5.4 | 0.2″ | 0.22 | 5185 | 1.5 | 4207 | 75.6% | 15.6% | 90.8%
HSC-SSP | $i<26.5$ | 5.4 | 0.1″ | 0.25 | 5124 | 2.3 | 4317 | 78.6% | 18.4% | 87.3%
Summary | N/A | N/A | N/A | N/A | 5237 | 5147 | 4858 | 93.1% | 5.8% | 97.1%

Motivated by the spurious-matching rates of different OIR catalogs (see §4.2
for the cross-matching reliability analysis), we first select a “primary”
counterpart for each X-ray source from, in priority order, SERVS, VIDEO,
CFHTLS, and HSC-SSP. After selecting the primary OIR counterpart, we associate
different OIR catalogs with each other using a simple nearest-neighbor
algorithm. Thanks to the much smaller positional uncertainties of the OIR
catalogs, we adopt a constant search radius of 1′′ for the OIR catalog
associations, which is the approach used by the Spitzer Data Fusion database
(Vaccari, 2015).

Using this approach, 4832 ($\approx 93\%$) X-ray sources have at least one
robust counterpart with $LR>LR_{\rm th}$. We consider an additional 26 X-ray
sources without any counterpart candidates having $LR>LR_{\rm th}$ to have
“acceptable” matches because there is only one unique counterpart in all four
OIR catalogs within $r_{\rm 99\%}$. When considering both the $LR>LR_{\rm th}$
counterparts and the acceptable counterparts, 4858 X-ray sources in our
catalog are considered to have reliable OIR counterparts ($93\%$). Of these
sources, 3968 are matched to SERVS as the primary counterpart, 367 are from
VIDEO, 386 are from CFHTLS, and 137 are from HSC.

Besides the 4858 X-ray sources with reliable/acceptable counterparts, most of
the remaining 384 sources have $f_{\rm spurious}\leq 0.05\%$ in at least one
band, and thus they are unlikely to be spurious X-ray detections. 289 of these
384 sources still have at least one OIR counterpart candidate within the
$r_{99\%}$ circle. Therefore, 5147 X-ray sources have at least one OIR
counterpart candidate within $r_{\rm 99\%}$. Of the other 95 sources, 90 still
have at least one OIR counterpart candidate within the $10^{\prime\prime}$
counterpart-searching radius. We still select counterparts for these sources
and the properties of these counterparts are included in the main X-ray
catalog. However, only the previously mentioned 4858 sources are considered to
be reliably matched and are flagged in the catalog. We find 5 sources that are
completely “isolated”, i.e., no counterpart candidates were found within a
10′′ search radius. Visual inspection of these sources shows that all of them
coincide with a bright star, thus making the pipeline OIR photometry
unavailable.

Fig. 15 presents the positional offsets between the X-ray sources and the
reliably matched sources. The small median positional offsets in the RA and
DEC directions demonstrate the quality of our astrometry, and the histograms
of the positional offsets for sources binned in different $\sigma_{x}$ show
that our empirically derived positional uncertainties are reliable. For each
source, we also generate postage-stamp images at X-ray, mid-IR, near-IR, and
optical wavelengths. For illustration, we show a random collection of 16 X-ray
sources with reliable counterparts in Fig. 16.

Figure 16: Postage-stamp images for 16 randomly selected X-ray sources in our
catalog. For each source, we show (1) Full-band X-ray image smoothed with a
Gaussian filter (upper-left panel). The unique source ID from Table A is shown
in this panel. (2) 3.4$\mu$m mid-IR image from SERVS (upper-right panel) (3)
Ks-band near-IR image from VIDEO (lower-left panel) (4) i-band optical image
from HSC-SSP (lower-right panel), re-sampled to a
0$\aas@@fstack{\prime\prime}$4 pixel size. Due to the large pixel size, the
X-ray image for each source is set at $2^{\prime}\times 2^{\prime}$. For the
OIR images, the sizes are set at $0.5^{\prime}\times 0.5^{\prime}$. In each
image, the X-ray position is marked as the cyan circle with the $r_{99}$
radius. The position of the most-probable mid-IR SERVS counterpart is marked
as the red circle with a 1$\aas@@fstack{\prime\prime}$5 radius. The positions
of VIDEO, CFHTLS, and HSC-SSP counterparts are marked as green, orange, and
yellow circles with a 0$\aas@@fstack{\prime\prime}$9,
0$\aas@@fstack{\prime\prime}$6, and 0$\aas@@fstack{\prime\prime}$3 radius,
respectively. The size of the OIR counterpart circles are 3 times the
positional uncertainty values reported in Table 4. The entire set of postage-
stamp images is available in the electronic version.

For the 4335 X-ray sources with primary counterparts from SERVS or VIDEO
(regardless of matching reliabilities), 269 of them have no optical
counterparts in CFHTLS and HSC-SSP. Visual inspection suggests that most of
these sources are genuinely optically-faint. For 33 of the 269 sources, the
optical counterpart is a bright star (or in the vicinity of one), and the
photometry is unavailable from the CFHTLS or HSC-SSP catalogs due to
saturation. There are also 1217 X-ray sources without a VIDEO counterpart, of
which 787 are not in the footprint of VIDEO. For the remaining 430 X-ray
sources without VIDEO photometry, visual inspection suggests that most of them
are indeed NIR-faint, except for these 42 sources that either coincide with a
bright star or are located on artifacts such as satellite tracks. To obtain
useful OIR information for sources without reliable optical or NIR photometry,
we search for counterparts in several additional OIR surveys with footprint in
our X-ray catalog region, including the Sloan Digital Sky Survey (York et al.,
2000) Data Release 12 (SDSS, Alam et al., 2015), the Two Micron All Sky Survey
(2MASS, Skrutskie et al., 2006), and the UK Infrared Telescope Deep Sky Survey
(the Deep Extragalactic Survey layer, UKIDSS-DXS; Warren et al. 2007). For our
X-ray sources catalog, we only search for counterparts in these catalogs that
are within 1′′ of the OIR positions of the primary counterparts. With the
supplementary catalogs, we recover the optical photometry for the 33 sources
that do not have pipeline photometry from CFHTLS and HSC-SSP. We also identify
an additional 333 sources with NIR photometry from 2MASS or UKIDSS-DXS. The
basic properties of counterparts in these supplementary catalogs are also
reported in the final source catalog (Table F).

There are also $1034$ sources with multiple counterparts having $LR>LR_{\rm
th}$ and $LR>0.5LR_{\rm primary}$ in various OIR catalogs. For these sources,
we select a “secondary” counterpart based on the following priority order: (i)
235 best matches from VIDEO; (ii) 48 second-best matches from SERVS; (iii) 79
second-best matches from VIDEO; (iv) 290 best matches from CFHTLS; (v) 223
best matches from HSC; (vi) 79 second-best matches from CFHTLS; and (vii) 80
second-best matches from HSC. Finally, there are 25 X-ray sources with three
reliable counterparts; these tertiary counterparts are from VIDEO (4), CFHTLS
(5) and HSC (16).

For the 1034 X-ray sources with secondary and/or tertiary counterparts, 869 of
them have a SERVS source as the primary counterpart. Due to the larger PSF
size of Spitzer IRAC ($\approx 2^{\prime\prime}$ at [3.6$\mu m$]) compared to
the other OIR catalogs used in this work, it is possible that some of these
secondary/tertiary counterparts from VIDEO, CFHTLS, or HSC-SSP are blended
with the primary counterparts in the Spitzer image. Among these 1034 X-ray
sources, a total of 318 of them are matched to a primary SERVS counterpart
which appears to be two sources separated by $<2^{\prime\prime}$ in higher
angular resolution bands. These counterparts are flagged in our final catalog.
Excluding these 318 X-ray sources with potentially blended SERVS counterparts,
the vast majority ($\approx 85\%$) of X-ray sources with secondary and/or
tertiary counterparts have a primary counterpart with $MR>0.9$, suggesting
that these additional counterparts are unlikely to be true counterparts of the
X-ray sources. For completeness, these secondary and tertiary counterparts are
also reported in our final catalog in Table F.

###  4.2 Counterpart identification reliability

We assess the reliability of the $LR$ matching results using the Monte Carlo
simulation approach described in Broos et al. (2007) and Xue et al. (2011).
Compared to the simple estimation based on matching OIR catalogs to a random
X-ray catalog, the Broos et al. (2007) method usually provides a more
realistic assessment of the matching reliability. As described in Broos et al.
(2007) and Broos et al. (2011), we consider our X-ray sources to consist of
two different intrinsic populations, the “associated population” and the
“isolated population”. The associated population is comprised of X-ray sources
that do have a real counterpart in the corresponding OIR catalog, and the
X-ray sources that should not have any OIR counterparts belong to the isolated
population.

For the associated population, counterpart-matching procedures can produce
three different outcomes: (1) an X-ray source is matched to its correct
counterpart (correct match, or CM), (2) an X-ray source is matched to an
incorrect counterpart (incorrect match, or IM), and (3) no counterparts were
recovered (false negative, or FN). The spurious fraction of the associated
population is defined as $N_{\rm IM}/(N_{\rm IM}+N_{\rm CM})$. For the
isolated population, there are two possible matching results: (1) no
counterparts are found (true negative, or TN), and (2) an OIR source is
identified as a counterpart (false positive, or FP). The spurious fraction of
the isolated population is defined as the number of FPs divided by the size of
the X-ray catalog. By definition, the spurious matches for these two
populations are intrinsically different. The chance for the X-ray sources in
the isolated population to have a counterpart is mostly determined by the
source surface density of the OIR catalog being matched. On the other hand,
since X-ray sources in the associated population must have a real OIR
counterpart within a reasonable search radius, the spurious fraction is
essentially determined by how well the $LR$ matching method can discern a real
counterpart from background sources.

In order to estimate the fractions of X-ray sources in both populations for
our catalog, we simulate each population separately. The details of the
simulation procedure can be found in the appendix of Broos et al. (2007) and
§5 of Broos et al. (2011). A brief summary of the simulations is given below:
(1) For the “associated population”, we remove all OIR sources considered to
be a match in §4.1, then move the position of each OIR source by 1′ in a
random direction. We then generate fake OIR “counterparts” for each X-ray
source in our catalog based on the X-ray and OIR positional uncertainties, and
the expected magnitude distributions derived in §4.1. (2) For the “isolated
population”, we create mock X-ray sources that are at least 20″ away from any
real X-ray sources.

A total of 100 simulations are carried out for each population, and we run the
$LR$ matching procedures on each simulation as described in §4.1. The
simulations of the isolated populations usually produce a much higher spurious
fraction (i.e., the number of false-positives divided by the size of the X-ray
catalog). For the SERVS, VIDEO, CFHTLS, and HSC-SSP catalogs, the median
spurious fractions of the isolated populations are 19%, 24%, 30%, and 40%,
respectively. For the associated populations, the spurious fractions (defined
as $N_{\rm IM}/(N_{\rm IM}+N_{\rm CM}$)) for SERVS, VIDEO, CFHTLS, and HSC-SSP
are 3%, 5%, 7%, and 9%, respectively.

For the $LR$ matching results with the real data, X-ray sources that were not
reliably matched to any counterparts (with a total number of $N_{\rm
negative}$) should contain a mixture of the FNs of the associated population
and the TNs of the isolated population. Therefore, we can use the median FN
and TN from simulations to estimate the fraction of X-ray sources in the
associated population ($f_{\rm AP}$):

$N_{\rm negative}=N_{\rm FN}\times f_{\rm AP}+N_{\rm TN}\times(1-f_{\rm AP}).$
(9)

With $f_{\rm AP}$, we can estimate the expected number of X-ray sources that
have a spurious match as the weighted sum of the numbers of IM and FP. The
false-matching rate, $f_{\rm False}$, should therefore be:

$f_{\rm False}=(N_{\rm IM}\times f_{\rm AP}+N_{\rm FP}\times(1-f_{\rm
AP}))/(N_{\rm positive}).$ (10)

Here we consider $N_{\rm positive}$ as the combination of both the “reliable”
and “acceptable” matches reported in Table 4.

We carry out simulations for each OIR catalog. The values of $f_{\rm False}$
and $f_{\rm AP}$ for each OIR catalog are also reported in Table 4. Due to the
high $f_{\rm AP}$ values, the false-matching rates of our matching results are
mostly determined by the spurious fractions of the associated populations,
which are much lower than those of the isolated populations. Adopting the
Chandra-matched counterpart magnitude density, $q(m)_{\it Chandra}$, does
reduce the false-matching rates compared to those derived using $q(m)_{\it
XMM-Newton}$. For the SERVS and VIDEO catalogs, the improvements are marginal
($<0.5\%$), while the improvements for CFHTLS and HSC-SSP are more significant
($\approx 2\%$ and $6\%$, respectively).

We further scrutinize the $LR$ matching reliabilities by making use of the 223
CSC sources and their multiwavelength matching results described in §4.1. We
assess the reliability of the matching results of these Chandra sources using
the Monte Carlo method above, and measure false-match fractions of 0.9%, 1.4%,
2.8%, and 3.3%, for SERVS, VIDEO, CFHTLS, and HSC-SSP, respectively. For each
catalog, we also directly compare the reliable matches obtained with XMM-
Newton and Chandra positions; 97%, 94%, 91%, and 87% of the reliable Chandra
matching results and the reliable XMM-Newton results are the same for the
SERVS, VIDEO, CFHTLS, and HSC catalogs, respectively. The high “identical
fractions” between the matching results obtained using Chandra positions and
XMM-Newton positions are slightly lower than the false-matching rates
calculated based on the Monte Carlo simulation because we only compare X-ray
sources with reliable counterparts at the Chandra and XMM-Newton positions in
each catalog. Similar to what was done for the full XMM-Newton catalog, we
also select “primary” counterparts for the Chandra sources using the same
priority orders. 85%, 10%, 1%, and 4% of the Chandra sources have their
“primary” counterparts from SERVS, VIDEO, CFHTLS, and HSC-SSP, respectively.
When comparing the primary counterparts of these Chandra sources and the
primary counterparts of the corresponding XMM-Newton sources, $\approx 97\%$
are identical, demonstrating that the matching results of the XMM-Newton
catalog are highly reliable.

###  4.3 Supplementary multiwavelength matching results with the NWAY Bayesian
catalog matching method

Figure 17: Illustrations of the comparison between the matching results using
XMM-Newton positions or Chandra positions for four X-ray sources in our
sample. The panel for each source shows images from SERVS [3.6$\mu$m](top-
left), HSC i-band (top-right), XMM-Newton 0.5–10 keV (bottom-left), and
Chandra 0.5–7 keV (bottom-right). X-ray positions are marked as blue circles
with a 99.73% error radius, with the XMM-Newton positions indicated using
solid lines and the Chandra positions identified using dashed lines. SERVS
counterparts identified with the $LR$ method are marked as orange circles with
a $2^{\prime\prime}$ radius, solid lines are the counterparts of the XMM-
Newton positions, and dashed lines are the counterparts of the Chandra
positions. SERVS counterparts of the XMM-Newton positions identified using
NWAY are shown as the red circles. For the vast majority of XMM-Newton sources
with Chandra counterparts from CSC, our counterpart-matching results are
identical to the results obtained using Chandra coordinates and positional
uncertainties.

We supplement the $LR$ matching results with the Bayesian catalog matching
tool NWAY (Salvato et al.,
2017).262626https://github.com/JohannesBuchner/nway. The fundamental
difference between the Bayesian approach and the likelihood-ratio approach is
that the former makes use of the distance and magnitude priors from multiple
catalogs simultaneously to select the most-probable counterpart in all
catalogs considered. NWAY also allows cases in which counterparts can be
absent, and the matching results were computed considering all possible
combinations. The details of the NWAY matching methodology are described in
Appendix B of Salvato et al. (2017).

NWAY computes three quantities for deciding the most-probable match,
$p\\_single$, $p\\_any$ and $p\\_i$, where each possible counterpart has a
different $p\\_single$ value based on its distance from the XMM-Newton
position. This value could be weighted by the priors supplied (e.g., $q(m)$
and $n(m)$ in Eq. 6 are similar to a magnitude prior). In our case,
$p\\_single$ is the posterior probability for a counterpart to be correctly
associated with the X-ray source based on the angular separation from the
X-ray position weighted by the magnitude-distribution prior, and the surface
densities of the X-ray and OIR catalogs. For each X-ray source, $p\\_single$
of all possible counterparts is considered to compute a single $p\\_any$
value, which represents the posterior probability of the X-ray source having
any correct counterparts (i.e., $p\\_any=0$ if there are no OIR counterparts
within the search radius of the X-ray source). The last quantity, $p\\_i$, is
the relative probability of a possible counterpart being the correct match.
For an X-ray source with multiple possible counterparts, the counterpart with
the highest $p\\_i$ ($p\\_i_{\rm Best}$) is considered to be the most-probable
match and is assigned the match_flag = 1 flag by NWAY. Counterparts with
$p\\_i$ higher than 50% of $p\\_i_{\rm Best}$ are also flagged by NWAY as
match_flag = 2.

Similar to our $LR$ approach, we make use of the Chandra sources in the XMM-
LSS field to compute the priors of the expected counterparts. We use the
“auto” functionality of NWAY with a 1.5′′ search radius for defining the
“real” counterparts. In addition to the magnitude priors, we include an
additional prior based on the Spitzer IRAC color from SERVS,
[$3.6\mu$m]/[$4.5\mu$m]. Since the majority of our X-ray sources are expected
to be AGNs, the distinct [$3.6\mu$m]/[$4.5\mu$m] mid-IR color of luminous AGNs
(see Fig. 24) provides additional discerning power. For a small number of
sources, this additional prior is useful for discerning two adjacent SERVS
sources with comparable magnitudes (see the top-right panel of Fig. 17 for
illustration).

After computing the magnitude and IRAC color priors using the Chandra sources,
we run NWAY on the full X-ray catalog with a search radius of 10′′. Based on
the results from $LR$ matching (§4.1), we do not assume a completeness prior
because only 0.01% of the X-ray sources are completely isolated. All four OIR
catalogs are considered simultaneously. We report the multiwavelength matches
with match_flag$=$1,2 in Table G supplementary to the $LR$ matching results.

Since NWAY matches all four OIR catalogs simultaneously, we cannot determine
the spurious-matching rates for the “associated” and “isolated” populations as
we did for estimating the spurious-matching rates for $LR$ results using Monte
Carlo simulations (see §4.2). Salvato et al. (2017) suggest that the NWAY
matching reliability can be determined by a $p\\_any$ threshold, which is
chosen based on re-running NWAY on randomly shifted “fake” X-ray catalogs.
However, this approach is equivalent to estimating the spurious matching rates
for the “isolated” population using the Broos et al. (2007) method, which is
usually much higher than the results obtained with the two-population approach
(see Broos et al. 2007, Xue et al. 2011, and §4.2 for details). Therefore, we
do not adopt any $p\\_any$ thresholds for the NWAY matching results. The NWAY
matching results can still be assessed by investigating the CSC-matched
subsample of 223 X-ray sources; the difference between the matching results
obtained using Chandra and XMM-Newton positions with NWAY are similar to the
$LR$ results described in §4.2.

We also use the 223 Chandra-detected subsample as a baseline for comparing
matching results obtained using the NWAY or $LR$ methods. We focus only on
comparing the SERVS counterparts, as the vast majority of $LR$ matching
results are decided based on the primary counterparts from SERVS. We confirm
that all Chandra sources have the same SERVS matching results using $LR$ and
NWAY. Therefore, we can use the Chandra results obtained with $LR$ to assess
the matching reliability of both $LR$ and NWAY matching results with XMM-
Newton positions. Examples of such comparisons are shown in Fig. 17. $96\%$ of
the sources have the same matching results from LR, NWAY, and Chandra. A small
fraction (two sources) of $LR$ matching results do not agree with those of
Chandra but could be recovered by NWAY. On the other hand, two of the NWAY
matching results do not agree with the Chandra results but could be identified
by LR. Five of the Chandra sources have different SERVS counterparts than both
the $LR$ and NWAY results. Chandra and OIR images of these sources suggest
that they are either two X-ray sources blended due to the XMM-Newton PSF, or
there are multiple OIR counterparts with very similar magnitudes and distances
to the X-ray position, and thus it is not surprising neither $LR$ nor NWAY
could successfully recover the correct counterparts. As demonstrated in Fig.
17 (bottom-left), these five sources have multiple counterparts with
comparable magnitudes and similar spatial separations from the XMM-Newton
position. This result suggests $LR$ and NWAY perform similarly for finding
SERVS counterparts. For the two X-ray sources with different LR and NWAY
counterparts, their X-ray fluxes are relatively low (with a median full-band
flux of $7.5\times 10^{-15}$ erg cm-2 s-1, which is $\approx 44\%$ of the
median flux of the full X-ray catalog). This is expected as fainter X-ray
sources have larger positional uncertainties, which leads to higher numbers of
counterpart candidates.

When further scrutinizing the $96\%$ of sources with identical SERVS
counterparts from LR, NWAY, and Chandra, we find that NWAY occasionally (for
$\sim 10\%$ of the X-ray sources) considers the best-fit combination to be the
one with counterparts in some of the other OIR catalogs being “absent”. For
instance, one of the X-ray sources has a reliable SERVS counterpart identified
by both NWAY and $LR$. For the SERVS counterpart, there is only one VIDEO
source within the 0.5′′ positional error circle of SERVS. For the $LR$
approach described in §4.1, the VIDEO source is assigned to the correct SERVS
counterpart. However, NWAY does not consider this VIDEO source to be among the
most-probable combination of counterparts from all four OIR catalogs that were
being matched simultaneously. This result is likely due to how NWAY computes
$p\\_i$. When multiple OIR catalogs are taken into account simultaneously,
$p\\_i$ represents the relative probability of counterparts from all OIR
catalogs being the correct match. In this example, the VIDEO counterpart has
an unlikely magnitude according to the VIDEO magnitude prior; therefore,
including the VIDEO source as a correct match would result in a lower $p\\_i$
compared to the case where the VIDEO source is excluded from the matched
counterparts. Similar mismatches are found when comparing the NWAY and $LR$
matching results for the full XMM-Newton catalog. Note that the p_any values
for these sources are generally lower (with a median of 0.16) compared to the
sources without such problems (their median p_any$=0.98$), but sources with
p_any$>0.98$ can still have this behavior. NWAY does not have this behavior
when no magnitude or color priors are used; however, without the inclusion of
magnitude and color priors, NWAY can only rely on the distance-based priors,
thereby losing critical discerning powers for matching XMM-Newton sources to
the dense OIR catalogs. Further corroborating the Bayesian method’s
effectiveness of counterpart-matching with multiple OIR catalogs is beyond the
scope of this work. Therefore, we list the NWAY matching results “as-is” in
Table G, and we consider only the $LR$ matching results listed in Table F when
exploring the multiwavelength properties of the X-ray sources reported in this
work. The matching results obtained using NWAY are shown in Table G, and the
descriptions of this table’s columns are listed in Appendix B. Only the
counterparts with match_flag$\geq 1$ are included.

##  5 Redshifts

###  5.1 Spectroscopic redshifts

Figure 18: Distribution of the redshifts in bins of $\Delta z=0.02$ for the 1782 X-ray sources with spectroscopic-redshift measurements from the literature. The photometric-redshift distribution for the 2105 sources with high-quality photometric redshifts is also plotted as the red dashed histogram in bins of $\Delta z=0.2$. The redshift spikes are likely associated with large-scale structure filaments (e.g., Luo et al., 2017; Xue, 2017). A comparison between the normalized redshift distribution of the X-ray sources and that of the $i$-band selected galaxies from the VIPERS survey is also shown in the insert with $\Delta z=0.01$ bins, which suggests that some of the redshift spikes (e.g., $z\approx 0.6$) of X-ray sources overlap with those of the general galaxy population.  Figure 19:  The blue histogram shows the cumulative distribution of the HSC i-band magnitudes for 4012 i-band-detected X-ray sources in the $4.5$ deg2 subfield covered by the N18 forced-photometry catalog (see §5.2). The cumulative distribution of the sources with spectroscopic redshifts is indicated by the green histogram, and the cumulative distribution of the sources with high-quality photometric or spectroscopic redshifts is indicated by the orange histogram. The top panel shows the fraction of sources with spectroscopic redshifts (i.e., the green histogram divided by the blue histogram) as a function of i-band magnitude. The fraction of sources with good photometric or spectroscopic redshifts as a function of i-band magnitude is shown as the orange curve.  Table 5:  Redshift catalogs used in this work. Column 1: Redshift survey name. Column 2: Survey instrument. Column 3: Survey sensitivity. Column 4: Targeting fields. Column 5: Survey area. Column 6: Total number of redshifts matched the main X-ray catalog. Column 7: Total number of redshifts assigned to the X-ray sources in the main catalog. Column 8: Reference  Catalog | Instrument | Survey sensitivity | Targeting fields | Area | $N_{\rm matched}$ | $N_{\rm assigned}$ | Reference
---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
SDSS | BOSS | $r\lesssim 22.5$ | XMM-XXL-North |  25 deg2 | 1075 | 1075 |  Dawson et al. (2013);
|  |  |  |  |  |  | Menzel et al. (2016)
PRIMUS | IMACS | $i\lesssim 23.5$ | XMM-LSS |  2.9 deg2 | 749 | 347 | Coil et al. (2011)
| (Low-Dispersion Prism) |  |  |  |  |  |
VIPERS | VIMOS | $i\lesssim 22.5$ | XMM-LSS |  7.8 deg2 | 332 | 161 | Garilli et al. (2014)
UDS Compilation | Multiple instruments | N/A | UDS |  0.8 deg 2 | 302 | 72 | N/A (see Footnote 25)
CSI | IMACS |  [3.6$\mu$m]${}_{\rm AB}\lesssim 21$ | XMM-LSS |  6.9 deg2 | 516 | 68 |  Kelson et al. (2014);
| (Uniform-Dispersion Prism) |  |  |  |  |  | Patel et al. (2015)
VVDS | VIMOS | $17.5\lesssim i\lesssim 24.5$ | XMDS+SXDS |  3 deg2 | 81 | 38 | Le Fevre et al. (2013)
UDSz | VIMOS/FORS2 | $K<23$ | UDS |  0.5 deg2 | 22 | 15 |  Bradshaw et al. (2013);
|  |  |  |  |  |  | McLure et al. (2013)
3D-HST | WFCS G141 Grism | $JH_{\rm IR}\lesssim 24$ | UDS |  191.2 arcmin2 | 15 | 6 |  Skelton et al. (2014);
|  |  |  |  |  |  | Momcheva et al. (2016)

The XMM-LSS region is covered by a number of spectroscopic redshift (spec-z)
surveys that target galaxies with various optical magnitude constraints: the
PRIsm MUlti-Object Survey (PRIMUS; Coil et al., 2011), the VIMOS Public
Extragalactic Redshift Survey (VIPERS; Garilli et al., 2014), and the VIMOS
VLT Deep Survey (VVDS; Le Fevre et al., 2013). As part of the SDSS Baryon
Oscillation Spectroscopic Survey (SDSS-BOSS) program, 3042 X-ray sources found
in the XMM-XXL-North field (25 deg2) with $r<22.5$ were all observed by the
SDSS-BOSS (Dawson et al., 2013; Menzel et al., 2016). Also, there are three
other redshift surveys in the XMM-LSS region that target near-IR selected
galaxies, including the spectroscopic observations of the UKIDSS Ultra-Deep
Survey (UDSz; Bradshaw et al., 2013; McLure et al., 2013), the 3D-HST Survey
(Skelton et al., 2014; Momcheva et al., 2016) in the UDS region, and the
Carnegie-Spitzer-IMACS Redshift Survey (CSI; Kelson et al. 2014). We list the
properties of each redshift catalog in Table 5.

We adopt the same nearest-neighbor matching criterion with a 1′′ matching
radius to associate these redshifts to each OIR catalog. The redshift for each
X-ray source is determined by the coordinates of its primary OIR counterpart.
In cases where redshifts from different catalogs do not agree with each other,
we choose redshifts using the following ordering (ranked by the spectral
resolution at r-band and reliability): SDSS, VVDS, VIPERS, UDSz, PRIMUS
(reliable), CSI (reliable), 3D-HST, PRIMUS (acceptable), and CSI (acceptable).
In addition to these redshift surveys, we include the compilation of $\approx
4000$ publicly available but unpublished redshifts in the UDS field.272727
These redshifts were obtained with Subaru FOCAS, AAT 2dF, VLT VIMOS, and
AAOmega, and the full redshift catalog is available at
http://www.nottingham.ac.uk/~ppzoa/UDS_redshifts_18Oct2010.fits, see
http://www.nottingham.ac.uk/astronomy/UDS/data/data.html for an overview of
this compilation. An additional 72 X-ray sources have spec-zs culled from this
catalog. We also search for publicly available spec-zs for all of our
counterparts not included in the aforementioned redshift catalogs in the NASA
Extragalactic Database (NED), but no additional secure redshifts were found.

Of the 5242 sources in our main X-ray source catalog, 1782 have spec-zs
ranging from $0<z<4.57$. Fig. 18 presents the redshift histogram in bins of
$\Delta z=0.02$. There are several redshift “spikes” indicative of large-scale
structures containing X-ray AGNs (e.g., Fig. 9 of Luo et al. 2017 and Fig. 20
of Xue 2017). Notably, the X-ray source redshift spike at $0.6<z<0.7$ appears
to coincide with one of the major large-scale structures seen in the VIPERS
redshift survey (see Fig. 14 of Garilli et al. 2014 and the insert panel of
Fig. 18). The cumulative histogram of the i-band magnitudes of the sources
with spec-zs is shown in Fig. 19 as the green histogram.

###  5.2 Photometric redshifts

Figure 20:  Spectroscopic and photometric redshifts for the 449 non-broad-line
AGN sources with high-quality photo-zs and spec-zs. The left panel shows the
histogram of the fractional difference between the photo-zs and the spec-zs.
The right panel shows the direct comparison between the photo-zs and the spec-
zs. The black dotted lines in both panels mark the $z_{\rm spec}=z_{\rm phot}$
relation. In the right panel, the red dashed lines mark the
$\mathopen{|}\Delta z\mathclose{|}/(1+z_{\rm spec})=0.15$ thresholds for
outliers.

High-quality photometric redshifts (photo-zs) for AGNs are not yet available
for our full survey region, but they are available in a number of smaller
subfields. In particular, in a $\approx 1$ deg2 area within the XMM-LSS
region, Nyland et al. (2017) have presented a “forced-photometry” catalog
using the Tractor image-modeling code (Lang et al., 2016). The forced-
photometry technique employs source-position and surface-brightness profile
priors from the high-resolution fiducial band of the VIDEO survey to model and
fit the fluxes of lower-resolution bands. Nyland et al. (2017) demonstrated
that their multi-band forced photometry of mixed resolution optical and IR
surveys using the Tractor led to a statistically significant improvement in
photometric-redshift accuracy compared to position-matched multi-band catalogs
(see §5.2 of Nyland et al. 2017 for details). For this work, we make use of a
similar forced-photometry catalog for the full 4.5 deg2 area with VIDEO and
SERVS coverage (Nyland et al. 2018, in preparation; N18 hereafter). The N18
catalog is similar to the Nyland et al. (2017) catalog, except the image
cutout width for each source has increased by a factor of two (from 10′′ to
20′′) and the sky noise and sky level are now calculated in each image cutout
using iterative sigma clipping. Also, N18 used IRAC data from the SERVS
DeepDrill survey (P.I. Mark Lacy), which expands upon the coverage of the
SERVS project by providing deep IRAC imaging to microJy-depth of the four
predefined Deep Drilling Fields for the LSST. In the XMM-LSS field, the
DeepDrill data more than double the footprint of the SERVS post-cryogenic
data, thus leading to higher-quality data along the edges of the SERVS
coverage where there is overlap with the VIDEO data. Thus, our IRAC 3.6 and
4.5 $\mu$m photometry is based on the DeepDrill data. We make use of the
13-band photometry from u′ to IRAC 4.5$\mu$m to derive photo-zs for the X-ray
sources in this region using the methods described in Yang et al. (2014). The
photometric bands include CFHTLS $u$-band; HSC-SSP g, r, i, z, and y bands
(wide layer); VIDEO Z, Y, J, H, and Ks bands (DR5); and Spitzer 3.6 $\mu$m and
4.5 $\mu m$ bands from the SERVS DeepDrill survey.

We match the N18 catalog to the coordinates of the primary counterparts of the
X-ray sources that are considered to be reliable matches using a 1′′ matching
radius. We exclude the 930 X-ray sources that are classified as broad-line
AGNs (see §6 for details) according to their optical spectra due to their much
higher photometric-redshift uncertainties. A total of 3418 X-ray sources
satisfy these criteria. Of these sources, $\approx 38\%$ of them are detected
(i.e., with Tractor measured signal-to-noise-ratio $>5$) in all 13 bands. The
25th, 50th, and 75th percentiles of the number of bands with detection for the
3418 X-ray sources are 10, 11, and 13. Since the flux uncertainties in N18 do
not account for uncertainties in the PSF homogenization processes, we adopt an
additional 3% systematic for the flux errors, which is typical of PSF modeling
uncertainties (e.g., §5.3 of Yang et al. 2014).

Following the approach of Yang et al. (2014), we measure the photo-zs using
the SED-fitting code eazy (Brammer et al., 2008) using the default galaxy
templates and settings, and an additional obscured AGN template from Polletta
et al. (2007). As described in §5.6 of Yang et al. (2014), we perform
iterative procedures to adjust the photometric zero points; the zero-point
corrections are $\lesssim 0.1$ mag. For each source, eazy calculates a
parameter $Q_{z}$ (see Eq. 8 of Brammer et al. 2008) to indicate photometric-
redshift quality. Of the 3418 non-broad-line X-ray sources with forced
photometry, we consider the 2105 ($\approx 62\%$) photo-zs with $Q_{z}<1$ as
reliable (see §6.3 of Yang et al. 2014). The fraction of sources with high-
quality photo-zs becomes higher for brighter sources. For instance, sources
with VIDEO $Ks$-band magnitude in the brightest 25th, 50th, and 75th
percentiles (corresponding to $Ks<19.77$, 20.83, and 21.78) have $77\%,76\%$,
and $71\%$ high-quality photoz-s, because fainter sources have larger
photometric uncertainties and fewer photometric points. With the deep NIR
coverage from VIDEO and SERVS, we can detect the Balmer break even for high
redshift sources, hence the range of our $Q_{z}<1$ photo-zs extends to
$z\approx 4$. There are 536 sources with $Q_{z}<1$ and reliable spec-zs. Of
these sources, 449 of them have spectroscopic classifications from at least
one of the public redshifts catalogs and are not classified as a broad-line
AGN. Since we excluded broad-line sources, the spectroscopic redshift range of
these sources is 0.02–1.5, with a median value of 0.79. We use these 449
sources to assess the quality of the 2105 photo-z measurements. The normalized
median absolute deviation (NMAD) is $\sigma_{\rm NMAD}=0.040$, with an outlier
fraction (defined as $\mathopen{|}\Delta z\mathclose{|}/(1+z_{\rm
spec})>0.15$) of $f_{\rm outlier}=8.7\%$, which is comparable to the
photometric-redshift reliability reported in Yang et al. (2014) for the CDF-N.
A small fraction of sources are found to be outliers. This is likely caused by
the photo-z code mistakenly identifying the location and strength of the
prominent spectroscopic feature, the Balmer break (the lack of radiation at
wavelength range $<3646$ Å ), due to photometric redshift uncertainties in one
or more bands. We note that the majority of the outliers have $z_{\rm
spec}<z_{\rm phot}$. This is expected for the $z_{\rm spec}\lesssim 1$ sources
(e.g., see Fig. 14 of Yang et al. 2014), because only less than three
photometric bands cover the rest-frame wavelength range of the Balmer break
and it is difficult to identify a spectral break with only three photometric
bands. Therefore, it is less likely for the aforementioned misidentifications
to cause a $z_{\rm phot}$ lower than these low-spec-z sources. For this work,
we do not include the broad-line AGN (BLAGN) templates as Yang et al. (2014)
did. This is primarily driven by the worse photometric redshift qualities when
including the BLAGN templates. In addition, Yang et al. (2018) estimated that
the fraction of broad-line AGNs missed by spectroscopic campaigns in the
COSMOS field is likely less than $\approx 18\%$. Considering the comparable
surface density of the spectroscopically confirmed BLAGNs in this work and
that in the COSMOS field, only a small fraction of sources would require an
additional BLAGN template. In fact, the vast majority of our sources
(excluding spectroscopically confirmed BLAGNs) can be well-characterized with
galaxy templates alone, and the high fraction (see below) of our sources with
high-quality photo-zs also justifies our choice of fitting templates.

Fig. 20 compares the photometric and spectroscopic redshifts for the 449 non-
broad-line sources with reliable photo-zs. The 4.5 deg2 area covered by N18
contains 1543 reliable photo-zs for sources that do not have spectroscopic
redshift measurements, increasing the fraction of sources with redshifts from
$\approx 32\%$ to $\approx 70\%$. We expect to expand the photometric-redshift
measurements to all of our X-ray sources in the full XMM-SERVS:XMM-LSS field
when the photometry catalog with data from both the SERVS DeepDrill survey
(Spitzer Program ID 11086; Lacy et al., in preparation) and the VEILS survey
(see Table 1) becomes available. We have also run our photometric-redshift
codes on all sources in the preliminary N18 catalog, and we report the photo-
zs for the 390,900 sources in Appendix C. The full details of the Tractor
catalog over the 4.5 deg2 field will be presented in Nyland et al. (2018, in
preparation).

Figure 21: A comparison between this work (solid red line), XMM-COSMOS (green
dashed line), COSMOS-Legacy (brown dash-dotted line), and Stripe 82–X (blue
dotted line). Distributions shown in panels from left to right are: 0.5–2 keV
flux, redshift, and $\log L_{\rm 2-10~{}keV}$, respectively. The left panel
shows the distribution of soft-band fluxes for the soft-band detected sources
in each catalog; no redshift information is required. The numbers of the soft-
band sources are listed in the left panel. For the middle and right panels,
the histograms are for the subset of sources with redshift measurements
(regardless of the detection bands), with source numbers marked in the right
panel.  Figure 22:  Properties of the 1782 X-ray sources with spectroscopic-
redshift measurements, including the (1) $L_{\rm 2-10~{}keV}$ vs. $z$
distribution (top-left), (2) $L_{\rm 2-10~{}keV}$ vs. hardness ratio (top-
right), (3) 0.5–10 keV flux vs. redshift (bottom-left), (4) 0.5–10 keV flux
vs. hardness ratio (bottom-right). Broad-line AGNs are marked as the red open
circles. In the right panels, the expected hardness ratios for power-law
spectra (with Galactic column density) with different photon indices are
plotted as the vertical dashed lines. Sources detected only in the soft or
hard bands have their HR set at $-1$ and 1, respectively.

##  6 Source properties and classification

Figure 23:  Left – Distributions of the optical flux in the r-band vs. full-
band (0.5–10 keV) X-ray flux. Lower limits for sources not detected in the
HSC-SSP wide survey r-band are displayed as the brown upward arrows. Right –
The near-IR flux in the Ks-band versus full-band X-ray flux. Lower limits for
sources not detected in VIDEO are also show as the upward arrows. Since only
$\approx 85\%$ of the X-ray catalog region is covered with VIDEO, some of the
X-ray sources have lower limits from 2MASS ($Ks=14.3$), UKIDSS DXS survey
($Ks=21$), and VIDEO ($Ks=23.8$). In both plots, the shaded regions mark the
“AGN” regime as defined by the $\log_{10}f_{x}/f_{o}>-1$ (left) or the
$\log_{10}f_{x}/f_{\rm Ks}>-1.2$ (right) thresholds as described in §4.5 of
Luo et al. (2017). For sources with spectroscopic redshift measurements, we
also mark those with $L_{\rm X}>3\times 10^{42}$ erg s-1 as the green
triangles. The 930 sources with optical spectra consistent with broad-line
AGNs are also marked as open red circles.

In this section we briefly discuss some of the properties of the 4858 sources
with reliable counterparts. For the 1782 X-ray sources with secure spec-zs, we
calculate their rest-frame 2–10 keV “apparent” luminosity assuming a
$\Gamma=1.7$ power-law spectrum corrected for Galactic absorption. Fig. 21
compares the flux, redshift, and luminosity distributions of our sample to
those from archival X-ray surveys, including XMM-COSMOS, COSMOS-Legacy, and
Stripe 82X. Fig. 22 displays the $L_{\rm X}-z$ distribution of our sample,
along with the $L_{\rm X}$ vs. HR, HR vs. full-band flux, and full-band flux
vs. redshift distributions. The comparisons in the middle and right panels of
Fig. 21 are limited to sources with available spec-zs in the Stripe-82 and
XMM-LSS regions. The left panel of Fig. 21 demonstrates that our catalog
occupies a valuable region of parameter space among X-ray surveys by more than
doubling the source counts of the XMM-COSMOS survey, which will enable a wide
range of science that was previously limited by either survey sensitivity or
cosmic variance.

For this work, we also include the basic AGN identification results in our
catalog. Detailed source classifications using multiwavelength SED and X-ray
spectroscopic fitting results will be saved for future works. For sources with
spectroscopic observations, we directly make use of the spectroscopic
classifications when available. Since each spectroscopic survey has its own
unique design and methodology, we only make use of the “broad-line”
classifications provided in the SDSS, VIPERS, VVDS, and PRIMUS catalogs to
identify broad-line AGNs. The information on spectroscopic classifications is
not yet publicly available for the other spectroscopic surveys. For each X-ray
source with optical spectroscopic coverage, we have included the spectroscopic
flags from all available redshift catalogs (see Column 184 of the main X-ray
catalog described in Appendix A). A total of 930 sources are classified as
AGNs based on the broad-line spectroscopic flags specified in the SDSS,
VIPERS, VVDS, or PRIMUS catalogs. Since 90% of the spec-zs for our X-ray
sources are culled from one of these four catalogs, we expect the vast
majority of the remaining X-ray sources with spectroscopic coverage to have