# PEARLS: NuSTAR and XMM-Newton Extragalactic Survey of the JWST North
Ecliptic Pole Time-Domain Field II

Xiurui Zhao Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Francesca Civano NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Christopher N. A. Willmer Steward
Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721,
USA  Silvia Bonoli Donostia International Physics Center (DIPC), Manuel
Lardizabal Ibilbidea, 4, San Sebastian, Spain  Ikerbasque, Basque Foundation
for Science, E-48013 Bilbao, Spain  Chien-Ting Chen Science and Technology
Institute, Universities Space Research Association, Huntsville, AL 35805, USA
Astrophysics Office, NASA Marshall Space Flight Center, ST12, Huntsville, AL
35812, USA  Samantha Creech  Department of Physics & Astronomy, University of
Utah, 115 South 1400 East, Salt Lake City, UT 84112, USA  Renato Dupke
Observatório Nacional, Rua General José Cristino, 77, São Cristóvão,
20921-400, Rio de Janeiro, RJ, Brazil  Department of Astronomy, University of
Michigan, 311 West Hall, 1085 South University Ave., Ann Arbor, MI 48109, USA
Department of Physics and Astronomy, University of Alabama, Box 870324,
Tuscaloosa, AL 35487-0324, USA  Francesca M. Fornasini Department of Physics
and Astronomy, Stonehill College, 320 Washington Street, Easton, MA 02357, USA
Rolf A. Jansen School of Earth and Space Exploration, Arizona State
University, P.O. Box 871404, Tempe, AZ 85287-1404, USA  Satoshi Kikuta
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan  Anton M. Koekemoer Space Telescope Science Institute, 3700
San Martin Drive, Baltimore, MD 21218, USA  Sibasish Laha Center for Space
Science and Technology, University of Maryland Baltimore County, 1000 Hilltop
Circle, Baltimore, MD 21250, USA  NASA Goddard Space Flight Center, Greenbelt,
MD 20771, USA  Stefano Marchesi Dipartimento di Fisica e Astronomia (DIFA),
Università di Bologna, via Gobetti 93/2, I-40129 Bologna, Italy  Department of
Physics and Astronomy, Clemson University, Kinard Lab of Physics, Clemson, SC
29634, USA  INAF, Osservatorio di Astrofisica e Scienza dello Spazio di
Bologna, via P. Gobetti 93/3, 40129 Bologna, Italy  Rosalia O’Brien School of
Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404,
USA  Ross Silver NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
S. P. Willner Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Rogier A. Windhorst School of Earth and
Space Exploration, Arizona State University, P.O. Box 871404, Tempe, AZ
85287-1404, USA  Haojing Yan Department of Physics and Astronomy, University
of Missouri, Columbia, MO 65211, USA  Jailson Alcaniz Observatório Nacional,
Rua General José Cristino, 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ,
Brazil  Narciso Benitez Saulo Carneiro Instituto de Física, Universidade
Federal da Bahia, 40210-340, Salvador, BA, Brazil  Javier Cenarro  Centro de
Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001,
Teruel, Spain  David Cristóbal-Hornillos  Centro de Estudios de Física del
Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001, Teruel, Spain
Alessandro Ederoclite Centro de Estudios de Física del Cosmos de Aragón
(CEFCA), Plaza San Juan, 1, E-44001, Teruel, Spain  Antonio Hernán-Caballero
Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1,
E-44001, Teruel, Spain  Carlos López-Sanjuan Centro de Estudios de Física del
Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001, Teruel, Spain  Antonio
Marín-Franch Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza
San Juan, 1, E-44001, Teruel, Spain  Claudia Mendes de Oliveira Departamento
de Astronomia, Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Universidade de São Paulo, São Paulo, Brazil  Mariano Moles  Centro de
Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001,
Teruel, Spain  Laerte Sodré Jr. IAG/USP - Departamento de Astronomia,
Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de
São Paulo, São Paulo, Brazi  Keith Taylor  Instruments4, 4121 Pembury Place,
La Canada Flintridge, CA 91011, U.S.A.  Jesús Varela Centro de Estudios de
Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001, Teruel, Spain
Héctor Vázquez Ramió Centro de Estudios de Física del Cosmos de Aragón
(CEFCA), Plaza San Juan, 1, E-44001, Teruel, Spain

###### Abstract

We present the second NuSTAR and XMM-Newton extragalactic survey of the JWST
North Ecliptic Pole (NEP) Time-Domain Field (TDF). The first NuSTAR NEP-TDF
survey (Zhao et al. 2021) had 681 ks total exposure time executed in NuSTAR
cycle 5, in 2019 and 2020. This second survey, acquired from 2020 to 2022 in
cycle 6, adds 880 ks of NuSTAR exposure time. The overall NuSTAR NEP-TDF
survey is the most sensitive NuSTAR extragalactic survey to date, and a total
of 60 sources were detected above the 95% reliability threshold. We constrain
the hard X-ray number counts, $\log N$–$\log S$, down to $1.7\times 10^{-14}$
erg cm-2 s-1 at 8–24 keV and detect an excess of hard X-ray sources at the
faint end. About 47% of the NuSTAR-detected sources are heavily obscured
($N\rm_{H}>10^{23}$ cm-2), and $18_{-8}^{+20}$% of the NuSTAR-detected sources
are Compton-thick ($N\rm_{H}>10^{24}$ cm-2). These fractions are consistent
with those measured in other NuSTAR surveys. Four sources presented
${>}2\sigma$ variability in the 3-year survey. In addition to NuSTAR, a total
of 62 ks of XMM-Newton observations were taken during NuSTAR cycle 6. The XMM-
Newton observations provide soft X-ray (0.5–10 keV) coverage in the same field
and enable more robust identification of the visible and infrared counterparts
of the NuSTAR-detected sources. A total of 286 soft X-ray sources were
detected, out of which 214 XMM-Newton sources have secure counterparts from
multiwavelength catalogs.

X-ray surveys(1824), Active galactic nuclei(16)

††facilities: NuSTAR, XMM-Newton, Chandra, MMT (Binospec, Hectospec, and
MMIRS), JWST, HST, Subaru/HSC, SDSS, J-PAS, WISE

##  1 Introduction

The Nuclear Spectroscopic Telescope Array (NuSTAR) mission, launched in June
2012, is the first telescope focusing hard X-rays (3–79 keV; Harrison et al.,
2013). The 100 times deeper hard X-ray sensitivity of NuSTAR compared with the
previous collimated or coded mask instruments allows the peak (20–40 keV) of
the Cosmic X-ray background (CXB) to be resolved into individual objects.
Indeed, about 35–60% of the CXB at 8–24 keV was resolved by previous NuSTAR
extragalactic surveys (Hickox et al., in prep).

NuSTAR performed a series of extragalactic surveys in its first two-year
baseline mission to probe AGN activity over cosmic time. The surveys followed
a wedding cake strategy covering from small areas with deep exposures and
broader surveys with shallow exposures (see, Zhao et al., 2021a, hereafter
Z21, for an overview).

JWST, successfully launched on Dec. 25, 2021, is a NASA/ESA/CSA Flagship
mission focusing on near- and mid-infrared wavelengths (0.6–28.5 $\mu$m) with
its 6.5 m aperture and state-of-the-art scientific instruments (Gardner et
al., 2006, 2023). JWST Interdisciplinary Scientist (IDS) R. Windhorst
allocated $\sim$47 hours of his guaranteed time to the North Ecliptic Pole
(NEP) time-domain field (TDF) is part of the “Prime Extragalactic Areas for
Reionization and Lensing Science” (PEARLS) project (GTO-2738; Windhorst et
al., 2023). JWST has observed this field in four orthogonal spikes in cycle 1.
Each observation includes eight filters of NIRCam observations and coordinated
parallel observations with NIRISS/WFSS. This field was selected to be located
within the JWST northern continuous viewing zone (CVZ) to enable time-domain
studies. Furthermore, this NEP-TDF has the best combination of low foreground
extinction and absence of AB$\leq$16 mag stars (Jansen & Windhorst, 2018). The
NEP-TDF has become a comprehensive multiwavelength survey.111A comprehensive
table can be found at http://lambda.la.asu.edu/jwst/neptdf/ The
multiwavelength coverage of the NEP-TDF approved to date is presented in Table
1.

Table 1: Approved NEP-TDF multiwavelength surveys. Telescope | PI | Exposure | Reference
---|---|---|---
NuSTAR | F. Civano | 3.3 Ms | Zhao et al. (2021a)
XMM-Newton | F. Civano | 120 ks | Zhao et al. (2021a)
Chandra | W. P. Maksym | 1.8 Ms | Maksym et al., in prep.
AstroSat/UVIT | K. Saha | 98 hrs |
HST/WFC3+ACS | R. Jansen & N. Grogin | 173 hrs |  O’Brien et al. (2024), Jansen et al., in prep.
LBT/LBC | R. Jansen | 11 hrs |
Subaru/HSC | G. Hasinger & E. Hu | 5 hrs | Taylor et al. (2023)
GTC/HiPERCAM | V. Dhillon | 16 hrs |
TESS | G. Berriman & B. Holwerda | 357 days |
MMT/MMIRS | C. N. A. Willmer | 68 hrs | Willmer et al. (2023)
JWST/NIRCam+NIRISS | R. A. Windhorst & H. B. Hammel | 49 hrs | Windhorst et al. (2023); Adams et al. (2023)
JCMT/SCUBA-2 | I. Smail & M. Im | 63 hrs | Hyun et al. (2023)
IRAM/NIKA 2 | S. H. Cohen | 30 hrs |
SMA | G. Fazio | 112 hrs |
VLA | R. A. Windhorst & W. Cotton | 47 hrs | Hyun et al. (2023); Willner et al. (2023)
VLBA | W. Brisken | 137 hrs |
eMERLIN | A. Thomson | 140 hrs |
LOFAR | R. Van Weeren | 72 hrs |
Spectroscopic |  |  |
J-PAS (56 filters) | S. Bonoli & R. Dupke | 29 hrs | Hernán-Caballero et al. (2023)
MMT/Binospec | C. N. A.Willmer | 26 hrs | Willmer et al., in prep.
MMT/MMIRS | C. N. A. Willmer | 11 hrs | Willmer et al., in prep.

This paper presents the multi-year NuSTAR and XMM-Newton extragalactic survey
in the NEP-TDF. The paper’s focus is the two X-ray source catalogs. The paper
is organized as follows. Section 2 describes the NuSTAR data reduction.
Section 3 describes the construction of simulated data and the resulting
reliability, completeness, sensitivity, positional uncertainty, and input-
measured relation of the NuSTAR NEP-TDF survey. Section 4 presents the NuSTAR
source catalog. Section 5 describes our XMM-Newton source detection and
astrometric corrections, the sensitivity, and the XMM-Newton catalog including
matching with NuSTAR. Section 6 describes matching XMM-Newton sources to
existing visible-wavelength and infrared (IR) catalogs using a maximum-
likelihood method. We present the X-ray to optical properties of these
sources. Section 7 discusses the number counts of the sources as a function of
flux, the X-ray hardness ratios, and the Compton-thick (CT) fraction. The
Appendixes present the source catalogs of both the NuSTAR and XMM-Newton NEP-
TDF surveys, spectroscopic redshifts of some VLA and Chandra detected sources
in the NEP-TDF, and a newly developed pipeline to analyze source variability
of NuSTAR observations.

Uncertainties are quoted at a 90% confidence level throughout the paper unless
otherwise stated. Magnitudes used here are in the AB system, and standard
cosmological parameters are adopted as follows: $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{M}=0.30$, and $\Omega_{\Lambda}=0.70$.

##  2 NuSTAR data processing

NuSTAR (3–24 keV) surveyed the NEP-TDF in both cycle 5 (PI: Civano, ID: 5192)
and cycle 6 (PI: Civano, ID: 6218, two-year program). The cycle 5 results were
published (Z21). This work focused on the cycle 6 and the combined cycles 5
and 6 data. The NuSTAR cycle 6 NEP-TDF survey comprises 12 observations taken
in four epochs spanning from 2020 Oct. to 2022 Jan. with a total of 880 ks
exposure time. The cycle 6 survey was designed with a primary focus on
variability, and therefore each epoch’s observations pointed to the same area
with similar effective position angles.222NuSTAR reaches similar effective
position angles every 3 month due to its square CCD, but the source might lie
on different sub-detectors in different epochs. Table 2 presents the details
of the individual NuSTAR observations in cycle 5 and cycle 6. This work,
following previous NuSTAR extragalactic surveys, focuses on the 3–24 keV band
because only the brightest sources can be detected at $>$24 keV owing to the
decrease of the effective area and significant increase of the background at
$>$24 keV (e.g., Masini et al., 2018a).

###  2.1 Data Reduction

Table 2: List of NuSTAR and XMM-Newton observations. ObsID | Date | R.A. | Dec. | Exp.
---|---|---|---|---
|  | (deg) | (deg) | (ks)
Cycle 5 NuSTAR |  |  |  |
60511001002 | 2019-09-30 | 260.8664 | 65.8298 | 73.5
60511002002 | 2019-10-02 | 260.7643 | 65.8305 | 77.6
60511003002 | 2019-10-04 | 260.6297 | 65.8316 | 68.7
60511004002 | 2020-01-03 | 260.4992 | 65.9184 | 89.8
60511005002 | 2020-01-04 | 260.7289 | 65.8757 | 84.7
60511006002 | 2020-01-05 | 260.8676 | 65.9159 | 83.0
60511007002 | 2020-03-01 | 260.5070 | 65.7602 | 65.2
60511008001 | 2020-03-02 | 260.7292 | 65.7406 | 70.2
60511009001 | 2020-03-03 | 260.9369 | 65.7399 | 68.3
Total |  |  |  | 681
Cycle 6 NuSTAR |  |  |  |
60666001002 | 2020-10-18 | 260.8664 | 65.8298 | 72.8
60666002002 | 2020-10-13 | 260.6219 | 65.8075 | 71.9
60666003002 | 2020-10-15 | 260.8534 | 65.8463 | 72.7
60666004002 | 2021-01-14 | 260.6508 | 65.8776 | 76.9
60666005002 | 2021-01-17 | 260.6541 | 65.7791 | 77.5
60666006002 | 2021-01-18 | 260.8448 | 65.8204 | 80.4
60666007002 | 2021-10-12 | 260.5930 | 65.9025 | 78.1
60666008002 | 2021-10-14 | 260.5868 | 65.7996 | 49.9
60666009002 | 2021-10-15 | 260.8223 | 65.8393 | 52.7
60666010002 | 2022-01-19 | 260.6164 | 65.8882 | 80.9
60666011002 | 2022-01-22 | 260.5980 | 65.7878 | 82.9
60666012002 | 2022-01-23 | 260.8546 | 65.8173 | 82.9
Total |  |  |  | 880
Cycle 6 XMM |  |  |  |
0870860101 | 2020-10-14 | 260.6917 | 65.8711 | 17.0
0870860201 | 2021-01-16 | 260.6917 | 65.8711 | 23.2
0870860301aaThis observation was entirely lost to high particle background during the observation. | 2021-10-14 | 260.6917 | 65.8711 | 0∗
0870860401 | 2022-01-24 | 260.6917 | 65.8711 | 21.9
Total |  |  |  | 62

The reduction of the cycle 6 observations used the same method as for the
cycle 5 data (Z21). In brief, the NuSTAR data were processed using HEASoft
v.6.29c and NuSTAR Data Analysis Software (NuSTARDAS) v.2.1.1 with the updated
calibration and response files CALDB v.20211115. The level 1 raw data were
calibrated, cleaned, and screened by running the nupipeline tool. Following
Z21, we removed the high-background time intervals (when the count rate in the
3.5–9.5 keV band was at least double the average count rate of the entire
observation) in each observation. The total exposure losses of the two NuSTAR
focal plane modules (FPMs) due to the high background were 6.5 ks and 8 ks for
FPMA and FPMB, respectively, corresponding to 0.8% of the entire cycle 6
NuSTAR NEP-TDF survey exposures.

###  2.2 Exposure Map Production

We generated the vignetting-corrected exposure map of each NuSTAR observation
in three energy bands: 3–24 keV, 3–8 keV, and 8–24 keV using the NuSTARDAS
tool nuexpomap. The exposure map of the entire cycle 6 survey was produced by
merging the 12 individual maps into a mosaic. That included merging the two
FPMs’ observations as FPMA+B. Figure 1 shows the cumulative areas as a
function of the vignetting-corrected exposure in the three energy bands. The
cycle 6 survey repeatedly observed the same region, so its exposure is
$\sim$60% deeper than the cycle 5 survey (Figure 1) but with $\sim$35% smaller
area coverage ($\sim$0.107 deg2 in cycle 6 compared with $\sim$0.16 deg2 in
cycle 5). To achieve the deepest exposure, we also merged the cycle 5 and
cycle 6 observations to achieve a central exposure time of $\approx$1.7 Ms
(FPMA+B). We used the 8–24 keV exposure map to present the 8–16 keV, and 16–24
keV exposure maps as they show only marginal differences.

Figure 1: Cumulative survey area as a function of the FPMA+B vignetting-
corrected exposure time. Colors distinguish the NuSTAR NEP-TDF surveys in
cycle 5 (blue), cycle 6 (red), and combined cycles 5+6 (black), and line types
distinguish energy bands as shown in the legend.

Figure 2: NuSTAR FPMA+B 3–24 keV mosaics of cycle 6 (left) and cycles 5+6
(right) observations. The NuSTAR-detected sources with (black circles, 25″
radius) and without (black squares, 45″ width) soft X-ray counterparts are
marked. Labels are source IDs in the respective catalogs.

###  2.3 Observation Mosaic Creation

For each of the 12 cycle 6 observations, summed FPMA+B mosaics were created in
five energy bands: 3–24 keV, 3–8 keV, 8–24 keV, 8–16 keV, and 16–24 keV. The
five bands were separated using the HEASoft Xselect tool. Each band was then
merged into a full-exposure mosaic using the Ximage tool. Loss of spatial
resolution due to the resampling is negligible because the pixel angular
resolution ($None$) of the standard NuSTAR sky binning by NuSTARDAS is much
smaller than the $\sim$18″ full width at half-maximum (FWHM) of NuSTAR. The
cycle 6 mosaic was also merged with the cycle 5 mosaic to achieve the deepest
sensitivity. The astrometric offsets of the NuSTAR NEP-TDF survey could not be
measured reliably due to the limited number of bright sources in the field,
but the previous NuSTAR COSMOS survey (Civano et al., 2015) found a NuSTAR
astrometric offset of 1″–7″, small compared to the NuSTAR FWHM. Therefore,
astrometric offsets should only marginally affect our results (Civano et al.,
2015), and we did not apply any astrometric correction when merging the
observations. (In any case, there is only one bright source in the FoV that
could have been used for astrometric correction.) Figure 2 shows the 3–24 keV
FPMA+B merged mosaics.

###  2.4 Background Map Production

The background map was used for both source detection and simulation. The
background of NuSTAR is spatially non-uniform across the field of view (FoV)
and is variable among different observations, adding complexities when
producing the background maps. We used the
nuskybgd333https://github.com/NuSTAR/nuskybgd package (Wik et al., 2014),
which was used for all previous NuSTAR extragalactic surveys, to produce
background maps of each cycle 6 observation following the same method as Z21.
We merged the cycle 6 background maps into an FPMA+B mosaic, which was then
merged with the cycle 5 mosaic into a cycles 5+6 mosaic.

To test the accuracy of the generated background maps, we compared the number
of counts in the observed images and the corresponding background maps. As the
background dominates the observation in most areas, the observed numbers of
counts should be consistent except for the regions where (bright) X-ray
sources exist. The comparison was based on 64 circular, 45″-radius regions
across the FoV in each observation, and the mean difference between the
observed images (Data) and the background maps (Bgd) is $\rm(Data-
Bgd)/Bgd=-0.7\%$ and 2.0% for FPMA and FPMB, respectively. The standard
deviations of the differences are 12.2% and 13.8% for FPMA and FPMB,
respectively. These suggest good modeling of the NuSTAR background and are
consistent with the accuracy obtained in cycle 5 (Z21) and by Civano et al.
(2015).

##  3 NuSTAR Simulations

Comprehensive simulations in each energy band (3–24 keV, 3–8 keV, 8–24 keV,
8–16 keV, and 16–24 keV) were used to (1) determine the reliability and
completeness of our source detection technique and the resulting source
catalogs, (2) measure the sensitivity of the surveys, and (3) demonstrate the
quality of our source detection technique by comparing the input and measured
source properties (e.g., positions and fluxes).

Table 3: Source detections in simulated and real data | 3–24 keV | 3–8 keV | 8–24 keV | 8–16 keV | 16–24 keV |
---|---|---|---|---|---|---
|  | Cycle 6 |  |  |  |
Simulations |  |  |  |  |  |
Detections in each simulated map | 53 | 51 | 49 | 49 | 43 |
Detections matched to input catalog | 38 | 36 | 29 | 29 | 16 |
DET ML$>$95% reliability threshold | 20.9 | 17.4 | 8.2 | 9.0 | 0.6 |
Real Data |  |  |  |  |  | Total
DET ML$>$95% reliability threshold | 28 | 24 | 13 | 15 | 3 | 35
|  | Cycles 5+6 |  |  |  |
Simulations |  |  |  |  |  |
Detections in each simulated map | 80 | 78 | 74 | 72 | 63 |
Detections matched to input catalog | 57 | 53 | 43 | 44 | 24 |
DET ML$>$95% reliability threshold | 32.9 | 27.7 | 14.1 | 15.9 | 1.3 |
Real Data |  |  |  |  |  | Total
DET ML$>$95% reliability threshold | 45 | 32 | 24 | 26 | 2 | 60

###  3.1 Generating Simulated Observations

We generated simulated observations in the five energy bands following Z21’s
procedure. To summarize, each iteration randomly places mock sources on the
background maps described in Section 2.4. The fluxes of the mock sources were
randomly assigned following the X-ray source flux distribution ($\log N$–$\log
S$) measured by Treister et al. (2009). The minimum fluxes in the 3–24 keV
bands were $3\times 10^{-15}$ erg cm-2 s-1 for cycle 6 and $2\times 10^{-15}$
erg cm-2 s-1 for cycle 5+6, about 10 times fainter than the expected limits of
each survey. Adopting a much fainter flux limit than the sensitivity of the
survey would result in many mismatched measured and input sources and produce
an incorrect reliability curve of source detection. The fluxes of the input
sources in each energy band were extrapolated from their 3–24 keV fluxes
assuming an absorbed power-law model with photon index $\Gamma=1.80$ and a
Galactic absorption $N\rm_{H}=3.4\times 10^{20}$ cm-2 (HI4PI Collaboration et
al., 2016). The fluxes were converted to count rates using conversion factors
(CF) of 4.86, 3.39, 7.08, 5.17, and $16.2\times 10^{-11}$ erg cm-2 count-1 in
the 3–24, 3–8, 8–24, 8–16, and 16–24 keV bands, respectively. The CF was
computed using WebPIMMS444https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3pimms/w3pimms.pl assuming the above spectral model. The simulated
observations of each exposure were then merged into mosaics in five energy
bands for both FPMA and FPMB, which were then combined into FPMA+B mosaics. We
used 1200 simulations for the NuSTAR NEP-TDF cycle 6 survey and 2400 for the
combined cycles 5+6 survey.

Figure 3: Left column: Reliability (equation 1) as a function of DET_ML. Right
column: Completeness (equation 2) at 95% reliability as a function of flux.
All values come from the cycle 6 simulations described in Section 3. Panels
from top to bottom show four different exposure-time ranges, as labeled. Line
types indicate energy ranges as indicated in the legends in the top panels.
Dotted horizontal lines in the left panels show 95% and 99% reliability.

Figure 4: Left column: Reliability (equation 1) as a function of DET_ML. Right
column: Completeness (equation 2) at 95% reliability as a function of flux.
All values come from the cycle 5+6 simulations described in Section 3. Panels
from top to bottom show four different exposure-time ranges, as labeled. Line
types indicate energy ranges as indicated in the legends in the top panels.
Dotted horizontal lines in the left panels show 95% and 99% reliability.

###  3.2 Source Detection on Simulated Observations

We performed source detection on the simulated cycle 6 and cycles 5+6 FPMA+B
mosaics using the technique developed by Mullaney et al. (2015). In summary,
source detection used SExtractor (Bertin & Arnouts, 1996) on the false-
probability maps produced by the simulated observations and background maps.
We defined the maximum likelihood (DET ML) of each detection, which measured
the chance that the detection is from the background fluctuation rather than
from a real source. A higher DET ML suggests a lower chance that the detection
is from the background fluctuation. Further details were described by Z21.

Table 4: DET_ML values required for 95% reliability | 3–24 keV | 3–8 keV | 8–24 keV | 8–16 keV | 16–24 keV
---|---|---|---|---|---
|  | Cycle 6 |  |  |
DET ML(20–200 ks) threshold | 11.77 | 11.83 | 12.93 | 12.83 | 15.58
DET ML(200–400 ks) threshold | 10.26 | 10.18 | 11.83 | 11.43 | 14.74
DET ML(400–800 ks) threshold | 9.68 | 9.78 | 11.24 | 10.70 | 14.44
DET ML(800-1100 ks) threshold | 8.67 | 8.79 | 10.37 | 9.99 | 14.26
|  | Cycles 5+6 |  |  |
DET ML(20–80 ks) threshold | 12.29 | 12.25 | 13.74 | 13.40 | 16.08
DET ML(80–200 ks) threshold | 11.70 | 11.85 | 12.77 | 12.46 | 14.95
DET ML(200–500 ks) threshold | 10.24 | 10.26 | 11.62 | 11.08 | 14.87
DET ML(500–1000 ks) threshold | 9.28 | 9.40 | 10.88 | 10.26 | 13.78
DET ML(1000-1800 ks) threshold | 8.10 | 8.50 | 10.08 | 9.53 | 13.36

The measured counts associated with a detected source might be contaminated by
other sources within 90″, corresponding to 85–90% encircled energy fraction
(EEF) of the NuSTAR point spread function (PSF). Therefore, we applied a
deblending process to the detected sources in each simulation following
Mullaney et al. (2015). The deblended source counts and background counts were
then used to update DET ML values for each detection.

The detections with the updated DET ML of each simulation were then matched
with the input catalog using a 30″ search radius. The average numbers of the
sources detected and matched to the input catalogs in each simulation are
listed in Table 3.

###  3.3 Reliability and Completeness

To evaluate the accuracy and efficiency of the source detection in the real
observations, we used the statistics of the simulated sources described in
Section 3.2. Reliability is the ratio of true detections, i.e., matching input
sources, to the total number of detected sources at or above a particular
DET_ML threshold:

${\rm Rel(DET\\_ML)}=\frac{N_{\rm matched}({\geq}\rm DET\\_ML)}{N_{\rm
detected}({\geq}\rm DET\\_ML)}$ (1)

Therefore, if 99 out of 100 detected sources with $\rm DET\\_ML\geq 15$ were
matched to input sources, then the reliability of the detection at $\rm
DET\\_ML\geq 15$ is 95%. Completeness is defined as the ratio of the number of
detected true sources to the number in the input catalog at a particular flux
assuming a particular realiability:

${\rm Completeness(flux)}=\frac{N_{\rm matched\&\geq Rel\\_({\rm
flux})}}{N_{\rm input(flux)}}$ (2)

Therefore, if 90 out of 100 input sources at flux $1\times 10^{-13}$ erg
cm-2s-1 were detected above the 95% reliability level, then the completeness
of the survey at this particular flux is 90% at the 95% reliability level. A
higher reliability level requires a higher DET_ML threshold, but that leads to
lower completeness. Reliability and completeness curves obtained from the
cycle 6 and cycles 5+6 simulations are plotted in Figures 3 and 4,
respectively.

The reliability and completeness curves heavily depend on the effective
exposure time because the spurious detection rate at a given threshold
decreases exponentially with exposure. As in cycle 5, the effective exposure
time across the entire NEP-TDF cycle 6 and cycles 5+6 survey area is
nonuniform (Figure 1) because of the observing strategy. We therefore analyzed
the reliability function in different exposure intervals as given in Table 4.
The exposure intervals were selected to keep a similar number of detected
sources in each interval to achieve similar statistics, and we chose an
exposure cutoff at 20 ks to avoid potentially spurious detections on the edge
of the observations. Table 3 reports the average number of sources detected at
$>$95% reliability level in each simulation.

###  3.4 Sensitivity Curves

The effective sky coverage of the survey at a particular flux is the
completeness at that flux multiplied by the maximum covered area. For
instance, if a survey covering 0.1 deg2 has 80% completeness at a particular
flux, the survey’s effective area at that flux is 0.08 deg2. As sensitivity
depends on the exposure time, the effective sky coverage of the NEP-TDF survey
was calculated by adding up the sky-coverage curves of all different exposure
intervals (Table 5). The effective sky-coverage curves in the five energy
bands of cycle 6 and cycles 5+6 surveys are plotted in Figure 5. The half-area
and 20%-area sensitivity of the three surveys in different energy bands are
reported in Table 6.

Table 5: Areas covered with different exposure times Cycle 5 | Cycle 6 | Cycles 5+6
---|---|---
Exposure | Area | Exposure | Area | Exposure | Area
ks | deg2 | ks | deg2 | ks | deg2
20–200 | 0.091 | 20–200 | 0.026 | 20–80 | 0.034
200–500 | 0.047 | 200–400 | 0.037 | 80–200 | 0.030
500–700 | 0.019 | 400–800 | 0.030 | 200–500 | 0.033
|  | 800–1100 | 0.014 | 500–1000 | 0.033
|  |  |  | 1000–1800 | 0.031

Observations in the 8–24 keV band are unique to NuSTAR. Therefore, Figure 6
compares the 8–24 keV sensitivities of the cycle 5, cycle 6, and cycles 5+6
NEP-TDF surveys with previous NuSTAR surveys. NEP-TDF currently reaches the
deepest flux in a contiguous NuSTAR survey.

Figure 5: Sky coverage as a function of flux at the 95% reliability level. Panels from top to bottom are for the five energy bands as labeled. As indicated in the legend, different line types show different survey components. The vertical dashed line shows the half-area flux of each survey component. (At the highest energies, the cycle 5 and cycle 6 lines overlap.) Figure 6: 8–24 keV sky coverage as a function of flux in NuSTAR surveys. Different line types represent different NuSTAR extragalactic surveys as indicated in the legend.  Table 6: NuSTAR Survey Sensitivities Energy (keV) | Half-area | 20%-area
---|---|---
NuSTAR | Cycle 5/6/5+6 | Cycle 5/6/5+6
| 10-14 erg cm-2 s-1 | 10-14 erg cm-2 s-1
3–24 | 4.6/3.1/3.3 | 2.4/1.7/1.6
3–8 | 2.2/1.5/1.7 | 1.1/0.80/0.74
8–24 | 5.2/3.6/3.8 | 2.7/2.0/1.7
8–16 | 3.0/2.1/2.1 | 1.5/1.1/0.95
16–24 | 9.8/6.7/6.6 | 5.2/3.9/3.1
XMM-Newton | Cycle 6 | Cycle 6
| 10-15 erg cm-2 s-1 | 10-15 erg cm-2 s-1
0.5–2 | 0.87 | 0.63
2–10 | 6.3 | 4.0

###  3.5 Positional Uncertainty

The simulations described in Section 3.1 can quantify the positional
uncertainties of the sources detected. Figure 7 shows the separations between
the detected and input-catalog positions in the cycles 5+6 survey simulations
as an example. The separation histograms follow a Rayleigh distribution
(Pineau et al., 2017). The best-fit Rayleigh scale parameter for all matched
sources are $\sigma_{\rm all,C6}$ = $None$ and $\sigma_{\rm all,C56}$ = $None$
for cycle 6 and cycles 5+6 surveys, respectively. Eliminating the faintest
sources by limiting the sample to sources detected above the 95% reliability
level gives smaller separations $\sigma_{\rm 95\%,C6}=6\farcs 6$ and
$\sigma_{\rm 95\%,C56}=6\farcs 5$. The separations are even smaller for
sources with 3–24 keV flux ${>}10^{-13}$ erg cm-2 s-1, $\sigma_{\rm
95\%,bright,C6}=3\farcs 8$ and $\sigma_{\rm 95\%,bright,C56}=3\farcs 7$. The
measured separations are consistent with the previous cycle 5 survey and other
NuSTAR extragalactic surveys, and therefore we used these distributions as the
expected positional uncertainty of real detections. The simulations did not
include the astrometric offsets, and therefore they do not reflect the full
positional uncertainty, but the effect is likely minimal.

Figure 7: Distributions of position offsets from the NuSTAR simulations of the
3–24 keV cycles 5+6 survey. Solid lines refer to the whole sample and dashed
lines refer only to sources above the 95% reliability level. The dashed red
curve shows the best Rayleigh fit to the offsets of sources above the 95%
reliability level.  Figure 8: Upper: Measured versus input 3–24 keV fluxes for
simulated sources. Lower: ratio of measured to input fluxes for the same
sources. Both panels show only sources above the 95% reliability level of the
cycles 5+6 survey. Sources in different exposure intervals are plotted in
different colors as indicated in the legend. Dashed lines in both panels show
equality. The excess at lower fluxes is due to the Eddington bias.

###  3.6 Fluxes

The fluxes of the simulated sources detected in each energy band were measured
and compared with the input fluxes to quantify the accuracy of the flux
measurement technique. We extracted the source counts and deblended background
counts of each matched source using the CIAO (Fruscione et al., 2006) tool
dmextract. The effective exposure of each source was measured from the
exposure maps (Section 2.2). The net counts were then converted to in-band
fluxes using the CF (Section 3.1). The counts were extracted in a 20″ circular
region, and we converted this aperture flux to total flux using an aperture
correction factor of $F({20\arcsec})/F_{\rm tot}=0.32$, as calculated from the
NuSTAR
PSF.555https://heasarc.gsfc.nasa.gov/docs/nustar/NuSTAR_observatory_guide-v1.0.pdf
Figure 8 shows the ratio of measured to input 3–24 keV fluxes. Flux
measurements for faint sources are over-estimated, as expected from Eddington
bias which favors the detection of faint sources with positive noise
deflections. This excess corresponds to the detection limits of the survey and
is also exposure-dependent (Figure 4). Therefore, the fluxes of the fainter
sources can be better measured with deeper exposures.

Z21 found an under-estimate of the measured fluxes for bright
($F_{3-24}>10^{-12}$ erg cm-2 s-1) sources. This was due to a computing error
when generating false probability maps where the false probability in the
center pixel of the bright sources was saturated. The bug led to an incorrect
measurement of the source position and therefore underestimating its flux.
This error did not affect the flux measurement of the real observations in the
NEP-TDF because all detected sources are much fainter than 10-12 erg cm-2 s-1.
The error is fixed in this work.

##  4 NuSTAR Source Catalog

To maximize the signal-to-noise ratio (SNR), we performed source detections on
the FPMA+B mosaics of the actual NuSTAR observations in the cycle 6 and cycles
5+6 surveys using the same detection strategy as in the simulations (Section
3.2). Source detection, requiring DET_ML above the 95% reliability level, was
performed separately in each of the five energy bands. The resulting
coordinates, source counts, background counts, DET_MLs, and vignetting-
corrected exposure times of the detected sources were then merged into a
master catalog by using a 30″ matching radius among the five energy bands. The
master catalog therefore includes all sources detected in at least one energy
band above the 95% reliability level. The coordinates of the sources reported
in the master catalog are taken from the detections that have the highest
DET_ML among the five energy bands. The positions of the sources detected in
cycle 6 and cycles 5+6 surveys are plotted in Figure 2.

The master catalog includes 35 and 60 sources for cycle 6 and cycles 5+6
surveys, respectively. The number of the sources detected above 95%
reliability level in each energy band and the merged master catalog are listed
in Table 3. Statistically, we expect about two to three spurious detections in
the 95% reliability master catalogs. Table 7 reports the number of sources
detected in each combination of energy bands.

Figure 9: Flux distributions of NuSTAR sources. Panels from left to right show
results for the cycle 5 (Z21), cycle 6, and cycles 5+6 surveys, respectively.
Panels from top to bottom show different energy bands as labeled in each
panel. Solid lines represent sources detected above the 95% reliability level
in the specific survey and band, and dashed lines represent all 60 sources
detected by NuSTAR. For sources not detected in a particular survey and energy
range, the flux plotted is the 90%-confidence upper limit.

Figure 9 shows the distribution of the source fluxes in different energy bands
from the various master catalogs. The source fluxes were calculated with the
method described in Section 3.6. For sources not detected in an energy band,
background counts were not deblended. We calculated 1$\sigma$ net count-rate
and flux uncertainties for the sources that were detected above the 95%
reliability level in a given energy band using Equations (9) and (12) of
Gehrels (1986) with $S=1$. For sources not detected above the 95% reliability
level, we calculated the 90% confidence level upper limits of net count-rates
and fluxes using Equation (9) of Gehrels (1986) with $S=1.645$.

The master catalogs of the NuSTAR detected sources in cycle 6 and cycles 5+6
surveys are made public with this paper. Table 9 explains each column in the
catalogs.

Variability detection is the prime goal of the NuSTAR NEP-TDF survey. We
developed a dedicated pipeline, briefly introduced in Appendix APPENDIX D,
using a Bayesian method to analyze the source variability in NuSTAR
observations. As a preliminary result, four sources showed variability in
cycles 5+6 at $p<$0.05 (${\sim}2\sigma$) in at least one energy band in the
26-months of observations. Systematic discussion of source variability in the
NuSTAR and XMM-Newton NEP-TDF will be presented in future work.

Table 7: Energy bands of detected sources Energy |  | Cycle 5 |  | Cycle 6 |  | Cycles 5+6
---|---|---|---|---|---|---
F+S+H |  | 9 (27%) |  | 13 (37%) |  | 17 (28%)
F+S+h |  | 6 (18%) |  | 4 (11%) |  | 5 (8%)
F+S |  | 1 (3%) |  | 2 (6%) |  | 4 (7%)
F+s+H |  | 0 (0%) |  | 2 (6%) |  | 2 (3%)
F+s+h |  | 5 (15%) |  | 5 (14%) |  | 12 (20%)
F+s |  | 3 (9%) |  | 0 (0%) |  | 0 (0%)
F+H |  | 0 (0%) |  | 2 (6%) |  | 2 (3%)
F+h |  | 2 (6%) |  | 0 (0%) |  | 1 (2%)
F |  | 0 (0%) |  | 0 (0%) |  | 1 (2%)
f+S+h |  | 1 (3%) |  | 1 (3%) |  | 1 (2%)
f+S |  | 1 (3%) |  | 2 (6%) |  | 3 (5%)
f+s+H |  | 1 (3%) |  | 0 (0%) |  | 3 (5%)
f+H |  | 2 (6%) |  | 1 (3%) |  | 2 (3%)
S+h |  | 0 (0%) |  | 1 (3%) |  | 1 (2%)
S |  | 1 (3%) |  | 1 (3%) |  | 1 (2%)
H |  | 1 (3%) |  | 1 (3%) |  | 5 (8%)
Total |  | 33 |  | 35 |  | 60

##  5 XMM-Newton NEP-TDF Survey

To provide lower-energy (0.5–10 keV) information, XMM-Newton observed the NEP-
TDF field simultaneously with the four cycle 6 NuSTAR epochs. The observations
utilized all three XMM-Newton cameras, i.e., MOS1, MOS2, and pn.
Unfortunately, the entire 16 ks of data in the third epoch were lost to high
particle background. Otherwise, each XMM-Newton epoch had exposure time
$\sim$20 ks, and the total effective exposure time is 62 ks. Details are in
Table 2. The XMM-Newton observations cover a field of 0.21 deg2, about 90% of
the NuSTAR NEP-TDF field. The two missing bottom corners of the field (Figure
10) contain one NuSTAR source (ID 38).

###  5.1 Data Reduction

The XMM-Newton data were reduced following Brunner et al. (2008); Cappelluti
et al. (2009); LaMassa et al. (2016); and Z21. Details of the XMM-Newton
Science Analysis System (SAS) packages are described in the XMM-Newton data
analysis threads.666https://www.cosmos.esa.int/web/xmm-newton/sas-thread-src-
find-stepbystep The observational data files (ODFs) of MOS1, MOS2, and pn were
generated using the SAS version 20.0.0 tasks emproc and epproc. High-
background time intervals of the three instruments were excluded using $>$10
keV count-rate thresholds of 0.2 and 0.3 counts s-1 for MOS and pn,
respectively. We also excluded data in energy bands that might be contaminated
by fluorescent emission lines, i.e., the Al K$\alpha$ line at 1.48 keV in both
MOS and pn and two Cu lines at $\sim$7.4 keV and 8.0 keV only in pn. The
specific energy intervals removed were 1.45– 1.54 keV in both MOS and pn data
and 7.2–7.6 keV and 7.8–8.2 keV in pn. We then used the clean event files to
generate the images of MOS 1,2 and pn in the 0.5–2 keV and 2–10 keV bands.

To generate exposure maps, we used the SAS task eexpmap. The maps were
weighted by each instrument’s energy conversion factor (ECF), which converts
count rate to flux. ECFs were calculated using WebPIMMs assuming an absorbed
power-law model with $\Gamma=1.80$ and Galactic column density
$N\rm_{H}=3.4\times 10^{20}$ cm-2, as for the NuSTAR observations (Section
3.1). The ECFs used for MOS and pn are 0.54 and $0.15\times 10^{-11}$ erg cm-2
count-1 in the 0.5–2 keV band, and 2.22 and $0.85\times 10^{-11}$ erg cm-2
count-1 in the 2–10 keV band, respectively.

Background maps were generated for each instrument after masking detected
sources. Preliminary source detection used a sliding-box method with SAS
package eboxdetect and detection likelihood LIKE set to $>$4 to avoid any
possible sources. (The detection likelihood is defined as ${\tt
LIKE}\equiv-\ln p$, where $p$ is the probability of a Poissonian random
fluctuation of the counts in the detection box which would have resulted in at
least the observed number of source counts.) We generated the background map
using SAS package esplinemap assuming a 2-component model of the XMM-Newton
background by setting fitmethod = model. This 2-component model considers
background from both the detector (particles) and the CXB.

Figure 10: XMM-Newton MOS+pn mosaics combining 0.5–10 keV observations from
all three epochs. The footprints of other surveys in the NEP-TDF field are
plotted in different colors as indicated in the key. SDSS and WISE catalogs
cover the entire XMM and NuSTAR regions.

###  5.2 Source Detection

To maximize sensitivity, we co-added the cleaned images, exposure maps, and
background maps of the three instruments into mosaic images for the two energy
bands using the SAS emosaic task. Figure 10 shows the merged mosaic. Source
detection was performed using the SAS eboxdetect and emldetect tasks, the
latter to optimize detection of the center of the source. Source detection was
performed in the 0.5–2 keV and 2–10 keV bands simultaneously to minimize
uncertainties in source positions and fluxes. A detection required mlmin$>$6
in either of the two bands. This threshold corresponds to a reliability of
97.3% in the 0.5–2 keV band and 99.5% in the 2–10 keV band based on
simulations of the XMM-COSMOS survey (Cappelluti et al., 2007), which has a
$\sim$60 ks depth similar to the XMM-Newton NEP-DTF survey. Source detection
excluded the margin of the FoV where the exposure time is $<$1 ks.

###  5.3 Astrometric Correction and Uncertainty

Before merging the three epochs of observations into mosaics to maximize the
sensitivity of the survey, we estimated the astrometric offsets of the three
observations. The astrometric offset of an XMM-Newton observation is typically
less than 3″ and on average is 1$\farcs$0–1$\farcs$5 (e.g., Cappelluti et al.,
2007; Ni et al., 2021). To determine the astrometric offset of our three
epochs, we matched $>$6$\sigma$ (mlmin$>$20) XMM-Newton sources to optical
sources from the Sloan Digital Sky Survey (SDSS)
DR16.777https://www.sdss4.org/dr16/ Only Type = Star sources were used, and
the matching radius was 4$\farcs$5\. XMM-Newton epochs 1, 2, and 4 had 13, 22,
and 15 matched SDSS counterparts, respectively. The median offsets in R.A. and
Decl. are $(\Delta\alpha,\Delta\delta)=(3\farcs 97,0\farcs 95$) for epoch 1,
(0$\farcs$88, 1$\farcs$13) for epoch 2, and (0$\farcs$06, 1$\farcs$46) for
epoch 4. We applied these offsets to the event and attitude files in each
observation and remade the images, background maps, and exposure maps with the
corrected files.

To test the astrometric corrections, we performed the source detection again
and measured the offsets of the same sources from their optical counterparts.
The average XMM-Newton to SDSS separations were reduced by 30% for epoch 1,
45% for epoch 2, and 41% for epoch 4 after the astrometric correction.
Furthermore, the median XMM-Newton offsets among different epochs decreased by
84%–96%, suggesting that the three epochs became better aligned. The resulting
images, background maps, and exposure maps of the three epochs were then
merged into mosaics. The new images have more high-count pixels than the old
images, again suggesting that the alignment is better corrected. The new
average X-ray-to-optical offset is 1$\farcs$22, and we take this to be the
systematic position uncertainty of the XMM-Newton NEP-TDF survey.

###  5.4 Sensitivity

The sensitivity curves of the XMM-Newton NEP-TDF survey are plotted in Figure
11. The sensitivity maps were generated using the SAS esensmap package
assuming a maximum likelihood ${\tt mlmin}>6$. The half-area and 20%-area
sensitivities are reported in Table 6.

Figure 11: XMM-Newton NEP-TDF sensitivity maps. The upper panel shows 0.5–2
keV, and the lower shows 2–10 keV. Different line types show different epochs
as indicated in the legend. Vertical dashed lines show the half-area and
20%-area sensitivities for the three epochs combined.

###  5.5 XMM-Newton Source Catalog

The final XMM-Newton NEP-TDF catalog includes 194 sources in the 0.5–2 keV
band and 172 sources in the 2–10 keV band at ${\tt mlmin}>6$. There were only
80 sources in common in the two bands giving a total of 286 individual sources
detected in at least one band. The source properties are listed in the XMM-
Newton source catalog, and descriptions of each column of the catalog are in
Table 10. The source flux distributions are plotted in Figure 12.

Figure 12: Flux distribution of sources detected in the 0.5–2 keV (top) and
2–10 keV (bottom) bands of the three-epoch combined XMM-Newton mosaic. Solid
lines represent the flux distribution of detected sources with ${\tt mlmin}>6$
in a given band. Dashed lines represent the flux distributions of all 286 XMM-
Newton sources with those not detected or with ${\tt mlmin}\leq 6$ in the
given band plotted at their 90% confidence upper limits.

###  5.6 Cross-match with NuSTAR

We cross-matched the XMM-Newton sources with the 60 sources detected in the
NuSTAR cycles 5+6 survey using a simple position match. The match radius was
the 20″ NuSTAR position uncertainty combined in quadrature with the position
uncertainty of individual XMM-Newton sources ($\sigma_{\rm XMM}$ from the
emldetect best-fit results) and the 1$\farcs$22 XMM-Newton systematic
uncertainty. The 20″ NuSTAR uncertainty is three times the best-fit Rayleigh
scale parameter ($\rm\sigma_{95\%,C56}=6\farcs 5$) of the simulated position
errors (Section 3.5). In all, 36 NuSTAR sources match at least one XMM-Newton
counterpart. Thirty of these have a single XMM-Newton counterpart, and six (ID
11/13/23/31/41/46) have two XMM-Newton counterparts within the search radius.
In all six cases, one of the XMM-Newton sources is both brighter and closer to
the NuSTAR position than the other, and we took this to be the primary
counterpart. One NuSTAR source (ID 51) has two XMM-Newton sources (ID 134/181)
just outside the search radius (22$\farcs$8 and 23$\farcs$3, respectively).
The two are in opposite directions and were both detected in the 2–10 keV band
with similar flux $F({\rm\hbox{2--10\,keV}})\sim 9\times 10^{-15}$ erg cm-2
s-1. This looks like a case of source confusion where both XMM-Newton sources
contribute to the NuSTAR detection.

Figure 13: Comparison between NuSTAR and XMM-Newton fluxes for the 37 NuSTAR
sources with XMM-Newton counterparts (black filled squares). The dashed line
represents the 1:1 relation, and the dotted lines show a factor of two
difference. The black open circles show the two XMM-Newton candidate
counterparts of NuSTAR ID 51. For undetected sources, the indicated upper
limits are 90% confidence. The gray crosses in the background are from the
NuSTAR simulations in the 3–8 keV band.

In all, 37 out of 60 NuSTAR sources have at least one XMM-Newton association.
Of the remaining 23, 17 (ID 1/4/5/9/14/16/17/18/40/42/44/47/48/49/50/56/59)
were undetected or below the 95% reliability level in the NuSTAR soft 3–8 keV
band, suggesting that they might be heavily obscured and therefore detectable
only in hard X-rays. The other six sources (ID 25/27/33/35/38/52) were above
the 95% reliability level in the 3–8 keV band but do not have XMM-Newton
counterparts. They might be variable sources that were bright only in NuSTAR
cycle 5, or some of them could be spurious NuSTAR sources. Statistically, only
2–3 spurious detections are expected in the NuSTAR 95% reliability catalog,
and therefore variability is likely to be a factor.

For comparison between NuSTAR and XMM-Newton, the XMM-Newton 2–10 keV fluxes
were converted to 3–8 keV assuming an absorbed power-law intrinsic SED with
photon index $\Gamma=1.80$ and Galactic absorption $N\rm_{H}=3.4\times
10^{20}$ cm-2. This gives a conversion factor of 0.62, and Figure 13 shows the
comparison. Most sources have comparable fluxes measured by the two
observatories. The tendency for NuSTAR fluxes to be higher than XMM-Newton
fluxes at the faint end is due to the Eddington Bias as demonstrated by Figure
8. Other offsets could arise from variability in the last three years or
different spectral shapes of the sources than assumed for converting the XMM-
Newton fluxes to the NuSTAR energy band.

##  6 Multiwavelength Counterparts

The JWST NEP-TDF has extensive multiwavelength coverage (Windhorst et al.,
2023). Because XMM-Newton has a better PSF than NuSTAR, we first matched XMM-
Newton sources with the visible-wavelength and infrared (IR) catalogs.

###  6.1 Visible-wavelength Catalogs

We matched X-ray positions to three visible-wavelength catalogs covering the
NEP-TDF: SDSS DR17 (Abdurro’uf et al., 2022), the HEROES catalog (Taylor et
al., 2023) made from Subaru Hyper Suprime-Cam (HSC; Aihara et al., 2018)
images, and the NEP portion (J-NEP; Hernán-Caballero et al., 2023) of the
Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS;
Benitez et al., 2014). We used the $i$-band catalogs as they include the
largest number of detected sources.

The SDSS catalog covers the entire field, and data were downloaded from the
public database.888https://www.sdss4.org/dr17/ The HSC images were reduced by
S. Kikuta, and the HSC NEP-TDF catalog was generated by C. N. A. Willmer
(Willmer et al., 2023). Sources with $m_{i}<17.5$ are saturated in the HSC
observations, and we replaced their magnitudes with the magnitudes in the SDSS
catalog. The J-NEP was performed with the single-CCD Pathfinder camera on the
2.55 m Javalambre Survey Telescope (JST) at the Javalambre Astrophysical
Observatory with 56 narrow filters and used the SDSS $u$, $g$, $r$, and $i$
filters. J-NEP covered about 80% area of the XMM-Newton field. We applied
magnitude cuts at $S/N>3$ (corresponding to $i$-band magnitudes $m_{i}\lesssim
22.5$, 25.8, and 24.5 for SDSS, HSC, and J-PAS, respectively) to the three
catalogs to ensure reliable detections and accurate measurements of the source
fluxes.

###  6.2 Infrared Catalogs

We used two near-IR (NIR) catalogs covering the NEP-TDF: the YJHK catalog
(Willmer et al., 2023) made with the MMT–Magellan Infrared Imager and
Spectrometer (MMIRS; McLeod et al., 2012) on the MMT, and the unWISE catalog
(Schlafly et al., 2019) made from five years of the Wide-field Infrared Survey
Explorer (WISE; Wright et al., 2010) observations. The unWISE wavelengths are
3.4 (W1) and 4.6 µm (W2).

The MMIRS catalog covers 30–40% of the XMM-Newton-observed field, and the S/N
$>$3 sensitivity cuts correspond to $m\lesssim 24.6$, 24.5, 24.1, and 23.5 (in
AB magnitudes) in the $Y$, $J$, $H$, and $K$ bands, respectively. The unWISE
catalog covers the entire XMM-Newton field, and the $S/N>3$ sensitivity cuts
correspond to $m\lesssim 21.5$ in the W1 band and 20.5 AB in the W2 band.

Figure 14: Illustrations of secure (top), ambiguous (middle), and unidentified
(bottom) associations of XMM-Newton sources. Negative images left to right are
HSC $i$, MMIRS $J$, and HST$+$JWST (11-filter mosaic: HST F275W, F435W, and
F606W; JWST F090W, F115W, F150W, F200W, F277W, F356W, F410M, and F444W). All
images are oriented north up, east left and centered at the centroid of the
XMM-Newton detections. The image scale is indicated in the top row. Solid
circles show the XMM-Newton position uncertainty, and dashed circles show the
5″ matching radius. Labels show $i$-band magnitudes measured from HSC (cyan
square), J-PAS (green circle), or SDSS (red cross) or IR magnitudes measured
by MMIRS ($J$-band, red square) or WISE (W1, green circle). Only ancillary
counterparts within the matching radius and with $\rm LR>LR_{\rm th}$ are
plotted. The ancillary counterparts with the highest $\rm LR$ are plotted as
filled symbols. XMM 17 is the bright Seyfert galaxy discussed by Willner et
al. (2023, their Figure 3). XMM 86 was not covered by JWST.

###  6.3 Multiwavelength Matching

We used a 5″ matching radius to identify candidate counterparts of the XMM-
Newton sources. (More than 95% of XMM-Newton sources are detected within this
radius based on the simulations made in the STRIPE 82 XMM-Newton survey:
LaMassa et al. 2016.) To choose among possible counterparts within the match
radius, we used a maximum likelihood estimator (MLE; Sutherland & Saunders,
1992) as applied for X-ray sources detected in previous XMM-Newton and Chandra
extragalactic surveys (e.g., Brusa et al., 2007; Civano et al., 2012; Marchesi
et al., 2016; LaMassa et al., 2016). These previous results showed $>$80%
reliability. The MLE method considers both the flux and the offset of the
candidate counterparts in the context of the position uncertainties of the
surveys and the flux distribution of survey sources. The likelihood ratio
($\rm LR$) that a candidate is the real counterpart is:

${\rm LR}=\frac{q(m)f(r)}{n(m)}\quad,$ (3)

where $m$ is the catalog magnitude of the candidate, $n(m)$ is the local
magnitude distribution of background sources, $q(m)$ is the expected magnitude
distribution of the real multiwavelength counterparts, and $r$ is the position
offset between the X-ray source and the candidate. In practice, $n(m)$ was
measured in an annulus between 5″ and 30″ from the X-ray source. The function
$q(m)$ is the normalization of $q^{\prime}(m)$, where $q^{\prime}(m)$ is the
magnitude distribution of catalog objects within 5″ of the X-ray source after
subtracting $n(m)$ and rescaling to the 5″ circular area. Civano et al. (2012,
their Figure 1) gave an example of $q(m)$. The function $f(r)$ is the
probability distribution of the positional uncertainties, assumed to be a two-
dimensional Gaussian $f(r)=1/(2\pi\sigma^{2})\times\exp(-r^{2}/2\sigma^{2})$,
where $\sigma$ is the quadrature combination of the position uncertainty of
the XMM-Newton source (Section 5.6) and the ancillary object (0$\farcs$2). The
choice of 0$\farcs$2 was validated by cross-matching our ancillary table with
the extragalactic sources (proper motion pm$<$10 mas yr-1) in the GAIA DR3
catalog (Gaia Collaboration et al., 2016, 2021). Table 8 lists the number of
sources matched by each survey.

Table 8: XMM-Newton Match Statistics Survey | band | XMM | matched | candidates | CP
---|---|---|---|---|---
HSC | $i$ | 285 | 251 | 514 | 197
J-PAS | $i$ | 261 | 141 | 178 | 131
SDSS | $i$ | 286 | 93 | 97 | 93
MMIRS | $J$ | 132 | 125 | 222 | 117
WISE | W1 | 286 | 210 | 272 | 210

We used the LR threshold ($\rm LR_{th}$) to distinguish whether an ancillary
object is the true counterpart of the XMM-Newton detection or is a background
source within the search radius. The $\rm LR_{th}$ was determined by balancing
the reliability and the completeness of the final selected sample. The
reliability and completeness of the matching can be estimated from the survey
statistics (Civano et al., 2012). The reliability $R_{i}$ for an individual
candidate $j$ is

$R_{i}=\frac{{\rm LR}_{i}}{\sum_{i}({\rm LR})_{i}+(1-Q)}\quad,$ (4)

where $Q$ is the fraction of XMM-Newton sources having at least one candidate
counterpart (i.e., the ratio of Table 8 column 4 to column 3). The LR was
summed over all potential counterparts within the search radius of a given
XMM-Newton source for all ancillary objects within the search radius. The
reliability ($R$) of the entire sample is defined as the ratio between the sum
of the reliabilities of all the candidate counterparts and the total number of
sources with $\rm LR>LR_{th}$. The completeness ($C$) of the sample is defined
as the ratio between the sum of the reliability of all the candidate
counterparts and the number of the X-ray sources that have ancillary objects
within the search radius.

A higher $\rm LR_{th}$ suggests a higher reliability of the matching but lower
sample completeness, while a lower $\rm LR_{th}$ suggests a lower reliability
of the matching but higher sample completeness. We selected $\rm LR_{th}$
following Brusa et al. (2007) by maximizing ($R+C$)/2. We applied this
criterion to the five ancillary catalogs (HSC, J-PAS, SDSS, MMIRS, WISE) and
the resulting $\rm LR_{th}$ are 0.3, 0.2, 0.2, 0.3, and 0.1, respectively. The
corresponding numbers of the XMM-Newton sources that have at least one
counterpart above the chosen $\rm LR_{th}$ are given in Table 8. We used the
HSC catalog as the primary reference for visible-wavelength counterparts
because it is the deepest and covers the most area. Similarly, we used the
MMIRS catalog as the primary for the infrared counterparts. Other catalogs
were checked if no counterpart was found in the primary catalog.

The identified counterparts of XMM-Newton sources can be separated into three
classes:

  * •

Secure: these are sources with a single counterpart with $\rm LR>LR_{th}$, or
it has more than one candidate counterpart but the $\rm LR$ of the primary
counterpart is four times higher than the $\rm LR$ of the secondary
counterpart. (For there to be more than one candidate, both primary and
secondary counterparts must have $\rm LR>LR_{th}$).

  * •

Ambiguous: these are sources with multiple candidate counterparts with the
$\rm LR$ of the primary counterpart being less than four times higher than the
$\rm LR$ of the secondary counterpart or the secure optical counterpart being
different from the IR counterpart.

  * •

Unidentified: these are sources with no optical or IR counterpart with $\rm
LR>LR_{th}$ within the search radius.

Figure 15: Distribution of separations between XMM-Newton sources and their
secure ancillary counterparts. The median separation is 1$\farcs$69.

The NEP-TDF also has Chandra coverage, which provides better localization of
some of the X-ray sources. Therefore, we utilized the Chandra NEP-TDF source
catalog (Maksym et al., in prep.) to help identify the ancillary counterparts
of the XMM-Newton sources with ambiguous counterparts. In ambiguous cases, we
selected the ancillary counterpart that is closer to the Chandra measured
position (which is also the primary counterpart of the XMM-Newton source in
most cases) as the secure ancillary counterpart of the XMM-Newton source. We
also visually inspected all identifications on the XMM-Newton, HSC, and MMIRS
images. Figure 14 shows three XMM-Newton sources with secure, ambiguous, and
unidentified ancillary counterparts.

The source XMM ID 17 (=NuSTAR ID 58 = J172241+6542.6, $z$ = 0.1791) shown in
Figure 14 is a heavily obscured Seyfert galaxy with column density $N_{\rm
H}\sim 10^{23}$ cm-2 measured by NuSTAR and $N_{\rm H}\geq 10^{23}$ cm-2 by
XMM-Newton. (See Section 7.2 for more discussion.) This heavily obscured
scenario is also supported by the JWST and HST imaging. The strong red spikes
seen on the JWST images suggest that the nucleus is a dusty point source. The
clear host-galaxy feature in yellow shown on the HST image also implies a
significantly obscured core.

A total of 214 XMM-Newton sources have secure ancillary counterparts. 19 XMM-
Newton sources have ambiguous ancillary counterparts, out of which 14, 3, 1,
and 1 have two, three, four, and five candidate ancillary counterparts within
the search radius and with $\rm LR>LR_{th}$. The coordinates and fluxes of the
optical and IR counterparts of the XMM-Newton sources are listed in Tables 9
and 10. The distribution of the separations between XMM-Newton sources and
their secure ancillary counterparts is shown in Figure 15; the median
separation is 1$\farcs$69.

###  6.4 Radio Counterparts

The NEP-TDF was observed in the radio “$S$ band” ($\nu=3$ GHz) by the Karl G.
Jansky Very Large Array (VLA; PIs: R. A. Windhorst & W. Cotton). The 48-hour
VLA survey (Hyun et al., 2023) covered an area of $\sim$0.126 deg2 (24′ in
diameter), centered at the bright (in both radio and X-ray) blazar (NuSTAR ID
29, $z=1.441$). Therefore, only about 55% of the XMM-Newton area was covered
by VLA. The Hyun et al. (2023) source list comprises 756 sources at S/N $>$
5\. The 1$\sigma$ noise is 1 $\mu$Jy beam-1 at the primary-beam center. As the
angular resolution is FWHM 0$\farcs$7, we matched the VLA catalog with the
ancillary counterparts of the XMM-Newton-detected sources using 0$\farcs$7 as
the matching radius and did not consider the unidentified sources. With this
procedure, 55 out of the 171 XMM-Newton sources covered by the VLA have VLA
counterparts. This fraction is consistent with what was discovered in COSMOS,
where $\sim$40% of the X-ray sources have VLA counterparts (Smolčić et al.,
2017; Marchesi et al., 2016). The radio-brightest source in the XMM-Newton
sample is the blazar (NuSTAR ID 29) with a 3 GHz flux of 0.2 Jy. The median
flux of the XMM-Newton matched VLA sample is 23 $\mu$Jy. Both the NuSTAR and
XMM-Newton catalogs report the VLA ID and fluxes from Hyun et al. (2023).

Willner et al. (2023) reported the 62 VLA sources that have JWST counterparts.
Six sources were detected by XMM-Newton (ID 17/29/49/65/179/197). Hyun et al.
(2023) also reported the James Clerk Maxwell Telescope (JCMT) SCUBA-2 850
$\mu$m survey of the JWST NEP-TDF with 114 sources detected at S/N$>$3.5. Four
XMM-Newton sources (ID 1/42/70/91) have JCMT counterparts.

###  6.5 HST and JWST counterparts

HST observations of the JWST NEP-TDF (GO15278, PI: R. Jansen and
GO16252/16793, PIs: R. Jansen & N. Grogin) were taken between 2020 September
25 and 2022 October 31. These observations include imaging with WFC3/UVIS in
the F275W (272 nm) filter and with ACS/WFC in the F435W (433 nm) and F606W
(592 nm) filters (O’Brien et al. 2024, R. A. Jansen et al., in prep.). The
2$\sigma$ limiting depths are magAB $\simeq$ 28.0, 28.6, and 29.5 mag in
F275W, F435W, and F606W, respectively, and the ACS/WFC observations cover a
total area of $\sim$194 arcmin2.

The JWST observations of the NEP-TDF (PI: R. A. Windhorst & H. B. Hammel, PID
2738) were taken in four epochs between 2022 August 26 and 2023 May 21
(Windhorst et al., 2023). The survey includes eight NIRCam filters with
5$\sigma$ point-source AB limits for each epoch of observation $\simeq$ 28.6,
28.8, 28.9, 29.1, 28.8, 28.8, 28.1, and 28.3 mag in F090W, F115W, F150W,
F200W, F277W, F356W, F410W, and F444W, respectively. Each NIRCam epoch of
observation covers an area of 2$\farcm$15 $\times$ 6$\farcm$36 with the four
epochs together (Figure 10) covering $\sim$55 arcmin2. The survey also
includes NIRISS grism data with 1$\sigma$ continuum sensitivity 25.9. Each
NIRISS epoch covers an area of 2$\farcm$22 $\times$ 4$\farcm$90.

The HST and JWST NEP-TDF surveys are much deeper than the HSC and MMIRS/WISE
catalogs, but they cover only the center 26% and 7% of the XMM-Newton survey
area, respectively. Therefore, we did not use the HST and JWST catalogs to
identify the multiwavelength counterparts of the XMM-Newton sources. Instead
we used the coordinates of the counterparts of the XMM-Newton sources (Section
6.3) to match the HST (Jansen et al., in prep) and JWST catalogs (Windhorst et
al., 2023, Windhorst et al., in prep). We used the F606W HST catalog and F444W
JWST catalog when matching, as they have the deepest sensitivities. In all,
102 XMM-Newton sources have HST counterparts, and 32 XMM-Newton sources have
JWST counterparts. The NuSTAR and XMM-Newton catalogs report the F606W and
F444W fluxes.

###  6.6 Redshifts

Some of the NEP-TDF X-ray sources have redshifts measured from optical
spectra. Spectra came from
Hectospec999https://lweb.cfa.harvard.edu/mmti/hectospec.html (Fabricant et
al., 2005) and Binospec101010https://lweb.cfa.harvard.edu/mmti/binospec.html
(Fabricant et al., 2019), both of which are mounted on the 6.5 m MMT.

Hectospec is multi-object spectrograph with 300 optical fibers. Its
1°-diameter field of view makes it an efficient instrument to survey the NEP-
TDF X-ray sources because of their relatively low areal density. Therefore, we
observed (PI: Zhao) the XMM-Newton-selected sources with Hectospec on 2022 Sep
1 and with a different fiber configuration on 2023 May 20. Each exposure was 2
hours split into six 1200 s exposures to avoid saturation of bright targets,
remove cosmic rays, and improve pipeline reduction. The 270 line mm-1 grating
provided spectral resolution $R\sim 1000$–2000) over the wavelength range
3800–9200 Å, and each exposure allows measuring redshifts of sources with
$m_{i}\leq 22$ AB. A limitation of Hectospec is that adjacent fibers cannot be
placed within 20″ of each other. In all, we obtained 41 spectra with good
enough S/N to measure the redshifts of XMM-Newton targets in the 2022 run and
37 spectra in the 2023 run. Those include spectra of both possible
counterparts of XMM-Newton ID 187. Besides the XMM-Newton targets, we also
observed 40 ($i\leq 21$ mag) targets selected from the VLA (Hyun et al., 2023)
and Chandra-detected (Maksym et al., in prep) sources. Table 11 in Appendix
APPENDIX C reports their redshifts and spectral types.

The Hectospec data were reduced using the IDL script
HSRED111111http://www.mmto.org/hsred-reduction-pipeline/ v2.0 (originally
written by Richard Cool) developed by the Telescope Data Center at SAO (Mink
et al., 2007). This pipeline provides fine-tuned wavelength calibrated,
improved cosmic-ray rejected, and sky-subtracted 1D spectra. The redshifts
were measured using a semi-automated and interactive Java toolkit, A Spectrum
Eye Recognition Assistant121212https://gitee.com/yuanhl1984/asera_pub/ (ASERA;
Yuan et al., 2013), which was developed to classify the spectra observed by
the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST; Wang et
al., 1996). The spectroscopic redshifts were measured by cross-correlating the
observed Hectospec spectra against a library of quasar, galaxy, and star
template spectra131313http://www.sdss.org/dr5/algorithms/spectemplates/ from
SDSS integrated into ASERA.

Figure 16: Spectroscopic redshifts of the XMM-Newton (black solid line) and
NuSTAR (red dashed line) sources.

Figure 17: The $i$-band magnitudes of XMM-Newton counterparts as a function of
X-ray fluxes. XMM-Newton sources with NuSTAR counterparts are plotted as open
symbols filled with green. The solid and dashed lines represent the classical
AGN locus, $X/O=0\pm 1$ (Maccacaro et al., 1988). Upper panels show the
distribution of sources in soft X-rays and lower panels those in hard X-rays.
The left panels show the entire sample of XMM-Newton sources. Symbols identify
sources that have single, multiple, or no candidate counterparts as indicated
in the legend. For the 18 XMM-Newton sources with ambiguous optical
counterparts, all candidate optical counterparts are plotted. The 66 XMM-
Newton sources without optical counterparts are plotted with 3$\sigma$ upper
limits $m_{i}>25.8$. The right panels show only sources that have secure
counterparts with spectroscopic identifications. Symbols indicate the type of
source.

Binospec is an imaging spectrograph covering 3900–10,000 Å (Fabricant et al.,
2019). C. N. A. Willmer obtained more than 1,378 optical spectra with Binospec
and successfully measured more than 1,000 redshifts of the sources in NEP-TDF
(Willmer et al., in prep). These include five additional XMM-Newton sources.
Therefore, a total of 82 XMM-Newton sources have spectroscopic redshifts. We
categorized the sources into quasars (presenting broad emission lines),
galaxies (including Type 2 AGN, which have only narrow emission lines), and
stars. Future efforts to identify type 2 AGN can include methods such as the
BPT diagram (e.g., Kewley et al., 2001; Kauffmann et al., 2003).

Photometric redshifts of the X-ray source counterparts were adopted from the
SDSS DR17 catalog (Abdurro’uf et al., 2022). Only photometric redshifts with
low root-mean-square (RMS) uncertainties, specifically the photoErrorClass
flag = $-1$, 1, 2, or 3 were considered. That added two XMM-Newton sources
without spectroscopic redshifts for a total of 84 XMM-Newton sources with
redshifts, reported in Tables 9 and 10.

###  6.7 X-ray to Optical Properties

The X-ray to optical flux ($X/O$) ratio has been historically used to identify
the nature of X-ray sources (e.g., Maccacaro et al., 1988). The ratio is
defined as:

$X/O\equiv\log(f_{\rm X}/f_{\rm opt})=\log(f_{\rm X})+m_{\rm opt}/2.5+C$ (5)

where $f_{\rm X}$ is the X-ray flux in a given band in units of erg cm-2 s-1,
$m_{\rm opt}$ is the optical AB magnitude in a given filter, and $C$ is a
constant depending on the bands chosen in X-ray and optical. Figure 17 shows
the $i$-band (HSC) magnitudes as a function of the soft (0.5–2 keV) and hard
(2–10 keV) X-ray fluxes of the XMM-Newton-detected sources. The constants used
to calculate $X/O$ are $C_{0.5-2}$ = 5.91 and $C_{0.5-2}$ = 5.44 for the soft
and hard bands, respectively (Marchesi et al., 2016).

The majority of X-ray (both XMM-Newton and NuSTAR) detected sources are AGN
with $-1<X/O<1$, as found in previous surveys (e.g., Stocke et al., 1991;
Schmidt et al., 1998; Akiyama et al., 2000; Marchesi et al., 2016). Previous
Chandra and XMM-Newton surveys (Hornschemeier et al., 2001; Fiore et al.,
2003; Civano et al., 2005; Brusa et al., 2007; Laird et al., 2008; Xue et al.,
2011) and NuSTAR surveys (Civano et al., 2015; Lansbury et al., 2017) detected
sources having $X/O>1$. These sources were associated with high redshifts or
large obscurations. Some sources with $X/O<-1$ are stars, as shown in Figure
17. Many galaxies are in the AGN locus. Most of these sources are likely to be
type 2 AGN rather than quiescent or star-forming galaxies because their 2–10
keV luminosities (Figure 18) are mostly $>$1042 erg s-1 (the conventional
threshold when separating AGN from galaxies; e.g., Basu-Zych et al., 2013).
Furthermore, only about five galaxies are expected in the FoV considering the
galaxy number density (Ranalli et al., 2005; Luo et al., 2017; Marchesi et
al., 2020).

###  6.8 Luminosity–Redshift Distribution

Figure 18 shows the 0.5–2 keV and 2–10 keV rest-frame luminosities of the 85
XMM-Newton sources as a function of redshift. The rest-frame luminosities were
calculated by converting their observed 0.5–2 keV and 2–10 keV fluxes with a
K-correction assuming X-ray spectral indices $\Gamma(\hbox{0.5--2\,keV})=1.40$
and $\Gamma(\hbox{2--10\,keV})=1.80$. The calculated luminosities were not
corrected for absorption, although the absorbing effect is partly mitigated by
the choice of $\Gamma$ = 1.40 in the 0.5–2 keV band.

Figure 19 shows the 10–40 keV rest-frame luminosities of the 22 NuSTAR sources
that have redshift measurements. The 10–40 keV rest-frame luminosities were
calculated by converting the observed 3–24 keV fluxes with a K-correction
assuming $\Gamma=1.80$. The brightest source in the FoV is a flat-spectrum
radio quasar (FSRQ) blazar (ID 29, $z=1.441$). Figure 19 also shows sources
detected in previous NuSTAR surveys. Most of the detected sources from
previous NuSTAR extragalactic surveys are well above the NEP-TDF sensitivity
line, consistent with the NuSTAR survey being the deepest. The all-sky Swift-
BAT survey is also shown in Figure 19. Its measured 14–195 keV luminosities
(Gehrels et al., 2004; Barthelmy et al., 2005) from the 105-month Swift-BAT
catalog (Oh et al., 2018) were converted to 10–40 keV luminosities (assuming a
$\Gamma=1.8$ power law model) for plotting. Swift-BAT samples sources mostly
in the local Universe with median redshift of $\left<z_{\rm
BAT}\right>=0.044$, while NuSTAR samples sources at $\left<z_{\rm
NuS}\right>=0.734$.

Figure 18: X-ray rest-frame luminosity versus redshift for the 84 XMM-Newton
NEP-TDF sources with redshifts. The upper panel shows soft X-rays, and the
lower panel shows hard X-rays. X-ray luminosities are as observed, not
corrected for absorption. Sources with spectroscopic redshifts are plotted
using blue squares, and a source with only a photometric redshift is plotted
as a red circle. The 20%-area sensitivities are plotted as black dashed lines.
Figure 19: 10–40 keV rest-frame luminosity versus redshift for the NuSTAR
sources with redshifts. Sources with spectroscopic (photometric) redshifts are
plotted as blue stars (red diamonds). The sensitivity of the NEP-TDF cycles
5+6 survey at 20% sky coverage is plotted as a dashed line. NuSTAR COSMOS (red
circles; Civano et al., 2015), ECDFS (green circles; Mullaney et al., 2015),
UDS (blue circles; Masini et al., 2018a), 40-month serendipitous (brown
triangles; Lansbury et al., 2017), and Swift-BAT 105-month (black open
circles; Oh et al., 2018) surveys are shown as well. The luminosities were not
corrected for intrinsic absorption.

##  7 Discussion

###  7.1 $\log N$–$\log S$

The cumulative hard X-ray source number-counts distributions (log$N$-log$S$)
in three energy bands (3–8 keV, 8–24 keV, and 8–16 keV) were calculated using
the NEP-TDF cycle 5 (681 ks) observations Z21. Here, we update the
log$N$-log$S$ distributions by using the combined cycles 5+6 (1.56 Ms) data,
which can provide constraints of log$N$-log$S$ at fainter hard X-ray fluxes.

The $\log N$–$\log S$ distribution is defined following Cappelluti et al.
(2009) as:

$N({>}S)\equiv\sum_{i=1}^{N_{S}}\frac{1}{\Omega_{i}}\rm~{}deg^{-2}\quad,$ (6)

where $N({>}S)$ is the surface density of sources detected above 95%
reliability level in a given energy band with flux greater than $S$, and
$\Omega_{i}$ is the sky coverage associated with the flux of the $i$th source
(Figure 5). The variance of $N({>}S)$ is

$\sigma^{2}_{S}=\sum_{i=1}^{N_{S}}(\frac{1}{\Omega_{i}})^{2}\quad.$ (7)

The $\log N$–$\log S$ distribution depends on the minimum flux limit and the
S/N limit of the sources (Cappelluti et al., 2009; Puccetti et al., 2009). We
selected a flux limit equal to 1/3 of the flux corresponding to the half-area
coverage sensitivity reported in Table 6 in each band (Masini et al. 2018a
,Z21). This reduces the effect of Eddington bias (Figure 8). To reduce the
large uncertainties in the flux of low-S/N sources (Appendix APPENDIX A and
Figure 24), we kept only sources detected with $\rm S/N>2.5$ (following
Puccetti et al., 2009). Here S/N is defined as $C_{\rm net}/(C_{\rm
tot}+C_{\rm bk})^{0.5}$, where $C_{\rm net}$ is the source net counts, $C_{\rm
tot}$ is the total counts, and $C_{\rm bk}$ is the background counts. For the
maximum flux, we adopted 10-13 erg cm-2 s-1 for the 3–8 keV and 8–24 keV bands
and $6\times 10^{-14}$ erg cm-2 s-1 for the 8–16 keV band to provide enough
statistics at the high-flux end.

To validate the selection of the minimum flux limit and the S/N limit, we
calculated the $\log N$–$\log S$ distributions in different energy bands using
the selected minimum flux limits and the S/N limit from the 2400 simulations
described in Section 2.4. The calculated $\log N$–$\log S$ distributions
reproduce the input $\log N$–$\log S$ distribution (Treister et al., 2009) in
the simulations, suggesting the selected minimum flux limits and the S/N
limits are reasonable for the real observations. Other choices of minimum flux
(e.g., 20%–area sensitivity) and S/N limits (e.g., S/Nlim = 2 or S/Nlim = 3)
were unable to reproduce the input $\log N$–$\log S$ distribution. A minimum
flux limit at 20%–area sensitivity leads to an $\sim$30% over-estimation of
$N({>}S)$ at the faint end, S/N${}_{\rm lim}=2$ leads to an over-estimation of
$N({>}S)$ by $\sim$35%, and S/N${}_{\rm lim}=3$ leads to an under-estimate of
$N({>}S)$ by $\sim$40% at the faint end.

Figure 20: Cumulative source number counts as a function of X-ray flux. Panels
show three energy ranges as labeled. The orange-shaded areas represents the
68%-confidence region at each energy. Black solid lines show results from
Harrison et al. (2016), and yellow shaded areas show those of Masini et al.
(2018b) using NuSTAR. Black points in the top panel show XMM-Newton results
from Cappelluti et al. (2009). Expectations from population-synthesis models
(Gilli et al., 2007; Ueda et al., 2014) are shown by dot-dash lines as
indicated in the legend.

Figure 20 shows the calculated $\log N$–$\log S$ distributions from the actual
cycle 5+6 observations. The NEP-TDF survey reaches fainter 8–24 keV fluxes
than previous NuSTAR extragalactic surveys (i.e., COSMOS, EGS, and ECDFS;
Harrison et al. 2016). The number of sources at the bright end in the 3–8 keV
and 8–24 keV bands is a little high but (at $\sim$1 $\sigma$) consistent with
previous measurements, especially given cosmic variance in the $\sim$0.16 deg2
area of the NEP-TDF survey. This excess cannot be explained solely by the
bright blazar in the FoV. The observed $\log N$–$\log S$ distributions are
also generally consistent with CXB population-synthesis models (e.g., Gilli et
al., 2007; Ueda et al., 2014). However, there may be an excess of hard X-ray
sources at the faint end of the 8–24 keV distribution, although again only at
the $\sim$1 $\sigma$) level. Extrapolating the Harrison et al. (2016) $\log
N$–$\log S$ distribution shows a possible excess, but Masini et al. (2018a)
found no such excess at 8–16 keV in the UDS field. If this excess is real,
more heavily obscured sources exist than predicted by the population-synthesis
models.

###  7.2 Hardness Ratio

Hardness ratio (HR) is useful to characterize the spectral shape of the XMM-
Newton and NuSTAR NEP-TDF sources. The HRs of different column densities were
estimated using a physical model which is typically used for modeling AGN
X-ray spectra. The model includes a line-of-sight component (modeled by an
absorbed power law), reflection component (modeled by borus02, Baloković et
al., 2018), and scattered emission of soft X-rays (modeled by a fractional
power law). The model was calculated with XSPEC as
phabs$\times$(zphabs$\times$powerlw+borus+constant$\times$powerlw). phabs
models the Galactic absorption. We assumed a photon index $\Gamma=1.8$ in both
powerlw and borus02 and a torus column density $N\rm_{H,Tor}=1.4\times
10^{24}$ cm-2, a covering factor of $f_{c}=0.67$ in borus02, and an
inclination angle $\theta_{\rm inc}=60\arcdeg$ following the torus properties
measured by Zhao et al. (2021b). We assumed a constant = 1% fraction of the
intrinsic emission being scattered (Ricci et al., 2017).

Table 10 reports the HRs of XMM-Newton sources. They are defined as
$(H-S)/(H+S)$ with 0.5–2 keV flux as the soft band flux $S$ and 2–10 keV flux
as the hard band flux $H$. Table 10 also reports $S$ and $H$, which were
calculated with the SAS emldetect tool. Figure 21 shows the HR distribution of
the 286 XMM-Newton sources. The expected HR for a given obscuration depends on
the source redshift as shown in Figure 21. About half (48%) of the XMM-Newton-
detected sources have HR larger than expected for column density
$N\rm_{H}=10^{22}$ cm-2 or have a lower limit of HR that implies an obscured
source. For the 85 XMM-Newton sources that have redshift measurements, 38% are
obscured. That lower percentage might be due to the bias from $m_{i}\leq 22$
mag selection for Hectospec observation: obscured sources are typically
fainter in the visible light than unobscured ones.

Figure 21: Top: log(HR) distribution of the 286 XMM-Newton-detected sources.
Dashed lines show the expected log(HR) for a source at $z=0.60$ (the mean
redshift of the XMM-Newton sources with spectroscopic redshifts) and different
obscuring column densities $N_{\rm H}$ as labeled. Bottom: log(HR) of XMM-
Newton sources versus redshift. Blue squares represent sources with
spectroscopic redshifts and red circles those with photometric redshifts.
Dashed lines show the expected HR $N_{\rm H}$ for different column densities
as labeled. The three CT-AGN candidates detected by NuSTAR (Figure 22) are
shown as green-filled symbols.

Figure 22: Top: log(HR) distribution of all 60 NuSTAR-detected sources versus
source ID. Dashed lines show expected HRs for $z=0.734$, the median redshift
of the NuSTAR sources having measured redshifts, and for values of $N_{\rm H}$
as labeled. Bottom: log(HR) of NuSTAR sources with spectroscopic (blue square)
or photometric (red circle) redshifts as a function of their redshifts. Dashed
lines are the expected HR for different $N_{\rm H}$ values as labeled. (The
green, blue, and black lines overlap.)

The HRs of the NuSTAR sources detected in the cycles 5+6 survey were
calculated using a Bayesian method (BEHR; Park et al., 2006) following Z21.
BEHR can estimate HR even for sources in the Poisson regime with a limited
number of counts. BEHR also calculates the mode and uncertainty of the HR
distribution of each source based on the source’s total and background counts.
Here, $S$ and $H$ were defined as net counts in the 3–8 keV and 8–24 keV
bands, respectively. The 1 $\sigma$ uncertainty was calculated by Gaussian-
quadrature numerical integration when the number of the net counts of either
energy band was less than 15 or by the Gibbs sampler method when the number of
net counts was larger. The differences in the effective exposure times between
the two bands were considered. The upper panel of Figure 22 shows the HR of
the 60 NuSTAR sources. We converted the soft and hard band fluxes to count
rate using the CF listed in Section 3.1 when calculating the model predicted
HR to directly compare with the BEHR calculated HR.

Unlike XMM-Newton, NuSTAR is sensitive to obscurations $N_{\rm H}>10^{23}$
cm-2 (e.g., Masini et al., 2018a). 47% of the NuSTAR detected sources are
obscured above that level, and 23% are Compton-thick (CT, $N_{\rm H}>10^{24}$
cm-2) assuming $z$ = 0.734 (median redshift of the NuSTAR sources). CT
candidates include sources that have lower limits on their HR. Figure 22 shows
HR as a function of redshift for the 22 NuSTAR sources with redshift
measurements. Of these, 23% are heavily obscured, and 14% are CT.

The HRs of the XMM-Newton sources and the model predictions used to compare
with the NuSTAR HRs were calculated assuming particular spectral shapes when
converting the count rates into fluxes. Different assumed column densities and
photon indices lead to different ECFs. The ECF changes by about 70% in the
0.5–2 keV band and about 20% in the 8–24 keV band assuming no intrinsic
absorption compared to a CT absorption. This might explain the discrepancy of
the column densities estimated using NuSTAR and XMM-Newton. Changing the
photon index has little effect: only $\sim$5% for photon indices $\Gamma=1.40$
or 2.20 rather than the assumed $\Gamma=1.80$. Therefore, a broadband spectral
analysis is needed to accurately measure the obscuration of these sources.
Full spectral analysis of the NuSTAR and XMM-Newton sources will be presented
by S. Creech et al. in prep.

###  7.3 CT Fraction

As shown in Section 7.2, XMM-Newton is more sensitive to distinguishing
between obscured and unobscured sources, while NuSTAR is more powerful in
determining whether a source is CT. Three CT sources (ID 46/51/54) with
redshift measurements are shown in Figure 22. Three additional sources (ID
39/42/48) lack redshift measurements but have $\rm HR>0.736$, the CT threshold
at $z=0$. Therefore, at least six sources are CT based on HR. For the rest of
the sources without redshift measurements, five are CT candidates if $z\geq
0.734$. Another 12 sources have HR uncertainty ranges that include the
$z=0.734$ CT threshold. A reasonable estimate is that $(3+3+5)/60=18\%$ of
sources are CT with limits of 6–23 sources or 10–38%. Additional redshift
measurements are needed to tighten the constraints on the CT fraction.

Figure 23: CT fraction in different surveys as a function of survey
sensitivity limit. The CT fraction measured here is plotted as a red star.
Blue and green circles represent the NuSTAR measurements in the COSMOS (Civano
et al., 2015) and UDS (Masini et al., 2018a) fields. The grey triangle,
square, and diamond show the Swift-BAT measurements (Burlon et al., 2011;
Ricci et al., 2015; Torres-Albà et al., 2021). Lines show the CT fractions
predicted by CXB synthesis models: Gilli et al. (2007) (black solid line),
Treister et al. (2009) (blue dash-dot line), Ueda et al. (2014) (green dot
line), and Ananna et al. (2019) (orange dashed line).

The CT fraction measured in the NEP field is consistent with the CT fraction
measured in other surveys as shown in Figure 23. The most directly comparable
values are for the NuSTAR COSMOS field (13%–20%; Civano et al., 2015) and the
NuSTAR UDS field (11.5%$\pm$2.0%; Masini et al., 2018a). For the Swift-BAT
all-sky survey, which samples the bright end of the nearby AGN population,
Burlon et al. (2011) and Ricci et al. (2015) measured a CT fraction of
$\sim$4.6%–7.6%. However, a recent analysis (Torres-Albà et al., 2021) of the
CT-AGN candidates in the BAT sample using high-quality NuSTAR observations
found that many candidates are less than CT-obscured. That brought the CT
fraction of the entire BAT sample down to 3.5%$\pm$0.5%. However, Torres-Albà
et al. (2021) also found that the CT fraction of the BAT sample depends on the
redshift range. A CT fraction of 20% was found for the $z\leq 0.01$ sample and
8% for $z\leq 0.05$ sample. This discrepancy was explained by BAT being biased
against the detection of CT sources at higher redshift. Figure 23 compares the
measured CT fractions with population-synthesis model predictions (Gilli et
al., 2007; Treister et al., 2009; Ueda et al., 2014; Ananna et al., 2019). The
recent Ananna et al. (2019) model is in good agreement with the hard X-ray
observed CT-AGN fraction at both bright and faint fluxes.

###  7.4 An obscured and variable Seyfert galaxy

In addition to the bright blazar mentioned in Section 6.8, there is another
prominent Seyfert galaxy (and radio source; Willner et al. 2023) in the TDF
field. The source XMM ID 17 (shown in Figure 14, NuSTAR ID 58) has XMM-Newton
$\rm HR\geq 0.99$ suggesting $N_{\rm H}>10^{23}$ cm-2 (Figure 21). The NuSTAR
$\rm HR=0.00_{-0.07}^{+0.05}$ also suggests $N_{\rm H}\sim 10^{23}$ cm-2
(Figure 22). The bright core seen in the JWST long-wave imaging but not at
shorter wavelengths supports the interpretation of high but not CT
obscuration. The source’s 2–10 keV luminosity $L(\hbox{2--10\,keV})=4.5\pm
0.5\times 10^{42}$ erg s-1) and 10–40 keV luminosity $L(\hbox{10--
40\,keV})=1.36\pm 0.08\times 10^{43}$ erg s-1 suggest a type 2 AGN. More
intriguing, this source is variable at 3$\sigma$ in 3–24 keV band and at
2.9$\sigma$ in the 3–8 keV band but is not significantly variable in the 8–24
keV band, suggesting a variable spectral shape. Its count rates increased by
115% in the 3–24 keV and 230% in the 3–8 keV band from 2019 Oct to 2022 Jan
(Figure 26). We did not find obvious variability of this source in either
visible (Zwicky Transient Facility, ZTF; Bellm et al., 2019; Masci et al.,
2019) or IR (NEOWISE; Mainzer et al., 2014). This suggests that the X-ray
variability of the source might be caused by the decreasing of the line-of-
sight obscuration rather than the variability of the intrinsic accretion rate.
However, further investigation is needed.

##  8 Conclusions

The NuSTAR extragalactic survey of the JWST NEP-TDF attained a total of 1.5 Ms
exposure and covered an area of $\sim$0.16 deg2. This makes it the deepest
NuSTAR extragalactic survey to date. The survey consists of 21 observations in
NuSTAR cycles 5 and 6 across seven epochs from 2019 Sep to 2022 Jan, enabling
a multi-year, multi-epoch study of this field in hard X-rays. Principal
results are:

  1. 1.

The NuSTAR cycle 6 survey was taken from Oct. 2020 to Jan. 2022 with a total
exposure of 880 ks acquired in 12 observations over four epochs covering an
area of $\sim$0.11 deg2. A total of 35 sources were detected above the 95%
reliability threshold in cycle 6. In the merged cycle 5 and 6 observations,
which reach the deepest sensitivity, 60 sources were detected above the 95%
reliability threshold.

  2. 2.

The survey’s 8–24 keV sensitivities at 20%-area are $1.98\times 10^{-14}$ erg
cm-2 s-1 for NuSTAR cycle 6 and $1.70\times 10^{-14}$ erg cm-2 s-1 for NuSTAR
cycles 5+6. A ${\sim}1\sigma$ excess of faint 8–24 keV sources compared to the
population-synthesis models hints that more faint, heavily obscured sources
might exist than predicted by the models.

  3. 3.

To enable broadband (0.3–24 keV) X-ray spectral fitting and more reliable
multiwavelength counterpart matching of the NuSTAR detected sources, a total
of 60 ks XMM-Newton observations were taken simultaneously with NuSTAR in
cycle 6. A total of 286 XMM-Newton sources were detected including more 3–8
keV sources at the bright end compared to previous number counts.

  4. 4.

Of the 60 NuSTAR sources, 37 have XMM-Newton counterparts. Of the 23 NuSTAR
sources without XMM-Newton counterparts, 17 appear to be heavily obscured.

  5. 5.

The NEP-TDF has extensive multiwavelength coverage, including Subaru/HSC,
J-PAS, and SDSS in optical and MMT/MMIRS and WISE in IR. A total of 214 XMM-
Newton sources have secure counterparts in multiwavelength catalogs, and 19
more have ambiguous counterparts. Deeper optical and IR observations covering
the entire FoV of the XMM-Newton NEP-TDF survey are needed to identify
counterparts of the remaining 53 XMM-Newton sources. In addition, VLA, HST,
and JWST surveyed a fraction of the XMM-Newton NEP-TDF and a total of 55, 102,
and 32 XMM-Newton sources have VLA, HST, and JWST counterparts, respectively.

  6. 6.

Optical spectra of XMM-Newton counterparts produced 82 high-confidence
redshifts. Two additional sources have photometric redshifts measured in SDSS
DR17. The 84 XMM-Newton sources with redshifts include 22 NuSTAR sources. In
addition, spectroscopic redshifts of 40 VLA and Chandra sources in the NEP-TDF
are reported in Table 11.

  7. 7.

Half (48%) of the XMM-Newton sources are obscured with $N_{\rm H}>10^{22}$
cm-2, and 47% of the NuSTAR sources are heavily obscured with $N_{\rm
H}>10^{23}$ cm-2). 18${}_{-10}^{+20}$% of the NuSTAR sources are Compton-
thick. Broadband spectral analysis is needed to accurately measure the column
densities of the sources (S. Creech et al., in prep).

  8. 8.

A type 2 AGN at $z=0.1791$ has X-ray obscuration $N_{\rm H}\sim 10^{23}$ cm-2,
and significant obscuration is supported by JWST and HST images. The source is
significantly variable with its 3–8 keV band flux having increased by 230% in
26 months.

  9. 9.

The prime goal of the NuSTAR NEP-TDF observations is to study hard X-ray
variability. Preliminary results for the 60 sources detected in cycles 5+6
show four sources varying with $p<0.05$ (${\sim}2\sigma$) in at least one
energy band in the 26 months of observations. A detailed study of the source
variability is in preparation.

  10. 10.

Subsequent to the work reported here, an additional 855 ks of NuSTAR
observations and 30 ks of XMM-Newton observations have been obtained in NuSTAR
cycle 8 (PI: Civano, pid 8180, Silver et al., in prep.). These targeted the
NEP-TDF simultaneously with JWST. A further 900 ks of NuSTAR observations and
40 ks of XMM-Newton observations were approved for NuSTAR cycle 9 (PI: Civano,
ID: 9267). Thus the NEP-TDF will acquire a total of 3.25 Ms NuSTAR
observations, making it the newest and deepest NuSTAR extragalactic survey.
The data will constitute five years of continuous hard X-ray monitoring of the
field, making it the first long-term monitoring, contiguous survey of hard
X-ray variability.

  11. 11.

The rich multiwavelength coverage and multi-year NuSTAR monitoring of the NEP-
TDF make it an ideal field for the next generation of hard X-ray surveys. The
High-Energy X-ray Probe (HEX-P) concept141414https://hexp.org (Madsen et al.,
2019) has a larger effective area, much better PSF, and lower background
compared with NuSTAR. This will allow $\sim$20 times deeper sensitivity in the
8–24 keV band compared with the current deepest NuSTAR NEP-TDF survey and
detect $\sim$40 times more hard X-ray sources. HEX-P will be able to resolve
more than 80% of the CXB into individual sources up to 40 keV (Civano et al.,
2023) and better constrain current population-synthesis models. Its broadband
coverage (0.2–80 keV) will allow X-ray spectral analysis of both obscured and
unobscured sources and thus more accurately constrain the CT fraction down to
10-15 erg cm-2 s-1 (Civano et al., 2023; Boorman et al., 2023).

The authors thank the anonymous referee for their helpful comments. XZ
acknowledges NASA funding under contract numbers 80NSSC20K0043 and
80NSSC22K0012. The authors thank Jinguo Liu for helping improve the code
efficiency when calculating the variability of the NuSTAR and XMM-Newton
sources, thereby shortening the calculation time by more than a factor of 10;
Cheng Cheng for helping reduce the Hectospec spectra; Alberto Masini for help
with the proposal preparation and for sharing the data of his previous papers;
Nelson Caldwell and the MMT observing team for the help in generating the
observing catalog and scheduling the Hectospec observations; Brian
Grefenstette for helpful discussion of NuSTAR and its data analysis; Karl
Foster and the NuSTAR observation planning team for their help in designing
the observation plan and scheduling the observations.

This work has made use of data from the NuSTAR mission, a project led by the
California Institute of Technology, managed by the Jet Propulsion Laboratory,
and funded by NASA. This research has made use of the NuSTAR Data Analysis
Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC,
Italy) and the California Institute of Technology (USA). This research made
use of data and software provided by the High Energy Astrophysics Science
Archive Research Center (HEASARC), which is a service of the Astrophysics
Science Division at NASA/GSFC and the High Energy Astrophysics Division of the
Smithsonian Astrophysical Observatory. This work is based on observations
obtained with XMM-Newton, an ESA science mission with instruments and
contributions directly funded by ESA Member States and NASA. The MMIRS,
Hectospec, and Binospec observations reported were obtained at the MMT
Observatory, a joint facility of the Smithsonian Institution and the
University of Arizona. This paper uses data products produced by the OIR
Telescope Data Center, supported by the Smithsonian Astrophysical Observatory.
This work makes use of the data from SDSS IV. Funding for the Sloan Digital
Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S.
Department of Energy Office of Science, and the Participating Institutions.
This work is partly based on the data from WISE, which is a joint project of
the University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, and NEOWISE, which is a project
of the Jet Propulsion Laboratory/California Institute of Technology.

## Data Availability

Electronic versions of the generated NuSTAR and XMM-Newton catalogs as
described in Appendix B can be found in VizieR at link_tbd. (Link will be
provided immediately after the paper is accepted.)

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##  Appendix APPENDIX A Measured to input flux and Signal to noise ratio

The accuracy of the NuSTAR source flux measurement is strongly correlated with
the S/N (as defined in Section 7.1). Figure 24 shows the simulation results.
The dispersion of the measured to input flux ratio is quite high at low S/N,
and there is a strong bias for measured fluxes to be higher than the true
flux, especially at low S/N.

Figure 24: Ratio of measured (3–24 keV) flux to true flux as a function of
measured signal to noise ratio. Points show the ratio for simulated (Section
3) individual sources with different exposure times indicated as shown in the
legend. Points include only (simulated) sources detected with $>$95%
reliability. The vertical dashed line indicates $\rm S/N=2.5$, which was the
cut for calculating $\log N$–$\log S$ (Section 7.1).

##  Appendix APPENDIX B NuSTAR and XMM-Newton Catalog Description

The description of each column of the 95% reliability level catalog of NuSTAR
detected sources in cycle 6 and cycles 5+6 survey is in Table 9. The
description of each column of the catalog of XMM-Newton detected sources is in
Table 10.

In future work, the NuSTAR sources can be referred to as “NuSTAR
JHHMMSS+DDMM.m” where the sequence (JHHMMSS+DDMM.m) is the contents of column
2 of either of the NuSTAR data tables. Similarly, the XMM sources can be
referred to as “TDFXMM JHHMMSS+DDMM.m” with the sequence given in column 2 of
the XMM-Newton data table.

##  Appendix APPENDIX C Hectospec observations of non-XMM targets in NEP-TDF

Table 11 reports the coordinates, redshifts, and spectral types of the 40 VLA
and Chandra sources in the NEP-TDF.

##  Appendix APPENDIX D Variability Calculation

Figure 25: 3–8 keV net count-rate posterior probability distribution of NuSTAR
source ID 58 in each epoch. Epochs are distinguished by color in the order
blue, orange, green, red, violet, brown, magenta (the same as Figure 27, which
shows dates for each epoch). Count-rate PPDs are count PPDs divided by
exposure time. Figure 26: “False-alarm” probability $p$ of each source. Colors
and point shapes show different energy bands as indicated in the legend. The
horizontal dashed line shows $p=0.05\approx 2\sigma$. Points above this line
have higher probability of being true variables.

Studying source variability is the prime goal of the NuSTAR NEP-TDF. Thanks to
the multi-year and multi-epoch observations in the field, NEP-TDF became the
first NuSTAR contiguous survey to study hard-X-ray (3–24 keV) variability.

The traditional method for analyzing X-ray-source variability (e.g., Yang et
al., 2016) is not suitable for NuSTAR contiguous surveys because that method
requires good counting statistics and negligible backgrounds. After adding all
seven epochs in cycles 5 and 6, the median NuSTAR-detected (3–24 keV) source
has 120 net source counts on top of 700 background counts. This gives low S/N
and an uncertain net count rate for individual epochs. Therefore, we developed
a dedicated pipeline to analyze source variability in the low-count regime.
This paper describes the pipeline and briefly summarizes the source
variability results. A future paper will provide a systematic discussion of
source variability in the NuSTAR and XMM-Newton NEP-TDF.

The pipeline follows the Bayesian approach developed by Primini & Kashyap
(2014) and used to generate the Chandra Source
Catalog151515https://cxc.cfa.harvard.edu/csc/ (CSC). The key calculation is
the probability distribution of the expected net source counts in each epoch.
This approach is able to deal with the Poisson (not Gaussian) statistical
noise and is valid in low-counts regimes because it uses Poisson likelihoods.
The net count posterior probability distribution (PPD) was calculated using
Equation 16 of Primini & Kashyap (2014) assuming non-informative prior
distributions. We used a circle with 20″ radius to extract the total and
background counts from each epoch’s image and background map. Thus we analyzed
only the inter-epoch variability rather than the intra-epoch’s variability. As
the sources are not detectable in every epoch, we used a fixed source position
(the one reported in the catalog) for all epochs and energy bands. Figure 25
shows the net count-rate PPDs for the most-likely variable source (ID 58).

The probability of source variability came from applying the $\chi^{2}$ test
following the CSC method (Nowak, 2016). The method computes the deviation
between the most probable flux in each epoch and the most probable flux in the
entire survey. The null hypothesis is that there is no variability, and the
“false-alarm” probability $p$ was calculated from equation 10 of Nowak (2016).
A smaller $p$ suggests a larger probability that variability exists. Figure 26
shows $p$ for the NuSTAR sources. Of the 60 sources, 44 were observed in all
seven epochs, and 9, 4, and 3 sources were observed in six, five, and one
epoch(s), respectively. Four sources (ID 21/25/29/58) show variability at
$p<0.05(\sim 2\sigma)$ in at least one band, and Figure 27 shows their light
curves. The same pipeline can be used for XMM-Newton data, and those results
will be presented in a future paper.

Figure 27: Light curves of the four sources that show the most variability. Sources are labeled at the top of each panel, and sections top to bottom show different energy ranges as labeled. Point colors for each epoch are the same as in Figure 25. Table 9: NuSTAR 95% reliability source catalog description. Col. | Description
---|---
1 | NuSTAR source ID used in this paper.
2 | Source name (use “NuSTAR JHHMMSS+DDMM.m”).
3–4 | X-ray coordinates (J2000) of the source in whichever energy band has the highest DET_ML.
5 | 3–24 keV band deblended DET ML ($-99$ if the source is not detected in a given band).
6 | 3–24 keV band vignetting-corrected exposure time in ks at the position of the source.
7 | 3–24 keV band total counts (source + background) in a 20″ radius aperture.
8 | 3–24 keV band deblended background counts in a 20″ radius aperture ($-99$ if the source is not detected in a given band).
9 | 3–24 keV band not deblended background counts in a 20″ radius aperture.
10 | 3–24 keV band net counts (deblended if detected & above DET ML threshold or 90% confidence upper limit if
| undetected or detected but below DET ML threshold) in a 20″ radius aperture.
11–12 | 3–24 keV band 1 $\sigma$ positive/negative net counts uncertainty ($-99$ for upper limits).
13 | 3–24 keV band count rate (90% confidence upper limit if not detected or detected but below the threshold) in a 20″
| radius aperture.
14 | 3–24 keV band aperture corrected flux (erg cm-2 s-1; 90% confidence upper limit if below 95% confidence threshold).
15–16 | 3–24 keV band positive/negative flux uncertainties (erg cm-2 s-1; $-99$ for upper limits).
17–28 | same as columns 5–16 but for 3–8 keV.
29–40 | same as columns 5–16 but for 8–24 keV.
41–52 | same as columns 5–16 but for 8–16 keV.
53–64 | same as columns 5–16 but for 16–24 keV.
65 | Hardness ratio computed using BEHR.
66–67 | Upper/lower limit of hardness ratio.
68 | XMM-Newton source ID from the XMM-Newton catalog ($-1$ if non-detection).
69,70 | Soft X-ray coordinates of the associated source ($-1$ if no XMM-Newton counterpart).
71 | NuSTAR to soft X-ray counterpart position separation in arcsec.
72 | 3–8 keV flux converted from XMM-Newton 2–10 keV flux (90% confidence upper limit if $\tt mlmin<6$).
73 | 3–8 keV XMM-Newton flux 1$\sigma$ uncertainty ($-99$ for upper limit).
74 | Flag for NuSTAR counterparts (S, P, Sec, C if the XMM source is the single, primary, secondary, or
| confusing counterpart of the NuSTAR source, respectively).
75 | Flag for ancillary class (S for secure, A for ambiguous, and U for unidentified)
76,77 | Ancillary coordinates of the associated source ($-99$ if no detection).
78 | Optical (HSC) $i$ band AB magnitude ($-99$ if no detection).
79,80 | MMIRS $J$ and $K$ band AB magnitude ($-99$ if no detection).
81,82 | WISE $W1$ and $W2$ band AB magnitude ($-99$ if no detection).
83 | VLA 3 GHz counterpart ID from Hyun et al. (2023).
84 | VLA 3 GHz flux density in $\mu$Jy (Hyun et al., 2023).
85 | HST F606W AB magnitude ($-99$ if no detection).
86 | JWST F444W AB magnitude ($-99$ if no detection).
87 | Spectroscopic redshift of the associated source.
88 | Photometric redshift of the associated source.
89 | Spectroscopic classification (Q for quasars, G for galaxies, S for stars, N/A if no measurement). Galaxies are defined
| as objects without broad emission lines and therefore include type 2 AGN.
90 | Luminosity distance in Mpc (70/0.3/0.7 cosmology, $-99$ if no redshift measurement).
91 | 10–40 keV band rest-frame luminosity ($-99$ if no redshift measurement).
92–93 | 10–40 keV band 1$\sigma$ positive/negative rest-frame luminosity uncertainty ($-99$ if no redshift measurement).
94 | Source ID in the Zhao et al. (2021a) NuSTAR cycle 5 catalog ($-99$ for non-detection in the cycle 5 catalog).
Table 10: XMM-Newton source catalog description. Col. | Description
---|---
1 | XMM-Newton source ID used in this paper.
2 | XMM-Newton source name (use “TDFXMM JHHMMSS+DDMM.m”).
3–4 | X-ray coordinates (J2000) of the source.
5 | 0.5–2 keV band DET ML.
6 | 0.5–2 keV band vignetting-corrected exposure time (in ks) at the position of the source.
7 | 0.5–2 keV band net counts of the source (90% confidence upper limit if $\tt mlmin<6$).
8 | 0.5–2 keV band net counts 1$\sigma$ uncertainty ($-99$ for upper limits).
9 | 0.5–2 keV band flux (erg cm-2 s-1; 90% confidence upper limit if $\tt mlmin<6$).
10 | 0.5–2 keV band flux 1 $\sigma$ error ($-99$ for upper limits).
11-16 | same as columns 5–10 but for 2–10 keV.
17 | Hardness ratio (90% confidence upper or lower limits if not constrained).
18 | Hardness ratio 1$\sigma$ uncertainty ($-99$ for upper limits and 99 for lower limits).
19 | NuSTAR source ID from the NuSTAR cycles 5+6 catalog ($-1$ if non-detection).
20 | Flag for NuSTAR cycle 56 counterparts (S, P, Sec, C if the XMM source is the single, primary, secondary,
| or confused counterpart of the NuSTAR source, respectively).
21 | NuSTAR source ID from the NuSTAR cycle 6 catalog ($-1$ if non-detection).
22 | Flag for NuSTAR cycle 6 counterparts (S, P, Sec, C if the XMM source is the single, primary, secondary,
| or confused counterpart of the NuSTAR source, respectively).
23 | Flag for ancillary class (S for secure, A for ambiguous, or U for unidentified)
24,25 | Ancillary coordinates of the associated source ($-99$ if no detection).
26 | Optical (HSC) $i$ band AB magnitude ($-99$ if no detection).
27 | Flag for SDSS detection (1 if SDSS has detection, $-1$ if SDSS has no detection)
28 | Flag for J-PAS detection (1 if J-PAS has detection, $-1$ if J-PAS has no detection)
29,30 | MMIRS $J$ and $K$ band AB magnitude ($-99$ if no detection).
31,32 | WISE $W1$ and $W2$ band AB magnitude ($-99$ if no detection).
33 | VLA 3 GHz counterpart ID from Hyun et al. (2023).
34 | VLA 3 GHz flux in $\mu$Jy (Hyun et al., 2023).
35 | HST F606W AB magnitude ($-99$ if no detection).
36 | JWST F444W AB magnitude ($-99$ if no detection).
37 | Spectroscopic redshift of the associated source ($-99$ if no measurement).
38 | Photometric redshift of the associated source ($-99$ if no redshift measurement).
39 | Spectroscopic classification (Q for quasars, G for galaxies, S for stars, N/A if no measurement). Galaxies are defined
| as objects without broad emission lines and therefore include type 2 AGN.
41 | 0.5–2 keV band rest-frame luminosity before correcting for absorption assuming a photon index of $\Gamma$ = 1.40
| ($-99$ if not detected in the 0.5–2 keV band).
42 | 0.5–2 keV band rest-frame luminosity 1$\sigma$ uncertainty.
43 | 2–10 keV band rest-frame luminosity before correcting for absorption assuming a photon index of $\Gamma$ = 1.80
| ($-99$ if not detected in the 2–10 keV band).
44 | 2–10 keV band rest-frame luminosity 1$\sigma$ uncertainty.
Table 11: Hectospec observations of 40 VLA and Chandra targets in NEP-TDF.  Name | RA | DEC | $z$ | Class
---|---|---|---|---
VLA 3 | 260.351313 | 65.814148 | 0.2923 | G
VLA 48 | 260.507012 | 65.740059 | 0.6297 | G
VLA 52 | 260.522058 | 65.680923 | 0.5010 | G
VLA 62 | 260.530900 | 65.924820 | 0.2720 | G
VLA 74 | 260.562717 | 65.810898 | 0.0806 | G
VLA 82 | 260.573729 | 65.660584 | 0.6312 | G
VLA 140 | 260.638762 | 65.653336 | 0.1785 | G
VLA 159 | 260.648546 | 65.797379 | 0.2953 | G
VLA 164 | 260.652038 | 65.93177 | 0.0415 | G
VLA 173 | 260.658704 | 65.849815 | 0.4972 | G
VLA 185 | 260.666254 | 65.671364 | 2.80 | QaaThis broad absorption-line quasar also has a JCMT detection.
VLA 198 | 260.674983 | 65.976944 | 0.0746 | G
VLA 200 | 260.678471 | 65.83725 | 0.5658 | G
VLA 222 | 260.692892 | 65.861908 | 0.2946 | G
VLA 246 | 260.71455 | 65.753357 | 0.5397 | G
VLA 260 | 260.721475 | 65.813164 | 0.545 | G
VLA 382 | 260.799721 | 65.837288 | 0.3759 | G
VLA 386 | 260.805617 | 65.730148 | 1.0415 | G
VLA 429 | 260.838487 | 65.837677 | 0.8905 | G
VLA 439 | 260.846929 | 65.744003 | 0.3774 | G
VLA 477 | 260.881892 | 65.722382 | 0.3748 | G
VLA 514 | 260.910617 | 65.905113 | 0.3579 | G
VLA 528 | 260.919458 | 65.831345 | 0.3762 | G
VLA 561 | 260.946979 | 65.874069 | 0.3820 | G
VLA 574 | 260.961083 | 65.761307 | 0.0964 | G
VLA 592 | 260.978937 | 65.782906 | 0.2923 | G
VLA 628 | 261.009637 | 65.638786 | 0.5643 | G
VLA 656 | 261.038017 | 65.746704 | 0.5567 | G
VLA 675 | 261.057729 | 65.784676 | 0.2946 | G
VLA 688 | 261.073267 | 65.855888 | 0.1055 | G
VLA 705 | 261.116296 | 65.777801 | 0.4136 | G
VLA 721 | 261.151712 | 65.851639 | 0.4464 | G
VLA 752 | 261.251333 | 65.815597 | 0.5010 | G
VLA 755 | 261.289646 | 65.827973 | 0.1816 | G
Cha 11 | 260.729742 | 65.926109 | 0.008 | G
Cha 38 | 260.404500 | 65.799156 | 0 | S
Cha 43 | 260.538454 | 65.827545 | 0.776 | G
Cha 47 | 260.397692 | 65.838997 | 0.6487 | G
Cha 50 | 260.804071 | 65.886581 | 0.8347 | Q
Cha 76 | 260.363158 | 65.852623 | 0.2762 | G