# The Swift Deep Galactic Plane Survey (DGPS) Phase-I Catalog

B. O’Connor Department of Physics, The George Washington University,
Washington, DC 20052, USA  Department of Astronomy, University of Maryland,
College Park, MD 20742-4111, USA  Astrophysics Science Division, NASA Goddard
Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  C.
Kouveliotou Department of Physics, The George Washington University,
Washington, DC 20052, USA  P. A. Evans School of Physics and Astronomy,
University of Leicester, University Road, Leicester, LE1 7RH, UK  N. Gorgone
Department of Physics, The George Washington University, Washington, DC 20052,
USA  A. J. van Kooten Department of Physics, The George Washington University,
Washington, DC 20052, USA  S. Gagnon Department of Physics, The George
Washington University, Washington, DC 20052, USA  H. Yang Department of
Physics, The George Washington University, Washington, DC 20052, USA  M. G.
Baring Department of Physics and Astronomy - MS 108, Rice University, 6100
Main Street, Houston, Texas 77251-1892, USA  E. Bellm DIRAC Institute,
Department of Astronomy, University of Washington, 3910 15th Avenue NE,
Seattle, WA 98195, USA  P. Beniamini Department of Natural Sciences, The Open
University of Israel, P.O Box 808, Ra’anana 4353701, Israel  Astrophysics
Research Center of the Open university (ARCO), The Open University of Israel,
P.O Box 808, Ra’anana 4353701, Israel  Department of Physics, The George
Washington University, Washington, DC 20052, USA  J. Brink Department of
Astronomy, University of Cape Town, Private Bag X3, Rondebosch 7701, South
Africa  South African Astronomical Observatory, P.O. Box 9, Observatory 7935,
Cape Town, South Africa  D. A. H. Buckley South African Astronomical
Observatory, P.O. Box 9, Observatory 7935, Cape Town, South Africa  Southern
African Large Telescope, P.O. Box 9, Observatory 7935, Cape Town, South Africa
Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch
7701, South Africa  Department of Physics, University of the Free State, P.O.
Box 339, Bloemfonein 9300, South Africa  S. B. Cenko Astrophysics Science
Division, NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD
20771, USA  Joint Space-Science Institute, University of Maryland, College
Park, MD 20742 USA  O. D. Egbo Department of Astronomy, University of Cape
Town, Private Bag X3, Rondebosch 7701, South Africa  South African
Astronomical Observatory, P.O. Box 9, 7935 Observatory, South Africa  E. Göğüş
Sabancı University, Faculty of Engineering and Natural Sciences, İstanbul
34956 Turkey  J. Granot Department of Natural Sciences, The Open University of
Israel, P.O Box 808, Ra’anana 4353701, Israel  Astrophysics Research Center of
the Open university (ARCO), The Open University of Israel, P.O Box 808,
Ra’anana 4353701, Israel  Department of Physics, The George Washington
University, Washington, DC 20052, USA  C. Hailey  Columbia Astrophysics
Laboratory, Columbia University, New York, NY 10027, USA  J. Hare Astrophysics
Science Division, NASA Goddard Space Flight Center, 8800 Greenbelt Rd,
Greenbelt, MD 20771, USA  Center for Research and Exploration in Space Science
and Technology, NASA/GSFC, Greenbelt, Maryland 20771, USA  The Catholic
University of America, 620 Michigan Ave., N.E. Washington, DC 20064, USA  F.
Harrison Cahill Center for Astrophysics, California Institute of Technology,
1216 East California Boulevard, Pasadena, CA 91125, USA  D. Hartmann
Department of Physics and Astronomy, Clemson University, Kinard Lab of
Physics, Clemson, SC 29634-0978, USA  A. J. van der Horst Department of
Physics, The George Washington University, Washington, DC 20052, USA  D.
Huppenkothen SRON Netherlands Institute for Space Research, Niels Bohrweg 4,
2333CA Leiden, The Netherlands  L. Kaper  University of Amsterdam, Science
Park 904, 1098 XH Amsterdam, The Netherlands  O. Kargaltsev Department of
Physics, The George Washington University, Washington, DC 20052, USA  J. A.
Kennea Department of Astronomy and Astrophysics, The Pennsylvania State
University, 525 Davey Lab, University Park, PA 16802, USA  K. Mukai CRESST II
and X-ray Astrophysics Laboratory, NASA/GSFC, Greenbelt, MD 20771, USA
Department of Physics, University of Maryland Baltimore County, 1000 Hilltop
Circle, Baltimore MD 21250, USA  P. O. Slane Center for Astrophysics, Harvard
& Smithsonian, 60 Garden St. Cambridge, MA 02138, USA  D. Stern Jet Propulsion
Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Mail
Stop 169-221, Pasadena, CA 91109, USA  E. Troja University of Rome Tor
Vergata, Department of Physics, via della Ricerca Scientifica 1, 00100, Rome,
IT  Z. Wadiasingh Department of Astronomy, University of Maryland, College
Park, Maryland 20742, USA  Astrophysics Science Division, NASA Goddard Space
Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  Center for
Research and Exploration in Space Science and Technology, NASA/GSFC,
Greenbelt, Maryland 20771, USA  R. A. M. J. Wijers Anton Pannekoek Institute,
University of Amsterdam, Postbus 94249, 1090 GE Amsterdam, The Netherlands
Department of Physics, The George Washington University, Washington, DC 20052,
USA  P. Woudt Department of Astronomy, University of Cape Town, Private Bag
X3, Rondebosch 7701, South Africa  G. Younes Astrophysics Science Division,
NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA
Department of Physics, The George Washington University, Washington, DC 20052,
USA

###### Abstract

The Swift Deep Galactic Plane Survey is a Swift Key Project consisting of 380
tiled pointings covering $\sim$40 deg2 of the Galactic Plane between longitude
$10$ $<$ $|l|$ $<$ $30$ deg and latitude $|b|$ $<$ $0.5$ deg. Each pointing
has a $5$ ks exposure, yielding a total of 1.9 Ms spread across the entire
survey footprint. Phase-I observations were carried out between March 2017 and
May 2021. The Survey is complete to depth $L_{X}$ $>$ $10^{34}$ erg s-1 to the
edge of the Galaxy. The main Survey goal is to produce a rich sample of new
X-ray sources and transients, while also covering a broad discovery space.
Here, we introduce the Survey strategy and present a catalog of sources
detected during Phase-I observations. In total, we identify 928 X-ray sources,
of which 348 are unique to our X-ray catalog. We report on the characteristics
of sources in our catalog and highlight sources newly classified and published
by the DGPS team.

X-ray astronomy (1810) — Surveys (1671) — Catalogs (205) — X-ray binary stars
(1811)

††journal: ApJS††facilities: Swift/XRT ††software: HEASoft, XRTDAS, swifttools
(Evans et al., 2023), PIMMS, Astropy (Astropy Collaboration et al., 2013)

##  1 Introduction

Since the inception and discovery of X-ray astronomy, from the detection of
Sco X-1 and the launch of the first X-ray satellite in 1970 (Uhuru; Giacconi
et al., 1971), a diverse assortment of X-ray emitting sources have been
discovered and sorted into numerous distinct classes. These classes include
chromospheric activity from young stars, cataclysmic variables (CVs),
symbiotic binaries, young stellar objects (YSOs), magnetars, and X-ray
binaries comprising a compact object, either a neutron star (NS) or black hole
(BH), and a low-mass (LMXBs) or high-mass (HMXBs) star.

Within our Galaxy, the brightest X-ray sources are known to be X-ray binaries
with peak X-ray luminosities in excess of $L_{X}$ $>$ $10^{36-39}$ erg s-1.
However, our Milky Way (MW) also hosts a significant population of faint X-ray
sources ($L_{X}$ $<$ $10^{33-35}$ erg s-1) (Muno et al., 2005a, b; Degenaar &
Wijnands, 2009, 2010). These sources are likely dominated by magnetic CVs
(Barrett et al., 1999; Wang et al., 2002; Revnivtsev et al., 2009; Pretorius
et al., 2013), quiescent LMXBs (Muno et al., 2005a, b), and quiescent
magnetars (Coti Zelati et al., 2018), among others. Their discovery is crucial
to expand our understanding of their source populations and their formation
pathways within our Galaxy.

X-ray surveys of the Galactic Plane (GP) present a prime opportunity for
discovery of these faint sources. Thus far, sensitive and high-resolution
X-ray satellites, such as XMM-Newton or Chandra (Wijnands et al., 2006; Jonker
et al., 2011; Nebot Gómez-Morán et al., 2013), have been used to search for
serendipitous faint X-ray sources within the true target’s field of view. Such
procedures, however, are not uniform in depth nor do they cover the full
extent of the GP, relying instead on pointings directed at known bright
sources. Therefore, dedicated, homogeneous X-ray surveys are required to
identify the population and number of faint X-ray sources within the Galaxy.

The Neil Gehrels Swift Observatory (Gehrels et al., 2004) X-ray Telescope
(XRT; Burrows et al., 2005) utilizes a CCD detector with sensitivity to X-ray
photons over the range $0.3$ $-$ $10$ keV. The instrument field of view (FOV)
is $23.6\arcmin\times 23.6\arcmin$ with an effective area of 110 cm2 at 1.5
keV and an angular resolution of $18\hbox{${}^{\prime\prime}$}$. The low
background ($10^{-6}$ cts s-1 pix-1; Evans et al. 2014), arcsecond source
localization, and fast slew rate, make the Swift/XRT optimal for surveys of
crowded environments, such as the GP (Reynolds et al., 2013), Small Magellanic
Cloud (Kennea et al., 2018), and the Galactic Bulge (Shaw et al., 2020;
Bahramian et al., 2021).

Here, we outline our Swift Deep Galactic Plane Survey (DGPS) strategy and
present the catalog of sources detected in Phase-I observations across the
$\sim$40 deg2 portion of the GP covered by the DGPS. We present the survey
design and strategy in §2. In §3 we discuss our source detection procedures
and the process for creating a unique source catalog. The catalog results,
discussion of implications, and overall conclusions are presented in §4, §5,
and §6, respectively.

Figure 1: The shaded blue regions show the line of sight of the DGPS survey
footprint through the Milky Way’s disk. The background image is an
illustration of the Milky Way with credit to NASA/JPLCaltech/ESO/R. Hurt.

##  2 Survey Footprint and Observing Strategy

The Swift Deep Galactic Plane Survey (PI: C. Kouveliotou) is a Swift Key
Project and NuSTAR Legacy Program111https://www.nustar.caltech.edu/page/59#g9
covering $\sim$40 deg2 of the GP (Figure 1) between Galactic longitude $10$
$<$ $|l|$ $<$ $30$ deg and latitude $|b|$ $<$ $0.5$ deg. The total sky
coverage of the Survey is 36 deg2 when correcting for tile overlaps and the
shape of the XRT FOV. The Survey encompasses 380 unique XRT pointings (see
Figures 2 and 3), each observed for $\sim$ $5$ ks for a total of $\sim$ $1.93$
Ms exposure carried out between March 2017 to May 2021. Approximately half of
these observations were performed between 2017 and 2019, and the second half
between 2020 and 2021. All observations were performed with the Swift X-ray
Telescope (XRT; Burrows et al., 2005) in Photon Counting (PC) mode.

The design of our survey (latitude and longitude range; Figures 2 and 3) was
driven by our primary science goal of thoroughly characterizing the magnetar
and HMXB populations in the MW by their persistent emission, while avoiding
the crowded Galactic center (Figure 1). We have additionally selected the
Survey footprint such that each tile has a $4\arcmin$ overlap with its
neighbor, taking into account the $23.6\arcmin$ XRT FOV.

In total, the Survey comprises 769 observations222An observation is defined as
all exposures covering a specific pointing obtained within a single UT day.
with Swift covering the 380 pointings (Figure 2), including those observed
during the DGPS Pilot Survey. This is due to the fact that in most cases
($\sim$70%) multiple observations of the same field were required to yield a
total of 5 ks exposure. In Figure 4, we display a histogram of exposure times
for these 769 single-epoch observations. We note that although a significant
fraction (47%) of single-epoch observations consisted of less than 2 ks of
exposure, the median cumulative exposure across the Survey footprint is 4.6 ks
(Figures 2 and 4). The fact that many tiles were observed multiple times was
extremely useful for the identification of variable X-ray sources (see §4.3
and §5.4).

On average, the survey is complete (§5.1) to a depth of $L_{X}$ $>$ $1.0\times
10^{34}$ erg s-1, to the edge of the Galaxy. However, it affords source
detection to limits of $L_{X}$ $\sim$ $1.0\times 10^{33}$ erg s-1 out to
$\sim$ $3$ $-$ $6$ kpc.

Figure 2: Swift/XRT exposure map of the DGPS footprint. The $4\arcmin$ overlap
region between adjacent tiles is clearly demonstrated. A few tile positions
were serendipitously observed twice, leading to a higher exposure (brighter
regions). The median exposure across all pixels is 4.6 ks. The variation in
exposure in the two observed regions of the GP is negligible.

Figure 3: Full XRT band ($0.3$ $-$ $10$ keV) mosaic of the Galactic plane
using an Aitoff projection in Galactic coordinates. The image covers the full
footprint of DGPS Phase-I. The pixel size is
$4.7\hbox{${}^{\prime\prime}$}$/pix, and images have been smoothed with a
Gaussian kernel (with FWHM of 3 pixels) to improve visual clarity. The image
has been divided by the exposure map (Figure 2) in order to smooth out
exposure related background in the overlapping regions. The dominant sources
of stray light at $l$ $\approx$ $-25^{\circ}$, $-20.5^{\circ}$, and
$13.5^{\circ}$ are the LMXBs 4U 1624-49, 4U 1642-45, and GX 13+01.

Figure 4: Top: Histogram of single-epoch Swift/XRT exposure time for all DGPS
observations. Bottom: Sky coverage as a cumulative function of the exposure
time (corrected for vignetting and bad pixels) across the entire DGPS Survey
footprint after mosaicing all observations. The total sky coverage of the
Survey is 36 deg2. The median exposure time is 4.6 ks. The overlap regions
between tiles lead to a higher exposure of up to 15-20 ks.

##  3 Swift/XRT Data Analysis

Here, we outline our process for analyzing all 769 DGPS observations. Due to
the long-term nature of the project, and the need for XRT to return to the
same field multiple times (Figure 4), we performed an initial analysis of all
data when it was first obtained (§3.1). After the end of Phase-I observations,
we performed a final processing (§3.2) of all observations to create the DGPS
Phase-I catalog.

To do this, we performed source detection on mosaics of the DGPS observations
(§2). Following the creation of a unique source catalog, we pulled additional
information (e.g., flux, hardness ratio (HR), variability) from the Living
Swift-XRT Point-source catalog333https://www.swift.ac.uk/LSXPS/docs.php
(LSXPS; Evans et al. 2023). LSXPS has processed all Swift/XRT observations,
including those comprising the DGPS, and this step avoids redundancy in re-
processing all of the data and increases the overall scientific impact by
allowing us to have an improved grasp on the source characteristics.

Through this process, we discovered that there exists a subset of DGPS sources
($\sim 14\%$) that are not in the LSXPS catalog (§3.2.1). These sources lack
some of the additional information that comes from LSXPS (e.g., HR
variability), and we discuss their significance further in §3.2.1 and §4.1.1.
All sources detected by DGPS in our analysis of the mosaics (e.g., Figure 5),
including those not found in LSXPS, are incorporated into our full catalog
(see also Appendix 5.3), and this includes those sources which were not
identified in LSXPS processing (Evans et al., 2023).

###  3.1 Quick-look Analysis

The identification and prompt follow-up of variable or transient sources
detected as part of the Survey required a rapid analysis of quick-look
data444https://www.swift.ac.uk/archive/ql.php as these became available $\sim$
$2-6$ hours after the observations. Quick-look data are not the final fully
processed data, and are instead treated as a preliminary first look in order
to identify sources displaying variability on a shorter timescale than the
fully processed data are available ($\sim$ $1$ $-$ $2$ weeks after the quick-
look data555https://swift.gsfc.nasa.gov/quick-
look/swift_process_overview.html). The former data, however, allowed for rapid
multi-wavelength follow-up observations. The single-epoch quick-look data was
initially processed within a day of each XRT observation.

In many cases ($\sim$ $70\%$), Swift did not perform the full $\sim$ $5$ ks
exposure in a single epoch (see Figure 4). Therefore, in order to reach the
full exposure for each tile, Swift carried out multiple observations666In most
cases, it took Swift three observations of varying length for an individual
tile to reach $5$ ks exposure., sometimes taken months apart. We utilized this
to better identify variability by comparing the source flux between each
observation. We additionally checked archival flux values from available X-ray
catalogs. We selected previously unknown or unclassified variable sources with
an unabsorbed X-ray flux brighter than $F_{X}$ $>$ $1.0\times 10^{-12}$ erg
cm-2 s-1 ($0.3$ $-$ $10$ keV) for Target of Opportunity (ToO) follow-up with a
variety of X-ray satellites, such as XMM-Newton, Chandra, NuSTAR, and NICER,
through our approved programs, see, e.g., Gorgone et al. (2019, 2021);
O’Connor et al. (2022, 2023a, 2023b).

###  3.2 Final Image Processing and Source Detection

The rapid quick-look analysis of DGPS observations does not reach the full
depth of the Survey. In order to produce a complete source catalog, we turned
towards a more robust, yet computationally intensive, data analysis pipeline
used to generate previous Swift X-ray catalogs (Evans et al., 2014, 2020).
This pipeline allows for the mosaicing of all observations within the DGPS.
However, the Swift DGPS covers $\sim$40 deg2 of the Galactic Plane and
performing source detection on regions of this size is not feasible due to the
computational cost. Therefore, in order to reduce the computation time, while
still achieving the maximum exposure across every part of the Survey, we
defined 124 small mosaics covering the entire Phase-I Survey area. The mosaics
were created such that there is an overlap for every mosaic, which means that
some pointings were part of multiple mosaics. This ensures that every possible
overlap of tiles was accounted for and allowed us to obtain the maximum
exposure at every location within the DGPS footprint. An example mosaic is
displayed in Figure 5.

Figure 5: Example exposure map and science image ($0.3$ $-$ $10$ keV) of a
DGPS mosaic. The mosaic is centered at $l,b$ = 333.87∘, 0.026∘. White circles
represent the location of sources detected in this image. The bright source to
the right of the image is MAXI J1651-501, a Type-I X-ray Burster uncovered
through DGPS observations (Gorgone et al., 2019). A weak stray light pattern
(concentric bands) is visible on the left end of the mosaic. The images have
been re-binned ($7.07\hbox{${}^{\prime\prime}$}$/pix) and smoothed with a
Gaussian kernel (with FWHM of 3 pixels) for display purposes.

The image processing, mosaic creation, and source detection algorithm are
described in detail in Evans et al. (2014, 2020). The pipeline made use of
HEASoft 6.29. The iterative source detection procedure classifies each source
using numerous quality flags, such as ‘good’, ‘reasonable’, or ‘poor’ (see
Evans et al. (2014, 2020) for
details777https://www.swift.ac.uk/2SXPS/docs.php.) These flags indicate the
level of significance of the detection and were calibrated using simulations
of point sources. The false positive rate for good sources is 0.3%, and
increases to 1% when also including reasonable sources, whereas including poor
sources yields a rate of spurious sources on the order of 10% (Evans et al.,
2020). These false positive rates are considered cumulative, and we note that
the actual false positive rate for reasonable and poor sources is $\sim$ $7\%$
and $\sim$ $35\%$, respectively. Therefore, we remove sources with a poor
quality flag.

The Evans et al. (2020) pipeline also includes quality flags to prevent
spurious sources in regions contaminated by stray light or extended sources
(e.g., supernova remnants) as well as sources which are possible aliases of
bright sources (see Table 5 of Evans et al., 2014). We have excluded all
sources occurring in the PSF of extremely bright sources, in regions of stray
light or known extended objects, as well as those due to optical
loading888https://www.swift.ac.uk/analysis/xrt/optical_loading.php. The field
flags were set manually by Evans et al. (2020).

After removing all sources with quality flags, we began by merging all
blindly-detected sources in the same mosaic across the different energy bands.
Source detection is run independently in four energy bands999The same energy
bands were previously used in the 1SXPS, 2SXPS, and LSXPS catalogs (Evans et
al., 2014, 2020, 2023).: the soft band (SB; $0.3$ $-$ $1$ keV), medium band
(MB; $1$ $-$ $2$ keV), hard band (HB; $2$ $-$ $10$ keV), and the full band
(FB; $0.3$ $-$ $10$ keV). We merged sources that were identified as the same
source, but in different energy bands, by defining a match as either being
within 10 pixels (1 pixel = 2.36′′) or consistent at the 99.7% level using
Rayleigh statistics. At this stage, we include only the statistical position
errors as each source within a single mosaic has the same astrometric
solution. This process yields a list of unique sources identified in each
mosaic.

As there is a one tile overlap between each mosaic, there are some duplicate
sources that must be removed. We therefore cross-matched the source lists
between every mosaic in order to remove duplicate sources which were
consistent at the $99.7\%$ confidence level (including both the statistical
and systematic error on the source positions). We are then left with a unique
list of sources detected across the entire DGPS footprint.

The source count rates and fluxes in each energy band were then pulled from
LSXPSusing the API tool101010https://www.swift.ac.uk/API/. We determined the
LSXPS counterpart to each DGPS source using a radius of
$20\hbox{${}^{\prime\prime}$}$ or the 99.7% combined error radius. As the
LSXPS is a low-latency, continuously updated catalog, we note that our cross-
match was performed on the LSXPS catalog of 2022 August 31. We note that we
only include sources in LSXPS that are detected in our DGPS mosaics, and,
therefore, only sources to the completeness limits of the DGPS.

The count rates were converted to a $0.3-10$ keV flux assuming a power-law
spectrum with photon index $\Gamma$ $=$ $1.7$ and the Galactic hydrogen column
density in the source direction from Willingale et al. (2013). We further took
from the LSXPS catalog the hardness ratios HR1=M$-$S/M$+$S, HR2=H$-$M/H$+$M,
and the Pearson’s $\chi^{2}$ probability that each source is variable based on
their LSXPS lightcurves binned by observation.

The source positions in LSXPS are based on either standard or astrometric
positions. We therefore used the API tool to build XRT enhanced positions
(Goad et al., 2007; Evans et al., 2009) for all DGPS sources. We successfully
built enhanced positions for 290 sources, and we accepted the position with
the smallest error. We used the final source positions to name DGPS sources in
the format: “DGPS JHHMMSS.S$\pm$DDMMSS”.

All sources and their properties (along with LSXPS ID; Evans et al. 2023) are
displayed in Table 2111111Table 2 is available in electronic form at the CDS
via anonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/ApJS/.. We detected a total of 802
sources of which 784 are detected in the FB, 724 in the HB, 668 in the MB, and
564 in the SB.

####  3.2.1 Sources with no LSXPS Counterpart

In addition to those sources described above, we detect $\sim$200 sources in
the DGPS mosaics which do not have LSXPS counterparts within
$60\hbox{${}^{\prime\prime}$}$ (Evans et al., 2023). We refer to these as non-
LSXPS sources throughout the manuscript. There are a number of plausible
reasons as to why these sources would not have been detected in the LSXPS
mosaics, including a different combination of observations used to build the
mosaics in LSXPS, hot pixels, which are harder to detect in stacked
observations, or a lower background to variable or transient sources in the
DGPS mosaics as they include less overall observations. Therefore, there is no
obvious reason to exclude these sources from our catalog.

After removing sources with field flags or those lying in the PSF of a bright
source, we are left with 126 sources, 83 classified as good and 43 as
reasonable. Based on simulations of Swift/XRT point sources (Evans et al.,
2014, 2020), these sources are detected at the 99% confidence level.

We utilized the Python API tool to call the Swift-XRT LSXPS Upper limit
server121212https://www.swift.ac.uk/LSXPS/ulserv.php (Evans et al., 2023),
which allows for the calculation of $3\sigma$ upper limits for any position
within the LSXPS footprint. We specifically called only the DGPS observations
covering the position of each source. Aperture photometry using a circular
region with a radius of 12 pixels ($28\hbox{${}^{\prime\prime}$}$) was then
performed on the images to determine the source and background counts in each
energy band. We then applied the Bayesian procedure of Kraft et al. (1991) to
determine whether the source is detected at the $3\sigma$ level, and, if
detected, the mean number of counts and $1\sigma$ errors. The Upper Limit
Server also computes a PSF correction to account for vignetting and the
encircled energy fraction of the circular aperture. After multiplying the
number of counts by this correction factor and dividing by the exposure time,
we obtain a count rate in each energy band. This is all done through the
mergeUpperLimits tool. These methods are identical to those utilized to
compute count rates for LSXPS sources.

However, we only find a $3\sigma$ detection for 35 out of 126 sources with 22
detections in the FB, 17 in the HB, 9 in the MB, and 6 in the SB. Of the 35
sources, 16 were detected in multiple bands using this method. This serves to
confirm that at least some of these sources, likely more than 35, are not
spurious in nature. We note that the Evans et al. (2020) source detection
algorithm does not necessarily require a $3\sigma$ statistical significance
for detection, and, in fact, the signal-to-noise ratio for many of these
sources is $\sim$ $2$. Instead, the algorithm computes a likelihood that the
source is real, which was calibrated using simulations (Evans et al., 2014,
2020). This could explain why only 35 of 126 sources are above the $3\sigma$
threshold according to Kraft et al. (1991).

We convert the count rate to an unabsorbed flux ($0.3$ $-$ $10$ keV) for each
source assuming the median ECF for all DGPS sources detected in LSXPS (§3.2).
This is dependent on the energy band, and we find median values of
ECF${}_{\textrm{FB}}=2.7\times 10^{-11}$ erg cm-2 cts-1 for the full band, and
ECF${}_{SB}=5.2\times 10^{-11}$ erg cm-2 cts-1, ECF${}_{MB}=6.6\times
10^{-11}$ erg cm-2 cts-1, and ECF${}_{HB}=4.5\times 10^{-11}$ erg cm-2 cts-1.
These ECFs were all determined assuming a power-law X-ray spectrum with photon
index $\Gamma$ $=$ $1.7$ and Galactic hydrogen column density (Willingale et
al., 2013).

For these non-LSXPS sources we record only the standard position derived by
the source detection algorithm as performed on the DGPS mosaics. We note that
these sources have no multi-epoch (i.e., variability) information, as they are
only detected in stacked observations (mosaics). Furthermore, due to their
faintness and low number of photons, the hardness ratio information is
limited, and instead we record clearly the bandpass in which the source is
detected. Due to these limitations, we record the non-LSXPS sources in a
separate table from those with additional LSXPS information. We report the
results for these 126 sources in Table 3131313Table 3 is available in
electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr
(130.79.125.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/ApJS/.. We
emphasize that these sources, in addition to those in Table 2, comprise the
full DGPS Phase-I catalog.

Figure 6:  Top: Histogram of the 90% X-ray position error for sources in the
DGPS catalog. Bottom: Radial separation $R$ divided by the 68% error of the
DGPS sources and the 68% error of other X-ray source error added in
quadrature. The radial separation is from the DGPS source to the X-ray
counterpart centroid from 4XMM, 2CSC, and 1SWXRT. The dashed red line shows
the expected Rayleigh distribution with $\sigma$ $=$ $1$.

##  4 Results

###  4.1 Cross-matching with External Catalogs

We cross-matched the 802 sources in Table 2 with a variety of radio, optical,
infrared, and X-ray catalogs in order to identify their multi-wavelength
counterparts. We defined a match as when the catalog and DGPS positions were
consistent at the 99.7% confidence level141414In order to convert between the
90% and 99.7% position error, we have assumed that our source position errors
follow Rayleigh statistics (Evans et al., 2014, 2020). when adding both
catalog and DGPS errors in quadrature. The distribution of 90% position errors
are shown in Figure 6 (top panel). The median 90% position error is
$4.6\hbox{${}^{\prime\prime}$}$, leading to a 99.7% error of $\sim$
$7\hbox{${}^{\prime\prime}$}$.

We began by searching the SIMBAD Astronomical Database (Wenger et al., 2000)
in order to identify any previous source classifications. As the SIMBAD
database does not include positional errors uniformly it is possible some real
associations were missed. For all other catalogs, we include the catalog’s
positional error added to the DGPS position error in quadrature.

We used astroquery (Ginsburg et al., 2019) to search the VizieR Database
(Ochsenbein et al., 2000) for the following X-ray catalogs: the Chandra Source
Catalog (CSC; Evans et al., 2010) Release 2.0, the XMM-Newton Serendipitous
Source Catalog (4XMM-DR9; Webb et al., 2020; Traulsen et al., 2020), 1SXPS
(Evans et al., 2014), and 2SXPS (Evans et al., 2020), 1SWXRT (D’Elia et al.,
2013). In addition to the number of matches in each X-ray catalog we report
the number of unique, previously unknown, X-ray sources. We additionally
searched the following optical, infrared, and radio catalogs: USNO-B1 (Monet
et al., 2003), Gaia EDR3 (Gaia Collaboration et al., 2021), the Two Micron All
Sky Survey (2MASS; Skrutskie et al., 2006), and the Very Large Array Sky
Survey (VLASS; Lacy et al., 2020). The results of our cross-matching analysis
are displayed in Table 1.

We find that 249 (31%) of DGPS sources were previously unknown to other X-ray
surveys (with the exception of LSXPS). In Table 2 we record whether a source
has a known X-ray counterpart. Figure 6 (bottom panel) shows the distribution
of offsets between X-ray source matches normalized by the 68% position
uncertainty of both sources added in quadrature. The distribution of position-
error-normalized offsets approximately follows a Rayleigh distribution with
scale parameter $\sigma$ $=$ $1$. However, there is some excess at $R/\sigma$
$>$ $3$ that may hint at an additional systematic position error that was not
included. We note that counterparts in 2SXPS are not included in this
calculation as their separations are tighter than a Rayleigh distribution due
to the use of a similar source detection algorithm on similar data, i.e., the
first half of the DGPS data obtained between 2017 and 2019 are included in the
2SXPS catalog. This leads to a bias towards the same centroid location for
counterparts in 2SXPS, whereas there is no overlap with 1SWXRT, and,
therefore, no bias against a Rayleigh distribution.

We determined the number of false associations by shifting all DGPS sources
randomly by $1-2\arcmin$ and repeating the cross-match. All matches found
after shifting are considered false positives. We repeated this procedure
multiple times. Due to the high density of optical and infrared sources in the
crowded GP, generally there are multiple counterparts within a typical X-ray
localization (e.g., between $2-4$ Gaia counterparts are found on average for
DGPS sources). This is reflected in the high false positive fraction ($>$
$77\%$). Therefore, the determination of the true counterpart is difficult
using XRT positions alone. Through our follow-up campaigns, we found that
Chandra observations were pivotal to the identification of the true multi-
wavelength counterpart (see §5.4).

Table 1: Results of multi-wavelength cross-matching with external catalogs using the combined $3\sigma$ source localization. The expected fraction of spurious matches was determined by shifting our source catalog by $1$ $-$ $2\arcmin$ and re-running our cross-matching algorithm.  External Catalog | Matches | Spurious Matches
---|---|---
X-ray Catalogs
2CSC | 186 | 2 (1.0%)
4XMM-DR9 | 264 | 3 (1.1%)
2SXPS | 463 | 3 (0.6%)
1SWXRT | 63 | 1 (1.6%)
Unique | 249 | –
Radio Catalogs
VLASS | 17 | 1 (5.9%)
Unique | 745 | –
Optical/nIR Catalogs
2MASS | 689 | 618 (90.0%)
GAIA | 699 | 635 (90.8%)
USNO-B1 | 562 | 431 (76.7%)
Unique | 58 | –

####  4.1.1 Cross-match of non-LSXPS Sources

We performed the same cross-matching analysis outlined in §4.1 on the 126 non-
LSXPS sources (Figure 8 and Table 3). We find 17 matches in the X-ray catalogs
searched, implying that these sources largely comprise a faint, previously
undiscovered population of X-ray sources. Of these 17 matches, 12 were in
4XMM-DR9, 7 in 2SXPS, and 7 in CSC 2.0. The sources with matches in these
catalogs are marked in Table 3

We further note that a cross-match of the non-LSXPS sources with SIMBAD
results in only 3 classified source matches, and 123 sources without a SIMBAD
counterpart. Therefore, a significantly larger fraction of those sources not
in LSXPS are previously unknown and unclassified, likely due to their
faintness and lower number of counterparts in other X-ray catalogs.

While only 17 (13%) of these sources have a known X-ray counterpart, compared
to 69% in of those also detected by LSXPS, this further implies (see also
§3.2.1) that at least some of these non-LSXPS sources are real. Moreover, the
7 sources detected in 2SXPS (Evans et al., 2020), but not in the re-analysis
for LSXPS (Evans et al., 2023), emphasizes that the combination of specific
observations used to create the mosaic is an important factor in the source
detection process.

###  4.2 Source Classification Breakdown

Our cross-match with the SIMBAD database (Wenger et al., 2000) resulted in a
total of 251 (27%) previously classified sources. However, we found that in
some cases the classification was incorrect or incomplete. Thus, while the
SIMBAD database provides a useful check as to whether a source is already
known (and cross-listings between the same source in other catalogs), it does
not provide a robust measure of the number of confidently classified sources
in our catalog.

Therefore, we performed an additional search of other external catalogs
containing classified source types, including the McGill Online Magnetar
Catalog151515https://www.physics.mcgill.ca/~pulsar/magnetar/main.html (Olausen
& Kaspi, 2014),
HMXBCAT161616https://heasarc.gsfc.nasa.gov/W3Browse/all/hmxbcat.html (Liu et
al., 2006),
LMXBCAT171717https://heasarc.gsfc.nasa.gov/W3Browse/all/lmxbcat.html (Liu et
al., 2007), Australia Telescope National Facility (ATNF) Pulsar Catalogue
(Manchester et al., 2005), The Million Quasars (Milliquas) v7.2 Catalogue
(Flesch, 2021), Symbiotic stars
catalogue181818https://heasarc.gsfc.nasa.gov/W3Browse/all/symbiotics.html
(Belczyński et al., 2000), the New Online Database of Symbiotic
Variables191919http://astronomy.science.upjs.sk/symbiotics/index.html (Merc et
al., 2019), X-ray catalog of Galactic O stars (Nebot Gómez-Morán & Oskinova,
2018), Catalog of X-Ray Detected Be
Stars202020https://home.gwu.edu/~kargaltsev/XDBS/ (XDBS; Gobat et al. 2022), a
catalogue of chromospherically active binary stars (Eker et al., 2008), the
Open Cataclysmic Variable
Catalog212121https://depts.washington.edu/catvar/index.html (Guillochon et
al., 2017; Jackim et al., 2020), and IP CVs from Koji Mukai’s
catalog222222https://asd.gsfc.nasa.gov/Koji.Mukai/iphome/catalog/alpha.html
(cross-matched as of 2022 August 31). This ensures we probe the majority of
known sources within these classes.

Figure 7: Breakdown of the source type for the 73 classified sources in the
full DGPS catalog.

In total we find 73 classified sources across the following categories:

  1. i)

4 pulsars,

  2. ii)

10 magnetars,

  3. iii)

12 HMXBs,

  4. iv)

4 LMXBs,

  5. v)

10 CVs (6 being IPs),

  6. vi)

5 Wolf Rayet (WR) stars,

  7. vii)

18 young stellar objects (YSO),

  8. viii)

5 quasars (QSO),

  9. ix)

3 symbiotic stars,

  10. x)

and 2 X-ray detected O stars.

The classification breakdown is demonstrated in Figure 7. We do not find any
associations with X-ray detected Be stars (Gobat et al., 2022), or
chromospherically activate binaries (Eker et al., 2008).

Thus, we find only $\sim$ 9% of DGPS sources are confidently classified. This
is likely a lower limit to the true number of classified sources in the Survey
given that many of the catalogs searched are over a decade old and may be
lacking in completeness. This further emphasizes the need for up-to-date
catalogs of source classifications and for machine learning techniques to
determine preliminary source classifications for large datasets (Yang et al.,
2021, 2022; Tranin et al., 2022), see §5.5.

In Figure 9 we display the X-ray flux distribution of DGPS sources compared to
known IP CVs, HMXBs, LMXBs, and magnetars. The large majority of DGPS sources
lie below the distribution of classified sources, emphasizing the difficulty
in classifying faint sources. This may suggest that the DGPS population of
sources could lie at further distances (leading to a lower observed flux), and
are, therefore, possibly more absorbed, due to a larger Galactic column
density.

Figure 8: Breakdown of the 928 X-ray sources (802 LSXPS $+$ 126 non-LSXPS) in
the full DGPS source catalog. Figure 9: Histogram of average flux values for
DGPS sources (gray), the non-LSXPS sources (blue), and known classified
sources (purple), including IP CVs, LMXBs, HMXBs, and Magnetars. The dotted
and dashed lines correspond to the 50% and 90% completeness flux of the DGPS,
respectively (see §5.1).  Figure 10: Examples of variable sources identified
in DGPS observations: IGR J18219-1347 is a BeXRB (O’Connor et al., 2022), XTE
J1810-197 is a magnetar candidate (Markwardt et al., 2003; Israel et al.,
2004), OAO 1657-41 is a HMXB (Polidan et al., 1978; Chakrabarty et al., 1993),
and AX J165420-43337 (also known as 1RXS J165424.6-433758) is a polar CV
(O’Connor et al., 2023a).

###  4.3 Variable X-ray Sources

The DGPS was aimed at uncovering new or variable X-ray sources within the GP.
This was done through the rapid analysis of quick-look data (§3.1) and the
comparison of source flux levels with archival observations. An example of
variable sources uncovered in DGPS observations is displayed in Figure 10. The
majority of sources displaying obvious variable behavior were already
classified (typically HMXBs, LMXBs, or magnetars; Figure 10), but we were also
able to classify a number of variable sources (e.g., Gorgone et al. 2019,
2021; O’Connor et al. 2022, 2023a, 2023b) through our follow-up programs, with
more classifications in progress.

For the purposes of the DGPS catalog, we make use of the Pearson’s $\chi^{2}$
variability test (see also Evans et al. 2014, 2020). This test computes the
probability that the source count rate is constant across all Swift
observations of the source. We consider a source variable if the probability
is $P_{\chi,\textrm{const}}$ $<$ $0.05$. Approximately half of DGPS sources
are expected to display variability (i.e., they are not constant) with a
probability higher than 95% (Figure 11).

In addition, following Eyles-Ferris et al. (2022), we compute the ratio of the
peak-to-mean X-ray flux, denoted by $R_{\textrm{flux}}$, as an indicator of
flaring sources. We display $R_{\textrm{flux}}$ for each source in Figure 12.
We find that only 50 sources in the Survey are consistent with
$R_{\textrm{flux}}$ $>$ $10$ and 138 with $R_{\textrm{flux}}$ $>$ $5$. Out of
the 50 sources with $R_{\textrm{flux}}$ $>$ $10$, only 31 satisfy
$F_{X}/\sigma_{F_{X}}$ $>$ $3$ (Figure 12). Thus only 31 of these sources have
accurate enough flux determinations that the increase in flux by an order of
magnitude is statistically significant.

If we further sort these to sources with $F_{X}$ $>$ $10^{-12}$ erg cm-2 s-1,
our threshold for source follow-up (§3.1), we find that only 11 sources
satisfy these criterion, all of which are classified and have a known X-ray
counterpart: 1 LMXB, 4 HMXBs, 3 magnetars, 1 pulsar, a pulsar wind nebula (Ng
et al., 2008), and the young star cluster Westerlund 1. This is in contrast to
a total of 151 sources with $F_{X}$ $>$ $10^{-12}$ erg cm-2 s-1 in the DGPS
catalog (115 of which have a known X-ray counterpart).

Figure 11: Cumulative distribution of the Pearson’s $\chi^{2}$ variability
test for all DGPS sources. The dashed line represents a threshold of
$P_{\chi,\textrm{const}}=0.05$, below which a source is considered variable.
Approximately $50\%$ of sources lie below this threshold.  Figure 12: The
ratio of the peak-to-mean X-ray flux $R_{\textrm{flux}}$ versus the ratio of
the mean X-ray flux $F_{X}$ and the X-ray flux error $\sigma_{F_{X}}$. The
points are colored by the log of the $0.3$ $-$ $10$ keV X-ray flux in erg cm-2
s-1. The black dashed line indicates a region of parameter space where sources
are likely flaring or highly variable.

##  5 Discussion

###  5.1 Completeness

We estimated the completeness of the DGPS catalog using the simulations
performed by Evans et al. (2014, 2020). Evans et al. (2014, 2020) performed
detailed simulations of source detection likelihood with Swift/XRT as a
function of flux and exposure time. The source detection algorithm utilized in
this work is most similar to Evans et al. (2020), which displayed a factor of
$3.5\times$ improvement in sensitivity compared to Evans et al. (2014) due to
differences in the detection procedure and a more accurate modeling of the XRT
PSF. Therefore, we estimate our completeness using Figure 6 of Evans et al.
(2020). We used the simulations corresponding to the inclusion of sources
classified as both ‘good’ and ‘reasonable’.

The median exposure time of DGPS tiles is $\sim$4.6 ks. Using the calculations
performed by Evans et al. (2020), this corresponds to a 50% completeness flux
of $1.3\times 10^{-13}$ erg cm-2 s-1 and a 90% completeness of $2.7\times
10^{-13}$ erg cm-2 s-1. However, as shown in Figure 2, the exposure varies
over the GP due to regions of overlap between tiles. Therefore, these
completeness values may underestimate the true fraction of faint sources
expected in the overlap regions (see Figure 2).

In order to account for this, we performed a Monte Carlo simulation to sample
exposure times from random locations within the Survey footprint (Figure 2).
We then estimated the 50% and 90% completeness using the same method outlined
above. We repeated this procedure for 20,000 locations in order to find a
distribution of completeness flux levels across the Survey. We find a 50%
completeness flux of $(1.3^{+0.3}_{-0.4})\times 10^{-13}$ erg cm-2 s-1 and a
90% completeness of $(2.7^{+0.4}_{-0.7})\times 10^{-13}$ erg cm-2 s-1. As
expected, these values are consistent with our initial estimate.

Figure 13: $\log N$ $-$ $\log S$ plot for the full Swift DGPS ($0.3$ $-$ $10$
keV) catalog. The best fit line is displayed in red corresponding to
$N(>S)\propto S^{-0.78}$. The green solid line displays the $\log N$ $-$ $\log
S$ for non-LSXPS sources. The dotted and dashed lines correspond to the 50%
and 90% completeness flux of the DGPS, respectively. The blue dotted line is
an estimate of the extragalactic source population (Ueda et al., 1999).

###  5.2 Luminosity Function

Using the full DGPS source catalog, we derive the slope and normalization of
the $\log N$ $-$ $\log S$ curve at Galactic latitudes $|b|$ $<$ $0.5$ (Figure
3). We adopt a power-law form of this curve as $N(>S)$ $=$ $KS^{\alpha}$,
where $K$ is a normalization factor. The slope of this curve yields insight
into the spatial distribution of X-ray source populations within our Galaxy.

In Figure 13, we display the $\log N$ $-$ $\log S$ derived from the mean
fluxes of DGPS sources in the $0.3$ $-$ $10$ keV energy range in units of erg
cm-2 s-1. The best fit power-law distribution has a slope $\alpha$ $=$
$-0.78\pm 0.03$. We have only fitted the distribution for fluxes above the 50%
completeness value (dotted line in Figure 13), where the curve rapidly
flattens. We note that including the non-LSXPS sources (§3.2.1) has no impact
on the value of the slope as they all lie below the completeness flux value.

Our value is similar to the slope derived with the ASCA GP Survey (Sugizaki et
al., 2001) of $-0.79\pm 0.07$, and consistent with the $-0.64\pm 0.15$ slope
derived for HMXBs (Grimm et al., 2002). Both values are flatter than the $-1$
expected for a uniform infinite-plane source distribution. However, past X-ray
surveys using different instruments have found values in agreement with
$\alpha$ $\approx$ $-1$ (Hertz & Grindlay, 1984; Dean et al., 2005). These
differences may be due to the survey area covered, with different populations
of X-ray sources probed, as well as instrument sensitivity. The DGPS covers
regions of the plane dominated by spiral arms (Figure 1) at low Galactic
latitudes, and therefore we would expect a shallow slope for the $\log N$ $-$
$\log S$ relation (Sugizaki et al., 2001; Grimm et al., 2002), whereas past
Galactic X-ray surveys also covered larger scale heights, leading to a steeper
slope. We note that the $\log N$ $-$ $\log S$ curve for extragalactic X-ray
sources is considerably steeper ($\alpha$ $\approx$ $-1.5$; Gioia et al. 1990;
Hasinger et al. 1993; Ueda et al. 1999; Luo et al. 2017), and in agreement
with the expectations for a 3D Euclidean Universe ($N$ $\propto$ $S^{-3/2}$).

In order to determine whether extragalactic sources visible through the plane
were contaminating our sample, we estimated their contribution following the
methods of Sugizaki et al. (2001) and by converting the $\log N$ $-$ $\log S$
fit ($2$ $-$ $10$ keV) from Ueda et al. (1999) to the $0.3$ $-$ $10$ keV flux,
assuming an extragalactic source spectrum with power-law photon index $\Gamma$
$=$ $2$ absorbed by $N_{H}$ $=$ $5\times 10^{22}$ cm-2. These values were
chosen under the assumption that the extragalactic source population comprises
only active galactic nuclei (AGN). The extragalactic population begins to
significantly contribute at fluxes less than $10^{-12}$ erg cm-2 s-1, and has
a negligible impact on the population of brighter sources.

###  5.3 Catalog Characteristics

Figure 14 shows the $0.3$ $-$ $10$ keV X-ray flux versus $HR_{1}$ and $HR_{2}$
for DGPS sources. For comparison we display the known population of IP CVs,
LMXBs (Liu et al., 2007), HMXBs (Liu et al., 2006), and magnetars (Olausen &
Kaspi, 2014) from the 2SXPS catalog (see Appendix C for details). We see that
the majority of our sources lie both below the completeness values (vertical
lines) and below the flux of classified sources (Figure 9), underscoring a
very large population of faint, unclassified sources. However, it is difficult
to classify these sources based on hardness ratios alone, as demonstrated by
Figure 15 (for details see Appendix C). There is significant overlap in the
population of classified sources, emphasizing the need for machine learning to
disentangle source properties in higher dimensional space (Yang et al., 2022;
Tranin et al., 2022).

The DGPS sources are distributed relatively uniformly across Galactic
longitude (Figures 16 and 17) within the Survey footprint (§2). For example,
the number of sources between $10$ $<$ $l$ $<$ $30$ deg and $330$ $<$ $l$ $<$
$350$ deg is 413 and 389, respectively. However, pockets of longitude with
less sources exist. We find that this is due, at least in part, to sources of
intense stray light (Figure 3) at $l$ $\approx$ $338$ $-$ $342$ deg and $l$
$\approx$ $12$ $-$ $14$ deg (see the black star in Figure 17; bottom panel).
This is caused by the fact that we excluded sources with an LSXPS field flag
indicating that they reside in regions of stray light, and, therefore, may be
the result of unreliable detections (§3.2). In Galactic latitude we see a
marked decrease in sources as we move away from the GP, as expected. In
Appendix B, we display additional characteristics of sources across the GP
(e.g., hardness ratios and variability).

Figure 14: Distribution of DGPS sources (gray circles) in terms of hardness
ratio and X-ray flux. For reference, we display LMXBs, IP CVs, HMXBs, and
magnetars from the 2SXPS catalog. Figure 15: Left: Location of DGPS sources
(gray circles) in the $HR_{1}$ $-$ $HR_{2}$ plane. The dashed lines represent
typical spectra for HMXBs, Magnetars, and stars as outlined in Appendix C. The
arrows mark the general location of these sources with respect to the lines.
Right: The mean hardness ratios of LMXBs, IP CVs, HMXBs, and magnetars from
2SXPS are shown for comparison.

Figure 16: Histograms of the number of sources detected per Galactic longitude
on both sides of the plane and in Galactic latitude (combining both sides of
the plane). We note that the dip in sources at $l$ $\approx$ $14$ deg and
$340$ deg are due to stray light contaminating those fields.

Figure 17: The location of DGPS sources in Galactic coordinates. The sources
are colored based on the logarithm of their X-ray flux. The blue crosses show
the locations of known magnetars. The black star (bottom panel) marks a
dominant source of stray light, leading to an obvious lack of sources at that
region of the Survey.

###  5.4 New or Newly Classified Sources

We followed up unclassified, variable sources using our approved ToOs on
Chandra, NuSTAR, NICER, and XMM-Newton, including XMM-Newton AO17 (Proposal
ID: 082186; PI: Kouveliotou), Chandra Cycles 19, 20, and 23 (Proposal IDs:
19500723, 20500298, and 23500070; PI: Kouveliotou), and NICER Cycle 3 and 4
(Proposal IDs: 4050 and 5097; PI: Kouveliotou). The DGPS was a NuSTAR Legacy
Survey until 2019, although since this time we have utilized Director’s
Discretionary Time (DDT) observations. In total, we carried out 3 XMM-Newton
ToOs, 9 NuSTAR ToOs, 9 Chandra ToOs, 6 NICER ToOs, and 20 Swift ToOs to follow
DGPS sources. In addition, we made use of multi-wavelength observations from
the Lowell Discovery Telescope (LDT), the South African Astronomical
Observatory (SAAO) 1-m telescope, and the Southern African Large Telescope
(SALT). The results of these campaigns were reported in Gorgone et al. (2019,
2021); O’Connor et al. (2022, 2023a, 2023b).

###  5.5 Machine Learning Classification of DGPS Sources

As shown in §4.2, the DGPS has detected a large number of unclassified X-ray
sources. The classification of hundreds of X-ray sources based on manual
compilation and analyses of multi-wavelength datasets is difficult and time
consuming. Instead, it is more efficient to turn to supervised machine
learning methods to perform the classification of a large number of sources
based on the properties of a training dataset comprising sources with already
known classes. Yang et al. (2022) performed such analysis for a subset of the
Chandra Source Catalog version 2.0 (CSCv2) using a publicly
available232323https://github.com/huiyang-astro/MUWCLASS_CSCv2 Python
framework and a training dataset of $\sim$3,000 sources with verified
classifications242424https://home.gwu.edu/~kargaltsev/XCLASS/. They first
applied a selection criterion to CSCv2 to remove Chandra sources with low
signal-to-noise, poor localization errors, or those that were either extended
or confused (see Yang et al. 2022 for details). The sources satisfying their
criteria are referred to as “good” CSCv2 sources (GCS). In total, they are
able to provide classifications to 66,359 CSCv2 sources, approximately 21% of
the CSCv2 catalog.

While Yang et al. (2022) have not yet extended their analysis to other X-ray
missions (see, however, Tranin et al. 2022), their results can provide useful
insight into the classification of a subset of DGPS sources. We note that one
of the main obstacles for extending these analyses to Swift is the
significantly larger localization uncertainties of X-ray sources precluding
accurate multi-wavelength cross-matching. Therefore, below we only review the
classifications of DGPS sources that have counterparts in CSCv2, which provide
much more accurate positions.

After performing a cross-match between DGPS sources and the CSCv2 catalog we
find 186 matches (Table 1). We then matched these sources to the results of
Yang et al. (2022), finding 45 classified GCSs in addition to 19 sources in
their training datset. These sources have a classification confidence
threshold (CT) indicating the confidence level, with CT$\geq$2 adopted for
confidently classified GCSs (CCGCSs). Out of the 45 GCS sources, only 8 are
CCGCSs. In Figure 18 we display the classification stacked histogram of all 45
sources. The largest number of CCGCSs are 4 YSOs, followed by 3 NSs, and 1 CV.

Although 3 NS candidates (2CXO J171428.6–383601, 2CXO J182524.7–114524 and
2CXO J181210.3–184208), which each lack any optical or infrared counterpart,
have been confidently classified, this may be due to a bias in the training
dataset against faint sources without multi-wavelength counterparts. A large
fraction of faint sources do not have multi-wavelength counterparts simply
because of the insufficient sensitivity of optical and infrared surveys
combined with the significant extinction in the GP. The classification
algorithm of Yang et al. (2022) may instead interpret the lack of multi-
wavelength counterparts as a sign of the NS class (which includes both
magnetars and isolated NSs). Indeed, upon further investigation, 2 out of 3 of
these NS candidates (2CXO J182524.7–114524 and 2CXO J181210.3–184208) have
infrared counterparts in UKIDSS, which is significantly more sensitive than
the 2MASS catalog used in Yang et al. (2022). The third source (2CXO
J171428.6–383601) may have an infrared counterpart in VVV, but the source lies
outside of the 95% localization region (0.9′′) from CSCv2 at an offset of
1.2′′. Based on the VVV sky density in this region of the GP, we compute a
probability of chance coincidence of between $25-37\%$, depending on whether
or not we account for the brightness of the counterpart.

Figure 18: Histogram of source classification breakdown for 45 GCSs and 8
CCGCSs based on results from Yang et al. (2022).

###  5.6 Constraints on the population of magnetars

The main targets of the Swift DGPS were magnetars and HMXBs. However, although
several of the already known sources from both populations were observed
(Figure 7), we did not concretely identify any new transient events associated
with magnetars, and classified only a single new HMXB (O’Connor et al., 2022).

Magnetars are generally identified during their bright X-ray outbursts. As
such, the quiescent magnetar population is poorly constrained. Using the
Magnetar Outburst Online Catalog252525http://magnetars.ice.csic.es/#/welcome
(Coti Zelati et al., 2018), we compiled the distance and quiescent X-ray
($0.3$ $-$ $10$ keV) luminosity for 15 magnetars. Their observed quiescent
luminosities lie between $10^{30-35}$ erg s-1 (Coti Zelati et al., 2018).
Using the best available distance for each event, we find quiescent X-ray
fluxes in the range $10^{-15}$ to $10^{-12}$ erg cm-2 s-1. Therefore, only 7
out of 15 magnetars would be detectable based on the DGPS 50% completeness
flux.

For example, we note here that the DGPS observed the field of the magnetar
Swift J $1818.0-1607$ (Blumer & Safi-Harb, 2020; Champion et al., 2020; Hu et
al., 2020) approximately $2.7$ yr before its discovery. Unfortunately the
source was not active and we were only able to obtain an upper limit
($3\sigma$) of $\lesssim 2\times 10^{-13}$ erg cm-2 s-1. This demonstrates
that quiescent magnetars exist in the region covered by the DGPS, but their
identification is difficult, possibly due to faintness. A significant benefit
of this survey is to constrain the quiescent luminosity of future magnetars,
or other transients, discovered in these regions.

In fact, Beniamini et al. (2019) found that based on the observed persistent
luminosity and $\log N$ $-$ $\log S$ distribution, the number of hidden
magnetars could outweigh the known population by a factor of up to $\sim$10\.
They found that the missing magnetars should have unabsorbed fluxes $<$
$10^{-13}$ erg cm-2 s-1, which is below the DGPS completeness values.

In the general spin-down model for magnetars the magnetic field evolution is
parameterized by $\dot{B}\propto B^{1+\alpha}$ (Colpi et al., 2000). Beniamini
et al. (2019) used the observed $\log N$ $-$ $\log S$ for magnetars to show
that both $\alpha$ $=$ $0$ and $-1$ can explain the observed population of
absorbed and unabsorbed magnetar fluxes. We perform a similar calculation
using the constraints of our Survey. Based on the DGPS $\log N$ $-$ $\log S$
(Figure 13) we have detected 144 sources at $>$ $1.0\times 10^{-12}$ erg cm-2
s-1 of which 10 are known magnetars (Figure 7) and 400 sources at $>$
$2.7\times 10^{-13}$ erg cm-2 s-1 (including the 144 mentioned above). Under
the assumption that none of these new sources are magnetars we constrain
$\alpha$ $<$ $-0.65$ at the 90% confidence level (CL). We note that the
assumption that none of the $\sim$1,000 sources in our Survey are magnetars is
likely too restrictive as there could be unidentified quiescent magnetars
hiding in this population. If instead we assume there are 10 (20) unidentified
magnetars with a flux between $2.7\times 10^{-13}$ to $1.0\times 10^{-12}$ erg
cm-2 s-1 the constraint is $\alpha$ $<$ $0.86$ ($2.15$). These results are
consistent with Beniamini et al. (2019).

The upper limit to $\alpha$ is therefore strongly dependent on the unknown
population of unidentified quiescent magnetars hiding in our sample.
Nevertheless, the identification of their quiescent population is extremely
difficult. This issue was explored in detail by Muno et al. (2008) using
constraints from XMM-Newton and Chandra. They searched for periodic
variability in deep X-ray observations of the GP region ($|b|$ $<$ $5$ deg),
but did not identify any new periods between 5 and 20 s. Based on their
analysis, Muno et al. (2008) found that $<540$ magnetars (90% CL) should exist
in the Milky Way. Due to the lower exposure times and photon counts of our
Survey compared to the deep XMM-Newton and Chandra data used by Muno et al.
(2008), a timing analysis of our sources is not as fruitful.

##  6 Conclusions

We have presented the results of the DGPS Phase-I observations, covering
Galactic longitude $10$ $<$ $|l|$ $<$ $30$ deg and latitude $|b|$ $<$ $0.5$
deg. These observations led to the identification of 928 unique X-ray sources
(Tables 2 and 3) of which 358 (40%) were previously unknown to other X-ray
surveys. Our results indicate a significant population of very faint X-ray
sources below $F_{X}$ $<$ $10^{-13}$ erg cm-2 s-1, emphasizing the necessity
for sensitive, next generation, wide-field X-ray telescopes (e.g., Athena,
Nandra et al. 2013; AXIS, Mushotzky et al. 2019; Lynx, Gaskin et al. 2019;
STAR-X, Zhang et al. 2022) to characterize the missing faint X-ray population
in our Galaxy.

The authors thank the anonymous referee for constructive feedback that
improved the manuscript. B. O. and C. K. acknowledge support from multiple
grants to follow-up DGPS sources: NASA Grants 80NSSC17K0335, 80NSSC20K0389,
80NSSC19K0916, 80NSSC22K1398, and 80NSSC22K0583, Chandra awards GO9-20057X and
GO2-23038X, and award number 46939-1-CCNS 22317F. P. B.’s research was
supported by a grant (no. 2020747) from the United States-Israel Binational
Science Foundation (BSF), Jerusalem, Israel. J. H. and Z. W. acknowledge
support from NASA under award number 80GSFC21M0002. This work made use of data
supplied by the UK Swift Science Data Centre at the University of Leicester.
This research has made use of the XRT Data Analysis Software (XRTDAS)
developed under the responsibility of the ASI Science Data Center (ASDC),
Italy. This research has made use of the VizieR catalogue access tool, CDS,
Strasbourg, France (DOI: 10.26093/cds/vizier). The original description of the
VizieR service was published in A&AS 143, 23. This research has made use of
the SIMBAD database, operated at CDS, Strasbourg, France. This research has
made use of data obtained from the Chandra Source Catalog, provided by the
Chandra X-ray Center (CXC) as part of the Chandra Data Archive. This research
has made use of data obtained from the 4XMM XMM-Newton serendipitous source
catalogue compiled by the 10 institutes of the XMM-Newton Survey Science
Centre selected by ESA. This research has made use of data and/or software
provided by the High Energy Astrophysics Science Archive Research Center
(HEASARC), which is a service of the Astrophysics Science Division at
NASA/GSFC.

##  Appendix A Additional GP Mosaics

Here we present additional mosaics of the DGPS observations in the SB, MB, and
HB (Figures 20 and 19). These mosaics complement the FB image of the plane
displayed in Figure 3.

Figure 19: Mosaic of the GP at positive galactic longitudes in the SB ($0.3$
$-$ $1$ keV), MB ($1$ $-$ $2$ keV), and HB ($2$ $-$ $10$ keV).

Figure 20: Mosaic of the GP at negative galactic longitudes in the SB ($0.3$
$-$ $1$ keV), MB ($1$ $-$ $2$ keV), and HB ($2$ $-$ $10$ keV). The background
variation acrsoss the plane is due to higher exposure in regions with
overlapping tiles and is not due to an intrinsic structure in the emission.

##  Appendix B Comparison of source properties in Galactic coordinates

Here we present additional figures demonstrating how source properties vary
with location in the Galactic Plane. Figure 21 shows the hardness ratio for
each source versus their location in Galactic coordinates. There appears to be
a clustering of sources in $HR_{2}$, but less so in $HR_{1}$. We note that the
hardness ratios are uncorrected for Galactic hydrogen column density, and that
a line of sight absorption effect may be at play here.

In Figure 22 (left) we show a histogram of Galactic latitude for variable and
constant sources. There is no discernible difference and a Kolmogorov-Smirnov
test supports the null hypothesis ($p-$value $=$ $0.7$) that they are drawn
from the same distribution.

We also show the source distribution in the hardness ratio plane separated
between $|b|$ $<$ $0.1$ deg and $|b|$ $>$ $0.1$ deg (Figure 22; right). There
is no obvious clustering of sources based on this separation criterion.

Figure 21: The location of DGPS sources in Galactic coordinates. The sources
are colored based on their hardness ratio (either $HR_{1}$ or $HR_{2}$). The
black star (bottom panels) marks a dominant source of stray light, leading to
an obvious lack of sources in that region of the Survey.

Figure 22: Left: Histogram of source location in Galactic latitude for
constant (gray) and variable (red) sources (see §4.3). Right: Distribution of
sources in the hardness ratio plane. Red squares are sources on the GP with
$|b|$ $<$ $0.1$ deg and gray circles are off-plane sources with $|b|$ $>$
$0.1$ deg

##  Appendix C Derivation of Hardness Ratios for X-ray Source Populations

The majority of sources detected with the DGPS are faint, with a low number of
source counts (i.e., $<30$ cts), and, therefore, an analysis of their X-ray
spectra does not provide strong constraints on the intrinsic source
properties. Therefore, we utilized the X-ray hardness ratios, comparing the
count rate between different energy bands, as a way to characterize source
spectra despite the small number of counts. The hardness ratios $HR_{1}$ and
$HR_{2}$ are defined as in Evans et al. (2014, 2020):

$HR_{1}=\frac{MB-SB}{MB+SB}\,\,\textrm{and}\,\,HR_{2}=\frac{HB-MB}{HB+MB},$
(C1)

where $SB=0.3-1$ keV, $MB=1-2$ keV, and $HB=2-10$ keV count rate. The use of
two hardness ratios is ideal for characterizing soft sources, and
distinguishing between different source classifications.

In order to characterize the expected location of different source classes in
the $HR_{1}$ $-$ $HR_{2}$ plane we assumed spectral properties belonging to
each class and varied the hydrogen column density (see also Rigoselli et al.,
2022). We did this for HMXBs assuming a power-law spectrum with photon index
$\Gamma$ $=$ $1$, for stars assuming an APEC spectrum with temperature $kT$
$=$ $1.085$ keV and 0.6 solar abundance, and for magnetars assuming a
blackbody with $kT$ $=$ $1$ keV. We varied the hydrogen column density
uniformly between $\log(N_{H}/\textrm{cm}^{-2})$ $=$ $18$ $-$ $23$. We
performed this calculation using PIMMS to compute the Swift/XRT count rate in
the SB, MB, and HB at each step in the grid. We then determined both hardness
ratios based on these values. We show the tracks of each source type in Figure
15. The majority of stars have thermal plasma temperatures less than $kT$ $<$
$1$ keV, such that they lie below the line in $HR_{1}$ $-$ $HR_{2}$ space.
Similarly, many HMXBs display harder spectra than $\Gamma$ $=$ $1$, and for
that reason lie above the line in $HR_{1}$ $-$ $HR_{2}$ space. In the case of
magnetars, their quiescent spectra are generally described by a softer
blackbody with $kT$ $\approx$ $0.4$ keV (Coti Zelati et al., 2017), suggesting
that quiescent magnetars will lie below the line drawn.

We further checked the observed location of different source classes in the
$HR_{1}$ $-$ $HR_{2}$ plane by obtaining the observed mean flux and mean
hardness ratios from the 2SXPS catalog. In Figure 15 (right) we show the
observed locations for magnetars from the McGill Online Magnetar Catalog
(Olausen & Kaspi, 2014), HMXBs from Liu et al. (2006), LMXBs from Liu et al.
(2007), and IP CVs from Koji Mukai’s online catalog. As expected, many HMXBs
lie above our computed line for $\Gamma$ $=$ $1$. Of further note is the broad
diversity observed for magnetars, possibly due to the observed outbursts by
Swift and the spectral cooling of the sources during outburst (Coti Zelati et
al., 2018).

##  Appendix D Tables of catalog contents

Here we provide a description of the contents available for the DGPS catalog:

  1. 1.

Sources with additional information pulled from LSXPS (Table 2)

  2. 2.

Sources not in LSXPS (Table 3)

The main difference between the catalogs is the availability of variability
and hardness ratio information. Both catalogs comprise the full result of the
DGPS Phase-I.

In these tables, the energy bands are coordinated such that they agree with
the Evans et al. (2023) definitions: band0 is the full band (FB; $0.3$ $-$ $1$
keV), band1 is the soft band (SB; $0.3$ $-$ $10$ keV), band2 is the medium
band (MB; $1$ $-$ $2$ keV), band3 is the HB (HB; $2$ $-$ $10$ keV).

Table 2: Contents for DGPS sources for which we were able to pull additional information from LSXPS. The table is accessible in electronic form through VizieR (Ochsenbein et al., 2000). Column | Units | Description
---|---|---
IAU Name |  | IAU name in format “DGPS JHHMMSS.S$\pm$DDMMSS”
LSXPS_ID |  | Numerical unique source identifier within LSXPS
RA | deg | Right Ascension (J2000)
DEC | deg | Declination (J2000)
Err90 | arcsec | 90% source position uncertainty
l | deg | Galactic longitude
b | deg | Galactic latitude
Rate_band0 | cts s-1 | FB ($0.3$ $-$ $10$ keV) count rate
Rate_band0_pos | cts s-1 | Positive count rate error
Rate_band0_neg | cts s-1 | Negative count rate error
Rate_band1 | cts s-1 | SB ($0.3$ $-$ $1$ keV) count rate
Rate_band1_pos | cts s-1 | Positive count rate error
Rate_band1_neg | cts s-1 | Negative count rate error
Rate_band2 | cts s-1 | MB ($1$ $-$ $2$ keV) count rate
Rate_band2_pos | cts s-1 | Positive count rate error
Rate_band2_neg | cts s-1 | Negative count rate error
Rate_band3 | cts s-1 | HB ($2$ $-$ $10$ keV) count rate
Rate_band3_pos | cts s-1 | Positive count rate error
Rate_band3_neg | cts s-1 | Negative count rate error
FixedPowUnabsFlux | erg cm-2 s-1 | FB X-ray flux ($0.3$ $-$ $10$ keV) assuming a photon index $\Gamma$ $=$ $1.7$
FixedPowUnabsFlux_pos | erg cm-2 s-1 | Positive flux error
FixedPowUnabsFlux_neg | erg cm-2 s-1 | Negative flux error
R_Flux |  | Ratio of peak-to-mean flux
HR1 |  | Hardness ratio between the MB and SB
HR1_pos |  | Positive error on hardness ratio
HR1_neg |  | Negative error of hardness ratio
HR2 |  | Hardness ratio between the HB and MB
HR2_pos |  | Positive error on hardness ratio
HR2_neg |  | Negative error of hardness ratio
GalacticNH | cm-2 | Hydrogen column density in the source direction (Willingale et al., 2013)
Exposure | s | Cumulative DGPS exposure at the source position
X-ray Match |  | “Y” if known X-ray source, otherwise “N”
Variable |  | “Y” if known source is variable, otherwise “N”
Table 3: Contents for the non-LSXPS sources. These are sources with no LSXPS counterpart. The table is accessible in electronic form through VizieR (Ochsenbein et al., 2000).  Column | Units | Description
---|---|---
IAU Name |  | IAU name in format “DGPS JHHMMSS.S$\pm$DDMMSS”
RA | deg | Right Ascension (J2000)
DEC | deg | Declination (J2000)
Err90 | arcsec | 90% source position uncertainty
X-ray Match |  | “Y” if known X-ray source, otherwise “N”
band0_KNB91_Detected |  | Source retrospectively detected in FB using LSXPS Upper Limit Server
|  | (0 = not detected; 1 = detected)
band3_KNB91_Detected |  | Source retrospectively detected in HB using LSXPS Upper Limit Server
band2_KNB91_Detected |  | Source retrospectively detected in MB using LSXPS Upper Limit Server
band1_KNB91_Detected |  | Source retrospectively detected in SB using LSXPS Upper Limit Server
band0_IsDetected |  | Source blindly detected in FB through iterative source detection on mosaics
|  | (0 = not detected; 1 = detected)
band3_IsDetected |  | Source blindly detected in HB through iterative source detection on mosaics
band2_IsDetected |  | Source blindly detected in MB through iterative source detection on mosaics
band1_IsDetected |  | Source blindly detected in SB through iterative source detection on mosaics
Rate_band0 | cts s-1 | FB ($0.3$ $-$ $10$ keV) count rate
Rate_band0_pos | cts s-1 | Positive count rate error
Rate_band0_neg | cts s-1 | Negative count rate error
Rate_band3 | cts s-1 | HB ($2$ $-$ $10$ keV) count rate
Rate_band3_pos | cts s-1 | Positive count rate error
Rate_band3_neg | cts s-1 | Negative count rate error
Rate_band2 | cts s-1 | MB ($1$ $-$ $2$ keV) count rate
Rate_band2_pos | cts s-1 | Positive count rate error
Rate_band2_neg | cts s-1 | Negative count rate error
Rate_band1 | cts s-1 | SB ($0.3$ $-$ $1$ keV) count rate
Rate_band1_pos | cts s-1 | Positive count rate error
Rate_band1_neg | cts s-1 | Negative count rate error
FixedPowUnabsFlux | erg cm-2 s-1 | FB X-ray flux ($0.3$ $-$ $10$ keV) assuming a photon index $\Gamma$ $=$ $1.7$
FixedPowUnabsFlux_pos | erg cm-2 s-1 | Positive flux error
FixedPowUnabsFlux_neg | erg cm-2 s-1 | Negative flux error

## References

  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Bahramian et al. (2021) Bahramian, A., Heinke, C. O., Kennea, J. A., et al. 2021, MNRAS, 501, 2790, doi: 10.1093/mnras/staa3868
  * Barrett et al. (1999) Barrett, P., Singh, K. P., & Mitchell, S. 1999, in Astronomical Society of the Pacific Conference Series, Vol. 157, Annapolis Workshop on Magnetic Cataclysmic Variables, ed. C. Hellier & K. Mukai, 180
  * Belczyński et al. (2000) Belczyński, K., Mikołajewska, J., Munari, U., Ivison, R. J., & Friedjung, M. 2000, A&AS, 146, 407, doi: 10.1051/aas:2000280
  * Beniamini et al. (2019) Beniamini, P., Hotokezaka, K., van der Horst, A., & Kouveliotou, C. 2019, MNRAS, 487, 1426, doi: 10.1093/mnras/stz1391
  * Blumer & Safi-Harb (2020) Blumer, H., & Safi-Harb, S. 2020, ApJ, 904, L19, doi: 10.3847/2041-8213/abc6a2
  * Burrows et al. (2005) Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, Space Sci. Rev., 120, 165, doi: 10.1007/s11214-005-5097-2
  * Chakrabarty et al. (1993) Chakrabarty, D., Grunsfeld, J. M., Prince, T. A., et al. 1993, ApJ, 403, L33, doi: 10.1086/186715
  * Champion et al. (2020) Champion, D., Cognard, I., Cruces, M., et al. 2020, MNRAS, 498, 6044, doi: 10.1093/mnras/staa2764
  * Colpi et al. (2000) Colpi, M., Geppert, U., & Page, D. 2000, ApJ, 529, L29, doi: 10.1086/312448
  * Coti Zelati et al. (2018) Coti Zelati, F., Rea, N., Pons, J. A., Campana, S., & Esposito, P. 2018, MNRAS, 474, 961, doi: 10.1093/mnras/stx2679
  * Coti Zelati et al. (2017) Coti Zelati, F., Rea, N., Turolla, R., et al. 2017, MNRAS, 471, 1819, doi: 10.1093/mnras/stx1700
  * Dean et al. (2005) Dean, A. J., Bazzano, A., Hill, A. B., et al. 2005, A&A, 443, 485, doi: 10.1051/0004-6361:20053513
  * Degenaar & Wijnands (2009) Degenaar, N., & Wijnands, R. 2009, A&A, 495, 547, doi: 10.1051/0004-6361:200810654
  * Degenaar & Wijnands (2010) —. 2010, A&A, 524, A69, doi: 10.1051/0004-6361/201015322
  * D’Elia et al. (2013) D’Elia, V., Perri, M., Puccetti, S., et al. 2013, A&A, 551, A142, doi: 10.1051/0004-6361/201220863
  * Eker et al. (2008) Eker, Z., Ak, N. F., Bilir, S., et al. 2008, MNRAS, 389, 1722, doi: 10.1111/j.1365-2966.2008.13670.x
  * Evans et al. (2010) Evans, I. N., Primini, F. A., Glotfelty, K. J., et al. 2010, ApJS, 189, 37, doi: 10.1088/0067-0049/189/1/37
  * Evans et al. (2023) Evans, P. A., Page, K. L., Beardmore, A. P., et al. 2023, MNRAS, 518, 174, doi: 10.1093/mnras/stac2937
  * Evans et al. (2009) Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2009, MNRAS, 397, 1177, doi: 10.1111/j.1365-2966.2009.14913.x
  * Evans et al. (2014) Evans, P. A., Osborne, J. P., Beardmore, A. P., et al. 2014, ApJS, 210, 8, doi: 10.1088/0067-0049/210/1/8
  * Evans et al. (2020) Evans, P. A., Page, K. L., Osborne, J. P., et al. 2020, ApJS, 247, 54, doi: 10.3847/1538-4365/ab7db9
  * Eyles-Ferris et al. (2022) Eyles-Ferris, R. A. J., Starling, R. L. C., O’Brien, P. T., & Evans, P. A. 2022, MNRAS, 515, 4402, doi: 10.1093/mnras/stac1977
  * Flesch (2021) Flesch, E. W. 2021, arXiv e-prints, arXiv:2105.12985.  https://arxiv.org/abs/2105.12985
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * Gaskin et al. (2019) Gaskin, J. A., Swartz, D. A., Vikhlinin, A., et al. 2019, Journal of Astronomical Telescopes, Instruments, and Systems, 5, 021001, doi: 10.1117/1.JATIS.5.2.021001
  * Gehrels et al. (2004) Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005, doi: 10.1086/422091
  * Giacconi et al. (1971) Giacconi, R., Kellogg, E., Gorenstein, P., Gursky, H., & Tananbaum, H. 1971, ApJ, 165, L27, doi: 10.1086/180711
  * Ginsburg et al. (2019) Ginsburg, A., Sipőcz, B. M., Brasseur, C. E., et al. 2019, AJ, 157, 98, doi: 10.3847/1538-3881/aafc33
  * Gioia et al. (1990) Gioia, I. M., Maccacaro, T., Schild, R. E., et al. 1990, ApJS, 72, 567, doi: 10.1086/191426
  * Goad et al. (2007) Goad, M. R., Tyler, L. G., Beardmore, A. P., et al. 2007, A&A, 476, 1401, doi: 10.1051/0004-6361:20078436
  * Gobat et al. (2022) Gobat, C., Yang, H., Kargaltsev, O., Hare, J., & Volkov, I. 2022, Research Notes of the American Astronomical Society, 6, 163, doi: 10.3847/2515-5172/ac8937
  * Gorgone et al. (2019) Gorgone, N. M., Kouveliotou, C., Negoro, H., et al. 2019, ApJ, 884, 168, doi: 10.3847/1538-4357/ab3e43
  * Gorgone et al. (2021) Gorgone, N. M., Woudt, P. A., Buckley, D., et al. 2021, ApJ, 923, 243, doi: 10.3847/1538-4357/ac2738
  * Grimm et al. (2002) Grimm, H. J., Gilfanov, M., & Sunyaev, R. 2002, A&A, 391, 923, doi: 10.1051/0004-6361:20020826
  * Guillochon et al. (2017) Guillochon, J., Parrent, J., Kelley, L. Z., & Margutti, R. 2017, ApJ, 835, 64, doi: 10.3847/1538-4357/835/1/64
  * Hasinger et al. (1993) Hasinger, G., Burg, R., Giacconi, R., et al. 1993, A&A, 275, 1
  * Hertz & Grindlay (1984) Hertz, P., & Grindlay, J. E. 1984, ApJ, 278, 137, doi: 10.1086/161775
  * Hu et al. (2020) Hu, C.-P., Begiçarslan, B., Güver, T., et al. 2020, ApJ, 902, 1, doi: 10.3847/1538-4357/abb3c9
  * Israel et al. (2004) Israel, G. L., Rea, N., Mangano, V., et al. 2004, ApJ, 603, L97, doi: 10.1086/382875
  * Jackim et al. (2020) Jackim, R., Szkody, P., Hazelton, B., & Benson, N. C. 2020, Research Notes of the American Astronomical Society, 4, 219, doi: 10.3847/2515-5172/abd104
  * Jonker et al. (2011) Jonker, P. G., Bassa, C. G., Nelemans, G., et al. 2011, ApJS, 194, 18, doi: 10.1088/0067-0049/194/2/18
  * Kennea et al. (2018) Kennea, J. A., Coe, M. J., Evans, P. A., Waters, J., & Jasko, R. E. 2018, ApJ, 868, 47, doi: 10.3847/1538-4357/aae839
  * Kraft et al. (1991) Kraft, R. P., Burrows, D. N., & Nousek, J. A. 1991, ApJ, 374, 344, doi: 10.1086/170124
  * Lacy et al. (2020) Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001, doi: 10.1088/1538-3873/ab63eb
  * Liu et al. (2006) Liu, Q. Z., van Paradijs, J., & van den Heuvel, E. P. J. 2006, A&A, 455, 1165, doi: 10.1051/0004-6361:20064987
  * Liu et al. (2007) —. 2007, A&A, 469, 807, doi: 10.1051/0004-6361:20077303
  * Luo et al. (2017) Luo, B., Brandt, W. N., Xue, Y. Q., et al. 2017, ApJS, 228, 2, doi: 10.3847/1538-4365/228/1/2
  * Manchester et al. (2005) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, AJ, 129, 1993, doi: 10.1086/428488
  * Markwardt et al. (2003) Markwardt, C. B., Ransom, S., Woods, P., et al. 2003, The Astronomer’s Telegram, 188, 1
  * Merc et al. (2019) Merc, J., Gális, R., & Wolf, M. 2019, Research Notes of the American Astronomical Society, 3, 28, doi: 10.3847/2515-5172/ab0429
  * Monet et al. (2003) Monet, D. G., Levine, S. E., Canzian, B., et al. 2003, AJ, 125, 984, doi: 10.1086/345888
  * Muno et al. (2008) Muno, M. P., Gaensler, B. M., Nechita, A., Miller, J. M., & Slane, P. O. 2008, ApJ, 680, 639, doi: 10.1086/527316
  * Muno et al. (2005a) Muno, M. P., Lu, J. R., Baganoff, F. K., et al. 2005a, ApJ, 633, 228, doi: 10.1086/444586
  * Muno et al. (2005b) Muno, M. P., Pfahl, E., Baganoff, F. K., et al. 2005b, ApJ, 622, L113, doi: 10.1086/429721
  * Mushotzky et al. (2019) Mushotzky, R., Aird, J., Barger, A. J., et al. 2019, in Bulletin of the American Astronomical Society, Vol. 51, 107.  https://arxiv.org/abs/1903.04083
  * Nandra et al. (2013) Nandra, K., Barret, D., Barcons, X., et al. 2013, arXiv e-prints, arXiv:1306.2307.  https://arxiv.org/abs/1306.2307
  * Nebot Gómez-Morán & Oskinova (2018) Nebot Gómez-Morán, A., & Oskinova, L. M. 2018, A&A, 620, A89, doi: 10.1051/0004-6361/201833453
  * Nebot Gómez-Morán et al. (2013) Nebot Gómez-Morán, A., Motch, C., Barcons, X., et al. 2013, A&A, 553, A12, doi: 10.1051/0004-6361/201220308
  * Ng et al. (2008) Ng, C. Y., Slane, P. O., Gaensler, B. M., & Hughes, J. P. 2008, ApJ, 686, 508, doi: 10.1086/591146
  * Ochsenbein et al. (2000) Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23, doi: 10.1051/aas:2000169
  * O’Connor et al. (2022) O’Connor, B., Göğüş, E., Huppenkothen, D., et al. 2022, ApJ, 927, 139, doi: 10.3847/1538-4357/ac5032
  * O’Connor et al. (2023a) O’Connor, B., Brink, J., Buckley, D. A. H., et al. 2023a, arXiv e-prints, arXiv:2306.05576, doi: 10.48550/arXiv.2306.05576
  * O’Connor et al. (2023b) O’Connor, B., Göğüş, E., Hare, J., et al. 2023b, MNRAS, 525, 5015, doi: 10.1093/mnras/stad2633
  * Olausen & Kaspi (2014) Olausen, S. A., & Kaspi, V. M. 2014, ApJS, 212, 6, doi: 10.1088/0067-0049/212/1/6
  * Polidan et al. (1978) Polidan, R. S., Pollard, G. S. G., Sanford, P. W., & Locke, M. C. 1978, Nature, 275, 296, doi: 10.1038/275296a0
  * Pretorius et al. (2013) Pretorius, M. L., Knigge, C., & Schwope, A. D. 2013, MNRAS, 432, 570, doi: 10.1093/mnras/stt499
  * Revnivtsev et al. (2009) Revnivtsev, M., Sazonov, S., Churazov, E., et al. 2009, Nature, 458, 1142, doi: 10.1038/nature07946
  * Reynolds et al. (2013) Reynolds, M. T., Miller, J. M., Maitra, D., et al. 2013, The Astronomer’s Telegram, 5200, 1
  * Rigoselli et al. (2022) Rigoselli, M., Mereghetti, S., & Tresoldi, C. 2022, MNRAS, 509, 1217, doi: 10.1093/mnras/stab2974
  * Shaw et al. (2020) Shaw, A. W., Heinke, C. O., Maccarone, T. J., et al. 2020, MNRAS, 492, 4344, doi: 10.1093/mnras/staa105
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163, doi: 10.1086/498708
  * Sugizaki et al. (2001) Sugizaki, M., Mitsuda, K., Kaneda, H., et al. 2001, ApJS, 134, 77, doi: 10.1086/320358
  * Tranin et al. (2022) Tranin, H., Godet, O., Webb, N., & Primorac, D. 2022, A&A, 657, A138, doi: 10.1051/0004-6361/202141259
  * Traulsen et al. (2020) Traulsen, I., Schwope, A. D., Lamer, G., et al. 2020, A&A, 641, A137, doi: 10.1051/0004-6361/202037706
  * Ueda et al. (1999) Ueda, Y., Takahashi, T., Inoue, H., et al. 1999, ApJ, 518, 656, doi: 10.1086/307291
  * Wang et al. (2002) Wang, Q. D., Gotthelf, E. V., & Lang, C. C. 2002, Nature, 415, 148, doi: 10.1038/415148a
  * Webb et al. (2020) Webb, N. A., Coriat, M., Traulsen, I., et al. 2020, A&A, 641, A136, doi: 10.1051/0004-6361/201937353
  * Wenger et al. (2000) Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9, doi: 10.1051/aas:2000332
  * Wijnands et al. (2006) Wijnands, R., in’t Zand, J. J. M., Rupen, M., et al. 2006, A&A, 449, 1117, doi: 10.1051/0004-6361:20054129
  * Willingale et al. (2013) Willingale, R., Starling, R. L. C., Beardmore, A. P., Tanvir, N. R., & O’Brien, P. T. 2013, MNRAS, 431, 394, doi: 10.1093/mnras/stt175
  * Yang et al. (2022) Yang, H., Hare, J., Kargaltsev, O., et al. 2022, ApJ, 941, 104, doi: 10.3847/1538-4357/ac952b
  * Yang et al. (2021) Yang, H., Hare, J., Volkov, I., & Kargaltsev, O. 2021, Research Notes of the American Astronomical Society, 5, 102, doi: 10.3847/2515-5172/abfcd4
  * Zhang et al. (2022) Zhang, W., Basu-Zych, A., Bautz, M., et al. 2022, in AAS/High Energy Astrophysics Division, Vol. 54, AAS/High Energy Astrophysics Division, 108.45


* [5] J. Burbea, Motions of vortex patches, Letters in Mathematical Physics 6 (1982), no. 1, 1–16.
  * [6] A. Castro, D. Córdoba, J. Gómez-Serrano, Uniformly rotating analytic global patch solutions for active scalars, Annals of PDE 2 (2016), no. 1, 1–34.
  * [7] A. Constantin, W. Strauss, E. Varvaruca, Global bifurcation of steady gravity water waves with critical layers, Acta Mathematica 217 (2016), no. 2, 195–262.
  * [8] G. H. Cottet, P. A. Raviart, Particle methods for the 1-D Vlasov-Poisson equations, SIAM Journal on Numerical Analysis 21 (1984), no. 1, 52–76.
  * [9] M. G. Crandall, P. H. Rabinowitz, Bifurcation from simple eigenvalues, Journal of Functional Analysis 8 (1971), 321–340.
  * [10] E. N. Dancer, Bifurcation theory for analytic operators, Proceedings of London Mathematical Society 26 (1973), 359–384.
  * [11] G. S. Deem, N. J. Zabusky, Vortex waves : Stationary ”V-states”, Interactions, Recurrence, and Breaking, Physical Review Letters 40 (1978), no. 13, 859–862.
  * [12] D. G. Dritschel, T. Hmidi, C. Renault, Imperfect bifurcation for the shallow-water quasi-geostrophic equations, Archive for Rational Mechanics and Analysis 231 (2019), no. 3, 1853–1915.
  * [13] R. S. Dziurzynski, Patches of electrons and electron sheets for the 1-D Vlasov-Poisson equation, PhD thesis University of California, Berkeley, (1987).
  * [14] A. Gagnebin, M. Iacobelli, Landau damping on the torus for the Vlasov-Poisson system with massless electrons, arXiv:2209.04676.
  * [15] C. García, Z. Hassainia, E. Roulley, Dynamics of vortex cap solutions on the rotating unit sphere, arXiv:2306.00154.
  * [16] C. García, T. Hmidi, J. Mateu, Time Periodic Solutions for 3D Quasi-Geostrophic Model, Communications in Mathematical Physics 390 (2022), no. 2, 617–756.
  * [17] C. García, T. Hmidi, J. Mateu, Time periodic doubly connected solutions for the 3D quasi-geostrophic model, arXiv:2206.10197.
  * [18] C. García, T. Hmidi, J. Mateu, Time periodic solutions close to localized radial monotone profiles for the 2D Euler equations, arXiv:2302.01279.
  * [19] J. Gómez-Serrano, On the existence of stationary patches, Advances in Mathematics 343 (2019), 110–140.
  * [20] Z. Hassainia, T. Hmidi, On the V-states for the generalized quasi-geostrophic equations, Comm. Math. Phys. 337 (2015), no. 1, 321–377.
  * [21] Z. Hassainia, T. Hmidi, F. de la Hoz, Doubly connected V-states for the generalized surface quasi-geostrophic equations, Archive for Rational Mechanics and Analysis 220 (2016) 1209–1281.
  * [22] Z. Hassainia, T. Hmidi, F. de la Hoz, J. Mateu, An analytical and numerical study of steady patches in the disc, Analysis and PDE 9 (2015), no. 10.
  * [23] Z. Hassainia, N. Masmoudi, M. H. Wheeler, Global bifurcation of rotating vortex patches, Communications on Pure and Applied Mathematics Vol. LXXIII (2020), 1933–1980.
  * [24] T. Hmidi, F. de la Hoz, J. Mateu, J. Verdera, Doubly connected V-states for the planar Euler equations, SIAM J. Math. Anal. 48 (2016), no. 3, 1892–1928.
  * [25] T. Hmidi, J. Mateu, Bifurcation of rotating patches from Kirchhoff vortices, Discrete and Continuous Dynamical Systems 36 (2016), no. 10, 5401–5422.
  * [26] T. Hmidi, J. Mateu, Degenerate bifurcation of the rotating patches, Advances in Mathematics 302 (2016), 799–850.
  * [27] T. Hmidi, J. Mateu, J. Verdera, On rotating doubly connected vortices, Journal of Differential Equations 258 (2015), no. 4, 1395–1429.
  * [28] T. Hmidi, C. Renault, Existence of small loops in a bifurcation diagram near degenerate eigenvalues, Nonlinearity 30 (2017), no. 10, 3821–3852.
  * [29] T. Hmidi, L. Xue, Z. Xue, Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc, arXiv:2210.08760, (2022).
  * [30] H. Kielhöfer, Bifurcation Theory: An Introduction With Applications to Partial Differential Equations, Springer (2011).
  * [31] T. Levi-Civita, Détermination rigoureuse des ondes permanentes d’ampleur finie, Mathematische Annalen 93 (1925), 264–314.
  * [32] P. Liu, J. Shi, A degenerate bifurcation from simple eigenvalue theorem, Electronic Research Archive 30 (2022), no. 1, 116–126.
  * [33] C. Mouhot, C. Villani, On Landau damping, Acta Mathematica 207 (2011), no. 1, 29–201.
  * [34] A. Nekrasov, On steady waves, Ivanovo-Voznesenk Polytechnic Institute 3 (1921).
  * [35] C. Renault, Relative equilibria with holes for the surface quasi-geostrophic equations, Journal of Differential Equations 263 (2017), no. 1, 567–614.
  * [36] E. Roulley, Vortex rigid motion in quasi-geostrophic shallow-water equations, Asymptotic Analysis 133 (2022), 397–446.
  * [37] E. Roulley, Periodic and quasi-periodic Euler-$\alpha$ flows close to Rankine vortices, arXiv:2208.13109. To appear in Dynamics of Partial Differential Equations.
  * [38] J. Shi, Persistence and Bifurcation of Degenerate Solutions, Journal of Functional Analysis 169 (1999), 494–531.
  * [39] G. Stokes, On the theory of oscillatory waves, Transactions of the Cambridge Philosophical Society 8 (1847), 441–455.
  * [40] D. Struik, Détermination rigoureuse des ondes irrotationelles périodiques dans un canal à profondeur finie, Mathematische Annalen 95 (1926), 595–634.
  * [41] Y. Yudovich, Nonstationary flow of an ideal incompressible liquid, USSR Computational Mathematics and Mathematical Physics 3 (1963), 1032–1066.