# The NuSTAR Serendipitous Survey: the 80-month catalog and source properties
of the high-energy emitting AGN and quasar population

Claire L. Greenwell Centre for Extragalactic Astronomy, Department of Physics,
Durham University, Durham, DH1 3LE, UK  Lizelke Klindt Centre for
Extragalactic Astronomy, Department of Physics, Durham University, Durham, DH1
3LE, UK  George B. Lansbury European Southern Observatory, Karl-Schwarzschild
str. 2, D-85748 Garching bei München, Germany  David J. Rosario School of
Mathematics, Statistics and Physics, Herschel Building, Newcastle University,
Newcastle upon Tyne, NE1 7RU, UK  Centre for Extragalactic Astronomy,
Department of Physics, Durham University, Durham, DH1 3LE, UK  David M.
Alexander Centre for Extragalactic Astronomy, Department of Physics, Durham
University, Durham, DH1 3LE, UK  James Aird Institute for Astronomy,
University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK  School of
Physics & Astronomy, University of Leicester, University Road, Leicester LE1
7RJ, UK  Daniel Stern Jet Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Mail Stop 169-221, Pasadena, CA 91109, USA
Karl Forster  Cahill Center for Astrophysics, 1216 East California Boulevard,
California Institute of Technology, Pasadena, CA 91125, USA  Michael J. Koss
Eureka Scientific, 2452 Delmer Street, Suite 100, Oakland, CA 94602-3017, USA
Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301, USA
Franz E. Bauer Instituto de Astrofísica and Centro de Astroingeniería,
Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306,
Santiago 22, Chile  Millennium Institute of Astrophysics, Nuncio Monseñor
Sótero Sanz 100, Of 104, Providencia, Santiago, Chile  Claudio Ricci
Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias,
Universidad Diego Portales, Av. Ejército Libertador 441, Santiago, Chile
Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing
100871, China  John Tomsick Space Sciences Laboratory, 7 Gauss Way, University
of California, Berkeley, CA 94720-7450, USA  William N. Brandt Department of
Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Lab,
University Park, PA 16802, USA  Institute for Gravitation and the Cosmos, The
Pennsylvania State University, University Park, PA 16802, USA  Department of
Physics, The Pennsylvania State University, University Park, PA 16802, USA
Thomas Connor Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive, Mail Stop 169-221, Pasadena, CA 91109, USA  Peter G.
Boorman Cahill Center for Astrophysics, 1216 East California Boulevard,
California Institute of Technology, Pasadena, CA 91125, USA  Astronomical
Institute, Academy of Sciences, Boc̆ní’ II 1401, CZ-14131 Prague, Czech
Republic  Adlyka Annuar  Department of Applied Physics, Faculty of Science and
Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor,
Malaysia  David R. Ballantyne Center for Relativistic Astrophysics, School of
Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA
30332-0430, USA  Chien-Ting Chen Science and Technology Institute,
Universities Space Research Association, Huntsville, AL 35805, USA
Astrophysics Office, NASA Marshall Space Flight Center, ZP12, Huntsville, AL
35812, USA  Francesca Civano NASA Goddard Space Flight Center, Greenbelt, MD,
USA  Andrea Comastri INAF - Osservatorio di Astrofisica e Scienza dello Spazio
di Bologna, Via Piero Gobetti, 93/3, 40129, Bologna, Italy  Victoria A.
Fawcett School of Mathematics, Statistics and Physics, Herschel Building,
Newcastle University, Newcastle upon Tyne, NE1 7RU, UK  Francesca M. Fornasini
Stonehill College, 320 Washington Street, Easton, MA 02357, USA  Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  Poshak Gandhi School of Physics & Astronomy, University of Southampton,
Southampton SO17 1BJ, UK  Fiona Harrison  Cahill Center for Astrophysics, 1216
East California Boulevard, California Institute of Technology, Pasadena, CA
91125, USA  Marianne Heida European Southern Observatory, Karl-Schwarzschild
str. 2, D-85748 Garching bei München, Germany  Ryan Hickox  Department of
Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH
03755, USA  Elias S. Kammoun Dipartimento di Matematica e Fisica, Università
Roma Tre, via della Vasca Navale 84, I-00146 Rome, Italy  IRAP, Université de
Toulouse, CNRS, UPS, CNES 9, Avenue du Colonel Roche, BP 44346, F-31028,
Toulouse Cedex 4, France  INAF – Osservatorio Astrofisico di Arcetri, Largo
Enrico Fermi 5, I-50125 Firenze, Italy  Lauranne Lanz Department of Physics,
The College of New Jersey, 2000 Pennington Road, Ewing, NJ 08628, USA  Stefano
Marchesi Dipartimento di Fisica e Astronomia (DIFA) Augusto Righi, Università
di Bologna, via Gobetti 93/2, I-40129 Bologna, Italy  INAF - Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti, 93/3, 40129,
Bologna, Italy  Department of Physics and Astronomy, Clemson University,
Kinard Lab of Physics, Clemson, SC 29634, USA  Gaël Noirot  Institute for
Computational Astrophysics and Department of Astronomy & Physics, Saint Mary’s
University, 923 Robie Street, Halifax, NS B3H3C3, Canada  Encarni Romero-
Colmenero South African Astronomical Observatory, PO Box 9, Observatory, South
Africa  Southern African Large Telescope, PO Box 9, Observatory, South Africa
Ezequiel Treister Instituto de Astrofísica, Facultad de Física, Pontificia
Universidad Católica de Chile, Casilla 306, Santiago 22, Chile  C. Megan Urry
Physics Department and Yale Center for Astronomy & Astrophysics, PO Box
208120, New Haven, CT 06520-8120, USA  Petri
V$\ddot{\mathrm{A}}$is$\ddot{\mathrm{A}}$nen South African Astronomical
Observatory, PO Box 9, Observatory, South Africa  Finnish Centre for Astronomy
with ESO (FINCA), University of Turku, FI-20014 Turku, Finland  Brian van
Soelen Department of Physics, University of the Free State, 9300 Bloemfontein,
South Africa

###### Abstract

We present a catalog of hard X-ray serendipitous sources detected in the first
80 months of observations by the Nuclear Spectroscopic Telescope Array
(NuSTAR). The NuSTAR serendipitous survey 80-month (NSS80) catalog has an
unprecedented $\sim$ 62 Ms of effective exposure time over 894 unique fields
(a factor of three increase over the 40-month catalog), with an areal coverage
of $\sim$ 36 deg2, larger than all NuSTAR extragalactic surveys. NSS80
provides 1274 hard X-ray sources in the $3-24$ keV band (822 new detections
compared to the previous 40-month catalog). Approximately 76% of the NuSTAR
sources have lower-energy ($<10$ keV) X-ray counterparts from Chandra, XMM-
Newton, and Swift-XRT. We have undertaken an extensive campaign of ground-
based spectroscopic follow-up to obtain new source redshifts and
classifications for 427 sources. Combining these with existing archival
spectroscopy provides redshifts for 550 NSS80 sources, of which 547 are
classified. The sample is primarily composed of active galactic nuclei (AGN),
detected over a large range in redshift ($z$ = 0.012–3.43), but also includes
58 spectroscopically confirmed Galactic sources. In addition, five AGN/galaxy
pairs, one dual AGN system, one BL Lac candidate, and a hotspot of 4C 74.26
(radio quasar) have been identified. The median rest-frame $10-40$ keV
luminosity and redshift of the NSS80 are
$\langle{L_{\mathrm{10-40\,keV}}}\rangle$ = 1.2 $\times$ 1044 erg s-1 and
$\langle z\rangle=0.56$. We investigate the optical properties and construct
composite optical spectra to search for subtle signatures not present in the
individual spectra, finding an excess of redder BL AGN compared to optical
quasar surveys predominantly due to the presence of the host-galaxy and, at
least in part, due to dust obscuration.

catalogs – galaxies: active – galaxies: nuclei – quasars: general – surveys –
X-rays: general

††software: Astropy (Astropy Collaboration et al., 2013, 2018, 2022),
Matplotlib (Hunter, 2007), NumPy (Harris et al., 2020) and SciPy (Virtanen et
al., 2020).

##  1 Introduction

A major focus of X-ray surveys over the last few decades has been
understanding the origin of the Cosmic X-ray Background (CXB). The CXB was
first discovered in the early 1960’s (see Giacconi et al., 1962), several
years before the identification of the cosmic microwave background (CMB;
Penzias & Wilson, 1965; Dicke et al., 1965). Unlike the CMB, which is truly
diffuse in origin, the CXB is found to be dominated by the emission from high-
energy distant point sources (Brandt & Alexander, 2015; Brandt & Yang, 2021):
Active Galactic Nuclei (AGNs), the observed manifestation of the accretion of
gas and dust onto a super-massive black hole (see Lynden-Bell, 1969).
Therefore the CXB essentially provides a fossil record of mass accretion onto
super-massive black holes throughout cosmic time. Consequently, ever since the
discovery of the CXB over five decades ago, a key objective of high-energy
astrophysics has been to measure the properties and evolution of AGN
throughout cosmic time using sensitive X-ray observations.

Huge progress in the resolution of the CXB has been made using X-ray
telescopes at low energies ($\lesssim 10$ keV). The most sensitive X-ray
surveys with Chandra (e.g., Hickox & Markevitch, 2007; Cappelluti et al.,
2017; Luo et al., 2017) and XMM-Newton (e.g., Moretti et al., 2003; De Luca &
Molendi, 2004; Worsley et al., 2005) have resolved $\approx$ 70–90% of the CXB
at low energies into AGNs at $z<$ 5–6. However, the energy flux density of the
CXB peaks at 20–30 keV (see e.g. Fig. 2 of Ananna et al., 2020) and, until
recently, observatories in this energy range (e.g., Swift-BAT; INTEGRAL) had
only resolved $\approx$ 1–2% of the CXB at these energies (e.g., Burlon et
al., 2011). The great breakthrough in resolving the peak of the CXB comes from
the Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al., 2013).
NuSTAR is the first orbiting observatory with focusing optics and significant
collecting area at $>10$ keV, allowing for a $\approx$ 2 orders of magnitude
improvement in sensitivity and an order of magnitude improvement in angular
resolution over previous non-focusing hard X-ray missions. Importantly, the
high-energy coverage at $3-79$ keV means that NuSTAR selects AGNs almost
irrespective of the absorbing column as it peels back the curtain of gas and
dust, missing only the most heavily obscured systems (with line-of-sight
column densities of $N_{\mathrm{H}}\geq 10^{23}$ cm-2). This has opened up the
possibility to study large, cleanly selected samples of high-energy-emitting
AGNs in the distant universe.

The NuSTAR extragalactic survey is the largest scientific project undertaken
to date with NuSTAR (Harrison et al., 2013, 2016a). It has resolved $\approx$
35% of the CXB at $8-24$ keV (Harrison et al., 2016a), provided the first
measurements of the $>10$ keV AGN luminosity function at $z>0.1$ (Aird et al.
2015a), and identified heavily obscured AGN (e.g., Civano et al., 2015;
Lansbury et al., 2017a; Masini et al., 2018). There are two main components to
the NuSTAR extragalactic survey: (i) dedicated surveys of well-studied blank-
fields ($\approx$ 3 deg2) including COSMOS (Civano et al., 2015), ECDFS
(Mullaney et al., 2015), EGS (Aird et al., in prep), GOODS-N (Aird et al., in
prep), and UDS (Masini et al., 2018), and (ii) a wide-area “serendipitous
survey” performed by searching archival NuSTAR observations for background
X-ray sources (Alexander et al., 2013; Lansbury et al., 2017b, hereafter L17).
The serendipitous survey is the largest component of the extragalactic survey
programme, providing the majority ($\approx$ 75–80%) of NuSTAR detected
sources.111We note that, although Galactic sources are identified in the
NuSTAR serendipitous survey, the majority are extragalactic; consequently, we
consider the NSS80 to be predominantly an extragalactic survey. See Tomsick et
al. (2017, 2018) for results on galactic sources detected in the NuSTAR
serendipitous survey. It provides a combination of deep and shallow wide-area
coverage, which fills out the $L_{\mathrm{X}}$–$z$ plane and identifies rare
CXB source populations not detected in the smaller-area dedicated NuSTAR
surveys. For example, our first full catalog, the 40-month serendipitous
survey catalog (Lansbury et al., 2017b) contained 497 sources over 13 deg2,
already a factor $>$ 4 larger volume than the dedicated surveys.

Here we provide an update to L17 with the 80-month serendipitous survey
catalog, hereafter NSS80. Due to an increase in the fraction of general
observer (GO) observations compared to the 40-month survey catalog (hereafter
NSS40), the areal coverage ($\sim$ 36 deg2), integrated exposure ($\sim$ 62
Ms), number of fields (894), and number of sources (1274) in the 80-month
catalog are a factor $\approx$ 3 larger than those presented in L17. The most
natural comparison survey to the NSS80 is the Swift-BAT survey (Baumgartner et
al., 2013; Oh et al., 2018), which has identified $\approx$ 1600 sources at
$>10$ keV in 105-months of observations over the entire sky. Comparable
serendipitous X-ray surveys have also been undertaken and regularly updated
with the Chandra (Evans et al., 2010, 2019), XMM-Newton (Webb et al., 2020),
and Swift-XRT (Evans et al., 2014, 2020) but at lower X-ray energies. A
substantially greater number of X-ray sources are detected in these surveys
($\approx$ 200,000–550,000) due to their larger areal coverage and/or greater
relative X-ray sensitivity than NSS80 at $<10$ keV. These catalogs, both
individually and in combination, provide a wealth of resource to the X-ray
astronomy community, greatly improving the range of possible studies. The
NuSTAR serendipitous survey (higher energy than Chandra, XMM-Newton, and
Swift-XRT; more sensitive and higher resolution than Swift-BAT) is an
important member of that line-up.

Our aim in this paper is to present an update to the NuSTAR serendipitous
survey catalogue, including salient information on the reduction of the NuSTAR
data and construction of the catalogue, the identification of multi-wavelength
counterparts, spectroscopic follow-up observations and identifications, in
addition to some brief scientific analyses to motivate further in-depth
studies with the NSS80. This approach is consistent with our previous NuSTAR
survey work (e.g., Alexander et al., 2013; Civano et al., 2015; Harrison et
al., 2016a; Lansbury et al., 2017b; Masini et al., 2018). In Section 2 we
detail the NuSTAR observations, data reduction and source-detection to
construct the 80-month catalog. We search for counterparts at lower X-ray
energies from Chandra, XMM-Newton, and Swift-XRT, described in Section 3.1,
and utilize a probabilistic approach with Nway to reliably cross-match to
infrared and optical counterparts, described in Section 3.2.222Nway provides
an improvement on simple distance-based matching, using a wider array of
information to find likely matches; see Salvato et al. (2018). To obtain
spectroscopic identifications for the NSS80 sources (redshifts and
classifications), we undertake an extensive follow-up campaign with ground-
based optical telescopes at multiple latitudes (Section 3.3). To characterise
the properties of the NSS80 sources, we use X-ray, multi-wavelength
photometry, and optical spectroscopy in Section 4. The basic X-ray properties
of the extragalactic NSS80 sample are given in Section 4.1, the MIR properties
of the sources are examined in Section 4.2, and in Section 4.3 we explore the
optical properties of the AGN, with a particular focus on red quasars and the
utilization of composite spectra to determine the origin of their observed
optical colors. Finally, in Section 5 we draw conclusions and summarise our
results. We assume a concordance flat $\Lambda$-cosmology with $H_{0}$ = 70 km
s-1 Mpc-1 , $\Omega_{M}$ = 0.3, and $\Omega_{\Lambda}$ = 0.7.

##  2 The NuSTAR data

The NuSTAR observatory (Harrison et al., 2013) was launched in 2012 and
consists of two grazing-incidence telescopes that focus X-rays onto two focal
plane modules (FPMA and FPMB) which cover a co-aligned field-of-view of
$\approx 12^{\prime}\times 12^{\prime}$. NuSTAR is sensitive to photons across
the $3-79$ keV energy range and achieves an angular resolution of 18′′ FWHM
and a half power diameter of 58′′, which enables 2 orders of magnitude
improvement in sensitivity over previous X-ray missions with sensitivity to
hard ($\gtrsim 10$keV) energies. In this work we present our analysis and
results for the $3-8$ keV (soft band), $8-24$ keV (hard band) and $3-24$ keV
(full band) energy bands (following the energy bands adopted in previous
NuSTAR survey work, see Alexander et al., 2013; Luo et al., 2014; Aird et al.,
2015; Lansbury et al., 2015; Harrison et al., 2016a; Lansbury et al., 2017b),
with the $3-24$ keV band being our main focus since it provides the best
sensitivity for the detection of relatively faint sources in the NuSTAR
extragalactic surveys.333Adopting a broad band pass ensures that faint sources
with low photon counts are still likely to be detected, compensating for the
drop in sensitivity at higher energies ($\sim 8-24$ keV) due to the decrease
in the effective area with increasing energy and the increased relative
contribution of instrumental background compared to lower energies.

In the following subsections we outline the selection of the NuSTAR
observations utilized in NSS80 (Section 2.1), describe the data-processing and
source-detection approaches (Section 2.2), summarise the properties of the
serendipitous survey source catalog (Section 2.3), and highlight key changes
between the 40-month and 80-month catalogs (Section 2.4).

###  2.1 The Serendipitous Survey Observations

The NSS80 is comprised of observations taken by NuSTAR over the period from
2012 July to 2019 March and provides a significant update over the NSS40
reported in L17 (2012 July to 2015 November).

The NuSTAR serendipitous survey is constructed by searching the background
regions for sources that are not associated with the original science target
in almost every NuSTAR pointing that is not associated with a dedicated survey
field. Following L17 we excluded observations from:

  * •

dedicated extragalactic survey fields: COSMOS (Civano et al., 2015), ECDFS
(Mullaney et al., 2015), EGS (Aird et al., in prep), GOODS-N (Aird et al., in
prep), and UDS (Masini et al., 2018);

  * •

Galactic surveys (Mori et al., 2015; Hong et al., 2016), i.e., all fields
within a 2 degree radius of the Galactic Center;

  * •

the Norma Arm survey (Fornasini et al., 2017);

  * •

fields where the total counts exceed $10^{6}$ within 120′′ of the on-axis
position due to a bright science target.

In addition, prior to processing the data, we also excluded solar system
fields (i.e., solar, lunar and planetary observations), nebular fields (e.g.,
supernova remnants), galaxy clusters, and fields of nearby galaxy nuclei
(e.g., M31). We further excluded fields found to have bad exposure maps (i.e.,
bad/hot pixels in exposure maps) or if more than two thirds of the field is
contaminated by excess background emission (see Section 2.2 and Figure 3).

Table 1 provides a summary of the NuSTAR serendipitous survey information.
Overall, NSS80 comprises 1457 individual NuSTAR exposures, performed over 894
unique fields, the majority of which come from post-NSS40 observations. These
fields yield an overall sky coverage of 36 deg2 and a cumulative exposure time
of 62.0 Ms, both a factor of $\sim 3$ increase over NSS40 as shown in Table 1.
Figure 1 shows how the number of fields included in the NSS samples has
gradually increased over time, while the average exposure per pointing has
remained roughly constant, driving this overall increase in both the sky
coverage and total exposure time. A key contribution to the increase in the
number of fields with time is the larger number of GO versus Legacy
observations, since the dedicated Legacy survey fields (described above) are
excluded from the serendipitous survey. A further contribution to the
increased area of NSS80 can be attributed to the Swift-BAT snapshot survey
(e.g., Oh et al., 2018), which is a Legacy survey comprising of multiple,
short exposures. Furthermore, two distinctive spikes in the number of fields
are evident: spike 1 (bin 2) includes 128 exposures before GO observations
were undertaken with NuSTAR during the period January – August 2013, and spike
2 (bin 10) includes 193 Cycle 3 GO observations performed during the period of
August 2017 – February 2018. These spikes coincide with a decrease in the
average exposure time indicating that more shallow observations were scheduled
in these periods.

Table 1:  Comparison of included observations in the NSS40 and NSS80 surveys.

|  | NSS40 | post-NSS40 | NSS80
---|---|---|---|---
|  | (L17) |  |
(1) |  Obs. start date | 2012/08 | 2015/12 | 2012/08
(2) |  Obs. end date | 2015/11 | 2019/04 | 2019/04
(3) |  Individual exposures | 510 | 947 | 1457
(4) |  Unique fields | 331 | 563 | 894
(5) |  Cumulative exp. time | 20.4 Ms | 41.6 Ms | 62.0 Ms
(6) |  Sky coverage | 13 deg2 |  |

Note. — Rows: (1) & (2) Observation date range for specific survey. (3) Number
of individual exposures. (4) Number of unique fields, each with contiguous
coverage comprised of one or more NuSTAR exposures. (5) Cumulative exposure
time in Ms. (6) Total sky area coverage in deg2.

Figure 1: The average exposure time (blue circles) and the number of NuSTAR
exposures (green stars) roughly per semester over the full 80-month period. In
general, the average exposure time shows little variation between the 40-month
(shaded grey area) and post-40-month observations, whilst we see an increase
in the number of exposures from the 40-month to the post-40-month survey,
resulting in an increase in the total exposure time per semester which can be
utilized for the NuSTAR serendipitous survey. In total, the 80-month
serendipitous survey includes 1457 individual exposures with a cumulative
exposure time of 62 Ms.

Table 2 lists the individual exposures in alphabetical order for the first 5
unique fields (i.e. comprising of non-overlapping pointings) in the NSS80 (the
full table will be made available online) and provides details including the
number of observations and the number of serendipitous sources detected in
each unique field. For 28% (247/894) of the fields there are multiple NuSTAR
exposures, ranging between two and 15 observations, which are combined
together into a single mosaic (see Section 2.2 and Figure 3). The
serendipitous survey fields have a median exposure time of 34 ks but cover a
wide range in individual exposure times (from $\sim$ 100 s to 1 Ms).

Table 2:  Details of the individual NSS80 NuSTAR observations for the first 5
unique fields (the full table will be made available online).

ID | Science Target | NSS40 | $N_{\rm obs}$ | Obs. ID | Obs. Start Date | R.A. | Decl. | $b$ | $t_{\rm exp}$ | $N_{\rm serendips}$
---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  | (deg) | (deg) | (deg) | (ks) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
1 | 1A_0535p262_SADA_18360 | … | 2 | … | … | 82.00 | 26.00 | -4.87 | 0.9 | 0
1a | … | … | … | 90401371001 | 2018 December 26 | … | … | … | 0.2 | …
1b | … | … | … | 90401371002 | 2018 December 27 | … | … | … | 0.7 | …
2 | 1E1048d1m5937 | … | 5 | … | … | 162.53 | -59.89 | -0.52 | 397.9 | 9
2a | … | … | … | 30001024003 | 2013 July 17 | … | … | … | 25.7 | …
2b | … | … | … | 30001024002 | 2013 July 17 | … | … | … | 26.6 | …
2c | … | … | … | 30001024005 | 2013 July 19 | … | … | … | 167.7 | …
2d | … | … | … | 30001024007 | 2013 July 25 | … | … | … | 119.1 | …
2e | … | … | … | 90202032002 | 2016 August 05 | … | … | … | 58.9 | …
3 | 1E1530m085 | 303 | 1 | 60061265002 | 2015 August 07 | 233.34 | -8.70 | 36.88 | 23.1 | 0
4 | 1E161348m5055 | … | 3 | … | … | 244.37 | -50.92 | -0.27 | 283.2 | 3
4a | … | … | … | 90201028002 | 2016 June 25 | … | … | … | 70.7 | …
4b | … | … | … | 30301017002 | 2017 June 02 | … | … | … | 70.3 | …
4c | … | … | … | 30301013002 | 2018 April 29 | … | … | … | 142.3 | …
5 | 1E1841m045 | … | 6 | … | … | 280.33 | -4.94 | -0.01 | 346.3 | 7
5a | … | 29a | … | 30001025002 | 2012 November 09 | … | … | … | 52.4 | …
5b | … | 29b | … | 30001025004 | 2013 September 05 | … | … | … | 37.8 | …
5c | … | 29c | … | 30001025006 | 2013 September 07 | … | … | … | 70.9 | …
5d | … | 29d | … | 30001025008 | 2013 September 12 | … | … | … | 41.6 | …
5e | … | 29e | … | 30001025010 | 2013 September 14 | … | … | … | 35.4 | …
5f | … | 29f | … | 30001025012 | 2013 September 21 | … | … | … | 108.2 | …

Note. — Columns: (1) ID assigned to each field. For fields with multiple
NuSTAR exposures (i.e., $N_{\mathrm{obs}}$ $>$ 1), each individual component
exposure is listed with a letter suffixed to the field ID (e.g., 1a and 1b).
(2) Object name for the primary science target of the NuSTAR observation(s).
(3) ID assigned to each field in the NSS40 (L17). (4) The number of individual
NuSTAR exposures for a given field. (5) NuSTAR observation ID. (6) Observation
start date. (7) and (8) Right ascension and declination (J2000) coordinates
for the aim-point, in decimal degrees. (9) The IAU Galactic latitude for the
aim-point, in decimal degrees (Blaauw et al., 1960). (10) Exposure time
(“ONTIME” in the NuSTAR image header; ks), for a single FPM (i.e., averaged
over FPMA and FPMB). For multiple exposures the total exposure time is
recorded. (11) The number of serendipitous NuSTAR sources detected in a given
field.

In Figure 2 we show an all-sky map of the 894 unique NuSTAR fields, color
coded by average exposure time. The white filled circles represent the NSS40,
whereas the post-NSS40 fields are shown with filled circles. Both the NSS40
and the post-NSS40 fields comprise pointings across the whole sky, with the
latter having a higher density of observations, as also shown in Figure 1. In
comparison to the NSS40, the number of post-NSS40 fields has increased by
$\approx$ 50% for a given amount of serendipitous sources per field; e.g., 169
NSS40 fields have 1-2 detected sources whereas 255 post-NSS40 fields have 1-2
serendipitous detections (see Section 2.2 for further information on source
detection procedures). The zoom-in panel shows the Galactic plane fields with
$|b|\leq 10^{\circ}$: 174 of the 894 NSS80 fields (19%) lie within the
Galactic plane, also a factor of $\sim$ 3 increase over that of NSS40.

Figure 2: Aitoff projection showing the distribution of the NuSTAR
serendipitous survey fields on the sky, in Galactic coordinates. The white and
color filled circles show the NSS40 and the post-NSS40 data, respectively. The
circle sizes correspond to the number of sources detected in a given field,
and the colors correspond to the cumulative exposure time (per FPM) for a
given field. The white area highlights the region $\pm$10∘ of the Galactic
plane.

###  2.2 Data processing and source-detection

Figure 3:  Upper left panel: Flowchart schematic illustrating the NuSTAR data
processing steps undertaken to reduce individual fields for the serendipitous
survey. A field can comprise multiple exposures (obsIDs) mosaicked into a
single counts image as illustrated on the right. Data from the two telescopes,
FPMA and FPMB, and the Coadded FPMA+B are indicated as “A”, “B” and “C”,
respectively, and the three energy bands are indicated in different colors
($3-8$ keV, 8$-$24 keV and $3-24$ keV). Upper right panel:  Example of real
counts images and exposure maps associated with stages (iii) to (v) for one of
the included processed fields, i.e., IC 2560. The data shown are for the
coadded images and the $3-24$ keV energy band only. This illustrates the
mosaicking of two exposures with different exposure times and orientations.
Information from both the image and the exposure map mosaics is used to
perform source-detection (step (iv)). In this example, three serendipitous
sources (circled) are detected. Lower panel:  Each image mosaic with counts
$<1\times 10^{6}$ is visually assessed to identify regions with excess
background contamination (EBC) which includes stray light, ghost rays,
aperture background and bright science target. If less than two-thirds of the
image is contaminated by excess background, a mask region is created and used
to mask detections from the final source list. Images with counts $>1\times
10^{6}$ or with EBC covering more than two-thirds of the image are excluded
from the catalog (38 exposures were removed in this way).

The reduction of the new (i.e. post-40 month) NuSTAR serendipitous fields
followed the custom pipeline procedure described by L17, which is broadly
consistent with the approach adopted in our previous NuSTAR survey studies
(Mullaney et al., 2015; Aird et al., 2015; Harrison et al., 2016b). An
overview of the NuSTAR data-reduction steps is shown in Figure 3 and described
briefly here, highlighting updates to the L17 procedure (see Section 2.4 below
for further discussion of differences between the final NSS80 and the prior
NSS40 catalogs).

Briefly, the raw event files were processed using the nupipeline procedure
from the NuSTAR Data Analysis Software (NuSTARDAS) v1.9.2
444https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/ (incorporated within
the HEASoft v6.24 software suite) and CIAO v4.7.0 to produce calibrated event
files. These event files were used to produce counts images for each
individual NuSTAR exposure (obsID), which comprises FPMA and FPMB data in the
full, soft and hard energy bands; we note the pixel size is 2.46$"$. We
produced exposure maps that account for the vignetting across the field-of-
view for each energy band (at fixed representative energies of 9.88 keV, 5.42
keV and 13.02 keV for the full, soft and hard bands, respectively) as well as
a single exposure map that does not include vignetting effects (used to
estimate the background count rate at each pixel; see below).

To optimise the depth of our datasets, we coadded the images and exposure maps
from the FPMA and FPMB detectors. This resulted in a total of 9 images and 9
exposure maps per field (3 energy bands for FPMA, FPMB and FPMA+B).555The
uncombined FPMA and FPMB exposure maps are useful to access regions of excess
background contamination; see lower panel of Figure 3. We produced single
mosaics for each energy band by combining observations covering the same sky
region within 12′ of the aim point for each obsID (step (iii) in Figure 3).
There are 54 observations previously included in NSS40 which were coadded with
more recent observations and re-analysed for NSS80. We note that this can lead
to small changes in the resulting source lists, including the detection of
fainter sources or the loss of sources close to the detection limit (see
further details in Section 2.3).

Source-detection [see step (iv) in Figure 3] was performed as described in
L17. To summarize, we first produced a “false probability" map for each energy
band, 666Regions close to the edge of the FoV, with $<$ 10% of the maximum
exposure in the 3–24 keV band and thus where the background is poorly
characterised, are excluded from the source detection process and estimates of
survey area coverage. which gives the probability that the observed counts
within a circular aperture of 20″ radius (justified by the tight core of the
NuSTAR PSF; see Civano et al., 2015; Mullaney et al., 2015) were produced
purely by a fluctuation of the background. The expected background is
estimated by convolving the image counts with an annular aperture of inner
radius 45″ and outer radius 90″and re-scaling to the 20″ source detection
region. These background estimates incorporate counts from any bright target
which will impact the sensitivity to faint serendipitous sources. Finally, we
created source lists by identifying distinct regions where the false
probability is less than $10^{-6}$ (equivalent to $\sim$ 5$\sigma$; see
Mullaney et al., 2015, for full details) using the SExtractor software (Bertin
& Arnouts, 1996). To produce a master source list, we merged the source lists
for the three individual energy bands and removed any sources within a 90″
radius of the science target position. See L17 and references therein for a
full description777As in L17, final source positions are (in order of
priority) full-band, soft-band, then hard-band..

Once the master source list was created, we visually inspected all the post-
processed fields (lower panel in Figure 3) to identify and mask out extended
areas that exhibit a high background rate due to stray light, ghost rays,
aperture background888The aperture background refers to unfocussed X-rays that
pass between the optics and the focal plane i.e. enter via the unbaffled
“sides” of the telescope (see Wik et al., 2014, for further detail). and/or
emission from the science target (illustrated in the lower panel of Figure 3).
These custom-made masks were then applied to both the background estimate and
source-detection procedures, to produce the final source list. We excluded
fields from our analysis when the excess background contamination exceeded two
thirds of the field (based on a visual estimation), resulting in the removal
of 38 fields. In addition to masking excess background contamination, L17 also
created custom-made regions to mask out sky areas which are clearly
overlapping with extended optical/IR counterparts associated with the NuSTAR
science target. However, for NSS80 we included this as a later post-processing
step to obtain an X-ray catalog independent of optical/IR information (see
Section 2.3). To be consistent in the construction of NSS80 we therefore
removed the masked regions for 31 of the 40-month fields with highly extended
optical hosts and reprocessed the data. For further details see Section 2.3.

Following L17, we measured count rates, fluxes, net source counts and its
errors for each detected source, and estimated upper limits for sources
undetected in a given band using the Bayesian approach from Kraft et al.
(1991). We also applied the deblending procedure described in Section 2.3.2 of
Mullaney et al. (2015), which increases the background estimates for a given
source due to the contribution of any other nearby serendipitously detected
sources that will not be accounted for in our smoothly varying background
maps. We then re-assessed the false probability of these sources using the
updated background estimates and excluded sources that no longer met our false
probability detection threshold in at least one of the energy bands. This
process assumes that the sources are all not capable of being resolved by
NuSTAR and are considered effectively point-like.

Figure 4: Sky coverage (solid angle) of the NSS40 (blue) and NSS80 (green)
surveys as a function of aperture-corrected flux sensitivity, for the three
main energy bands, i.e., full ($3-24$ keV), soft ($3-8$ keV) and hard ($8-24$
keV). Note the factor of $\sim$3 increase in the sky coverage with NuSTAR
between the 40-month and 80-month catalogs. The sensitivity curves include
fields at all Galactic latitudes for both NSS40 and NSS80 (cf. the curves
shown in L17 for both the full survey and the subset of fields that lie
outside the Galactic plane, $|b|>10^{\circ}$).

Figure 5: Sky coverage of the NSS40 and NSS80 surveys as a function of flux
sensitivity, for the hard ($8-24$ keV) energy band. The green and blue solid
lines show the area curves for the overall NSS40 and NSS80 surveys,
respectively. We compare with the other completed components of the NuSTAR
extragalactic surveys program, which include the following dedicated deep-
field surveys: COSMOS (dash-dotted black line), ECDFS, EGS, GOODSN and UDS

. The total area for these deep-field surveys is shown as a black solid line.
We also compare to cycle 5 of the NuSTAR extragalactic survey of the James
Webb Space Telescope North Ecliptic Pole (NEP) time-domain field shown in a
dotted black line (Zhao et al., 2021b).

To determine the sensitivity curve for a given background and exposure map, we
calculated the flux limit at the detection threshold for every point in the
NuSTAR image, with the exclusion of the peripheral regions and any regions
that are masked due to high background as described above or corresponding to
extended optical galaxies and nearby galaxy clusters (see Section 2.3 below).
We then summed the sensitivity curves of the 894 unique fields for each of the
three energy bands to obtain the total areal coverage of the NSS80, which
results in a factor $\sim$3 increase in sky coverage compared to NSS40 (see
Figure 4). In Figure 5, we also compare NSS40 and NSS80 to the dedicated
NuSTAR deep-field surveys collectively and the NuSTAR survey of the North
Ecliptic Pole (NEP) region (Zhao et al., 2021b). The NSS80 has the largest
areal coverage at all fluxes but is most comparable to the deep-field surveys
near the low flux tail. Consequently the combination of NSS80 with the deep-
field surveys allows for a factor $\sim$2 improvement in analyses of the faint
end of the hard X-ray source population, in addition to an order of magnitude
increase at brighter fluxes.

With the total area coverage, we can estimate the number of spurious X-ray
detections in NSS80 due to background fluctuations. Our 36 deg2 survey
corresponds to $\approx$370,000 independent 20″radius regions, which with our
strict (i.e. low) false probability threshold of $10^{-6}$ (cf. the higher
thresholds adopted in Mullaney et al., 2015; Civano et al., 2015) corresponds
to an expectation of 0.37 spurious sources in a given band (Nandra et al.,
2005). We thus expect 1.11 spurious X-ray sources due to performing source
detection independently over three bands, although we note that this number is
conservative as the 3–24 keV band overlaps with the other energy bands and is
thus not completely independent.

###  2.3 The Serendipitous Survey Source catalog

The master source list comprises 1488 serendipitous NuSTAR sources that are
significantly detected in at least one energy band, independently of any prior
multi-wavelength information. Based on findings in L17, the majority of the
X-ray detected sources in NSS80 are expected to be AGN which should reside in
background field galaxies that are not associated with the science target.
However, due to the high-sensitivity of NuSTAR and the large areal coverage of
NSS80, a small and non-negligible fraction are X-ray emitting sources within
nearby highly extended galaxies associated with the science target (e.g.,
X-ray binaries and ultra-luminous X-ray sources), X-ray AGN residing in nearby
galaxy clusters, or X-ray emitting sources within the Galaxy. In NSS80 we
therefore distinguish between X-ray detected sources lying within highly
extended optical galaxies and nearby galaxy clusters from those hosted in
fainter field galaxies. To enable easy and efficient use of NSS80, all NuSTAR
sources residing in highly extended optical galaxies and galaxy clusters are
placed in a secondary catalog to complement the primary catalog that is
dominated by AGN in field galaxies. To identify NuSTAR sources in highly
extended optical galaxies or nearby galaxy clusters we selected sources that
lay within

  * •

the isophotal radius ($D_{25}$) of RC3 galaxies (Third Reference Catalog of
Bright Galaxies; de Vaucouleurs et al., 1995) where the $R$-band surface
brightness $\mu_{R}$ = 25 mag arcsec-2, including the SMC and LMC; or

  * •

the radii of Abell clusters obtained from Abell (1958) or, if unavailable, a
median value of 0.5′ as a radius; or

  * •

the 2$\times$ half-mass radius of Galactic globular clusters (Harris, 1996).

In addition, source-detections from fields covering the Eta Carinae nebula
(e.g., 1E1048d1m5934 and ASASSN_18fv) are also reported in the secondary
catalog. Figure 6 shows example cutouts of identified fields with highly
extended optical hosts. The flagged secondary serendipitous sources are marked
with blue circles (the primary and L17 sources are indicated with white
circles and green diamonds; refer to Figure 7) and the respective optical
catalog is flagged in the left corner. We found 214 sources to be associated
with highly extended galaxies, galaxy clusters or globular clusters, and we
refer to the overall catalog of these sources as the secondary NSS80 catalog;
22/214 secondary NSS80 sources were included in NSS40. By comparison the
primary serendipitous survey source catalog contains 1274 sources; hereafter
all statistics reported for NSS80 refer to the primary source catalog.

Figure 6: Example DSS $R$-band cutouts centred on the NuSTAR aim point for a
given observation (green cross). Sources within the radius of RC3 galaxies
(Third Reference Catalog of Bright Galaxies; de Vaucouleurs et al., 1995),
Milky Way (Galactic) globular clusters (MWGC) or Abell clusters are flagged as
secondary sources and indicated with blue circles. The white circles and the
teal-green diamonds mark primary and L17 serendipitous sources, respectively
(see Figure 7 for further details).

Table 3 provides the numbers of sources in the primary NSS80 catalog that are
detected in different energy bands as well statistics regarding optical
counterparts, spectroscopic follow-up and successful redshift measurements.
The total number detected in the full, soft, and hard bands are 1078 (85%),
706 (55%), and 406 (32%), respectively. In total, we have obtained redshifts
for 550 NSS80 sources, of which 547 can be spectroscopically classified; see
Figure 16 and Section 3.3 below.

Table 3:  Source statistics for the primary NSS80 catalog.

Band | $N$ | $N_{\mathrm{spec}}$ | $N_{z}$ | $N_{\mathrm{\textit{z},failed}}$ | $N_{\mathrm{r,det}}$ | $N_{\mathrm{r\,<\,22}}$
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Any band | 1274 | 594 | 550 | 44 | 1015 | 765
F$+$S$+$H | 257 | 174 | 165 | 9 | 221 | 190
F$+$S only | 315 | 170 | 157 | 13 | 275 | 212
F$+$H only | 81 | 35 | 32 | 3 | 68 | 46
F only | 422 | 166 | 153 | 13 | 326 | 233
S only | 131 | 39 | 35 | 4 | 88 | 59
H only | 68 | 10 | 8 | 2 | 37 | 25

Note. — Columns: (1) F, S, and H refer to sources detected in the full (3–24
keV), soft (3–8 keV), and hard (8–24 keV) energy bands, respectively. “F + H”,
for example, refers to sources detected in the full and hard bands only, but
not in the soft band, and “S only” refers to sources detected exclusively in
the soft band. (2) The number of sources detected post-deblending for a given
band or set of bands. (3) The number of sources for which (ground-based)
optical spectroscopic observations were undertaken. (4) The number of sources
with spectroscopic redshift measurements and the associated percentage
(including robust and uncertain counterpart associations based on our Nway
analysis; see Sections 3.2 & 3.3). (5) The number of sources for which
spectroscopic observations were undertaken, but lack a reliable redshift
measurement (the majority of which have faint, red continuum spectra); see
Table 15 and Figure B5. (6) The number of sources with an associated optical
counterpart detected in the $r$-band; magnitudes are obtained from SDSS,
PanSTARRS, USNOB1 and NSC (NOAO Source Catalog). (7) The number of sources
with an associated optical counterpart brighter than $r=22$ (detectable with
current groundbased telescopes).

Both the primary and secondary source catalogs are provided as electronic
tables. In Appendix A we give a detailed description of the columns that are
provided in the catalog. In addition, we also created an online library of the
894 unique fields to allow for quick and easy verification of the X-ray and
optical counterpart information for each of the NuSTAR fields. The online
library will be accessible at https://www.nustar.caltech.edu/page/59 and in
Figure 7 we show an example of one of these fields. In Table 4 we give a
summary of the subsets of this primary catalog as discussed in future
sections.

Table 4: Summary of the primary catalog subsets and selection flags. Subset | Number | Selection Flag | Section | Description
---|---|---|---|---
(1) | (2) | (3) | (4) | (5)
Primary (all) | 1285 | – | 2.1 |  The full catalogue, excluding sources within highly extended optical galaxies and clusters
Unique | 1274 | MainCAT | 2.1 |  All unique detections, i.e. excluding objects with multiple optical counterpart candidates
Reliable | 962 | NWAY_RFlag | 3.2 |  Sources with a high probability Nway match in either CatWISE20 or PS1-DR2
Spectroscopic | 594 | SpecCAT | 3.3 | Sources with spectroscopic observations
BL | 287 |  Classification is ‘BL’ or ‘BL?’ | 3.3.3 |  Sources with broad permitted emission line widths ($FWHM\geq 1000$ km s-1)
NL | 198 |  Classification is ‘NL’ or ‘NL?’ | 3.3.3 | Sources with narrow permitted emission line widths
Extra-galactic | 492 |  SpecCAT, zQuality!=‘F’ or ‘C’ and zspec$>0$ | 3.3.3 |  Sources with spectroscopic redshifts indicating extra-galactic origin
Figure 7: Example image of the NSS80 survey library. The online library will
be accessible at https://www.nustar.caltech.edu/page/59. Left cutout: The
$3-24$ keV coadded NuSTAR image of one of the 894 NSS80 unique fields, Kepler
(field ID 413); $N_{\mathrm{exp}}=3$ individual exposures (each 12′ $\times$
12′) are combined with a total exposure time of $t_{\mathrm{exp}}=364.36$ ks.
For comparison, the NSS40 field ID and total exposure time is recorded in the
top right corner. NSS80 detections are marked with white circles and the
corresponding serendip number and NSS40 detections are shown with teal-green
diamonds – 3 additional NuSTAR serendipitous sources are detected in the new
post-NSS40 data. The science target is marked with a green cross at the centre
of each field (aim point). Fields which are masked post processing due to
excess background contamination (e.g., stray light, ghost rays, bright science
target) are flagged in the bottom left corner, and the Galactic latitude of
the science target is shown in the bottom right corner. Right cutout: DSS2
$R$-band image centred on the NuSTAR science target position. The same
labelling as on the left is used to indicate NSS40 and NSS80 serendipitous
sources. Galactic plane fields with latitudes $|b|<10^{\circ}$ are flagged in
the bottom left corner.

###  2.4 Key changes in NSS80 with respect to NSS40

As discussed in Section 2.2, when constructing the NSS80 sample, we mainly
adopted the same underlying methodology and data processing procedures as in
NSS40 to be consistent between the two NuSTAR serendipitous surveys.
Nevertheless, there are several significant changes and updates with respect
to NSS40. The key differences are summarised below.

  * •

NSS40 combined individual exposures of the same science target to increase the
sensitivity. In NSS80 we extend this approach to coadd all exposures performed
over the 80-month period within a 12′ search radius of the aim point (i.e.,
all overlapping sky regions were automatically identified and coadded),
providing improved sensitivity in fields with multiple overlapping
observations.

  * •

NSS40 excluded obsIDs with exposure times $<$ 1 ks from the analysis. NSS80
now coadds all of the data (which satisfied our criteria mentioned in Section
2.1), including any low-exposure time data.

  * •

Preceding source-detection, serendipitous detections which could be associated
with highly extended optical/IR hosts were manually masked and removed in
NSS40. NSS80 retains these in a secondary catalog, based on a later post-
processing step; see Section 2.3.

To quantify how many serendipitous sources were added/removed due to the
aforementioned alterations, we assessed overlapping fields between the NSS40
and NSS80. Of the 331 NSS40 unique fields, we reprocessed 50 fields – 6 which
include only NSS40 observations while 44 fields include post-NSS40
observations as well. For these 50 fields, we detected an additional 111
sources: 89 sources arise from the deeper or wider data and 22 by including
highly extended optical host mask regions originally excluded. 36 NSS40
sources were not detected in our coadded fields; we summarise potential
reasons to explain these undetected sources in Table 14. 32 of the 36
undetected NSS40 sources have updated false probabilities, based on the deeper
co-added data, that no longer satisfy our detection threshold, indicating that
they were likely spurious detections in the NSS40 sample. This is particularly
noticeable for NSS40 sources with detections in a single energy band only. Of
the remaining 4 undetected NSS40 sources, 1 lies in an excess background
region and 3 sources are on the peripheries of coadded fields.

Overall, 444/497 NSS40 sources are included in the primary NSS80 catalog,
17/497 are included in the secondary NSS80 catalog, and 36/497 sources are
excluded. Additionally, L17 constructed a secondary catalog of which 8/64 are
included in the primary NSS80 and 5/64 in the secondary NSS80 catalog. Hence,
in total, 452 and 22 NSS40 sources are included in the primary and secondary
NSS80 catalogs, respectively.

##  3 The Multi-wavelength Data

The compiled NSS80 presented in this work is independent of prior multi-
wavelength information. To further explore the source properties, such as
luminosities and source classifications, we require multi-wavelength
information to draw a more complete picture of the properties and nature of
individual sources. Since our primary focus for the NSS80 is extragalactic
sources, we also require optical counterparts to establish redshift
measurements from which a range of other properties can be inferred. However,
since the positional accuracy of NuSTAR ranges between $\approx$ 8′′ to
$\approx$ 20′′ for bright to faint sources (90% confidence; see e.g., Lansbury
et al., 2017b), it is desirable to have more accurate X-ray positions to
search for reliable optical/IR counterparts. To achieve this we first searched
for lower-energy (soft) X-ray counterparts with more accurate source positions
(see Section 3.1) and, subsequently, searched for IR/optical counterparts to
the X-ray sources (see Section 3.2), which were then used in our spectroscopic
follow-up campaign (see Section 3.3).

###  3.1 Lower-energy X-ray Counterparts

Table 5:  The number of NuSTAR serendipitous sources with lower-energy X-ray
counterparts.

|  | CSC2.0 | 4XMM-DR10s | 4XMM-DR10 | 2SXPS | Any
---|---|---|---|---|---|---
(1) |  $N_{\mathrm{Total}}$ / $N_{\mathrm{Coverage}}$ | 300 / 408 | 492 / 651 | 394 / 553 | 661 / 949 | 956 / 1249
(2) | $N_{\mathrm{Single}}$ | 211 | 382 | 349 | 617 | 907
(3) | $N_{\mathrm{Multiple}}$ | 89 | 110 | 45 | 44 | 214
(4) | $N_{\mathrm{Best}}$ | 300 | 317 | 168 | 171 |  †956
(5) |  $\langle\Delta$RA$\times\cos$(Decl.)$\rangle$ | $-0.50\pm 0.60^{\prime\prime}$ | $0.55\pm 0.52^{\prime\prime}$ | $0.20\pm 0.61^{\prime\prime}$ | $-0.28\pm 0.49^{\prime\prime}$ |
(6) |  $\langle\Delta$Decl.$\rangle$ | $0.36\pm 0.49^{\prime\prime}$ | $-0.13\pm 0.40^{\prime\prime}$ | $0.20\pm 0.51^{\prime\prime}$ | $0.71\pm 0.34^{\prime\prime}$ |
(7) | $\langle\theta\rangle$ | 10.7′′ | 11.2′′ | 12.6′′ | 10.9′′ |

Note. — Rows: (1) The total number of NuSTAR sources in the primary catalogue
with a lower-energy X-ray counterpart within a search radius of 30′′
($N_{\mathrm{Total}}$) compared to the total number of primary NuSTAR sources
with Chandra, XMM-Newton and/or Swift-XRT coverage ($N_{\mathrm{Coverage}}$);
the coverage was determined by matching sources without a soft X-ray
counterpart with observations within the default radius on HEASARC, and then
checking the exposure maps for non-zero exposure times at the NuSTAR
coordinates. The final column enumerates the number of unique NuSTAR sources
with a match in any catalog. (2) The number of NuSTAR sources with a single
match within 30′′ to the specific lower-energy X-ray catalog. (3) The number
of NuSTAR sources with multiple matches within 30′′ to the specific lower-
energy X-ray catalog. (4) The number of NuSTAR sources where the position from
a given lower-energy X-ray catalog is taken to be the most reliable (i.e., the
best), and consequently the adopted, lower-energy X-ray position. The order of
preference is: Chandra, XMM-Newton and then Swift-XRT. †In addition to the 956
unique sources with automatically matched counterparts described in the table,
a further 8 sources (1 Chandra \+ 4 XMM-Newton \+ 3 Swift-XRT) were manually
identified, resulting in a total of 964 NSS80 sources with a lower-energy
X-ray counterpart. (5) & (6) The mean positional offsets in right ascension
(5) and declination (6) of the NuSTAR position relative to the lower-energy
X-ray counterpart (see Figure 8 top panel). (7) The mean angular offset
between the NuSTAR and lower-energy X-ray positions in arcsec. These values
are computed for all CSC2.0, 4XMM-DR10/s and 2SXPS matches.

To search for lower-energy (soft) X-ray counterparts, we used Chandra, XMM-
Newton, and Swift-XRT observations. We cross matched the NuSTAR sources to (1)
the Chandra Source Catalog Release 2.0 (CSC2.0; Evans et al., 2019), (2) the
Fourth XMM-Newton Serendipitous Source Catalog, Tenth Data Release (4XMM-DR10;
Webb et al., 2020) and its stacked version (4XMM-DR10s; Traulsen et al.,
2020), and (3) the Swift-XRT Point Source Catalogue (2SXPS; Evans et al.,
2020), using a search radius of 30′′ for each NuSTAR source position
(consistent with L17). There is a trade-off between completeness and the
number of false associations when cross-matching between different surveys,
and thus here and in Section 3.2 we select cross-matching radii carefully with
this balance in mind. As discussed in L17, the uncertainty in the NuSTAR
positions dominates the errors in the source matching. We would expect to
exclude a true match in a very small fraction of cases ($<$0.5%) and for
$\sim$7% of the associations to be false (L17).

We identified lower-energy X-ray counterparts for 956 NuSTAR sources between
the four lower-energy X-ray catalogs. In addition, we manually identified a
potential lower-energy X-ray counterpart for a further 8 sources which have
faint lower-energy X-ray emission (yet not statistically significant) in the
vicinity of the NuSTAR position (1 Chandra, 4 XMM-Newton and 3 Swift-XRT; see
Appendix A), leaving a total of 964 NSS80 sources (76%) with an identified
lower-energy X-ray counterpart. Accordingly we were unable to identify lower-
energy X-ray counterparts for 310 NSS80 sources, of which 94.5% (293/310) have
lower-energy X-ray coverage with either one of the lower-energy X-ray
observatories: 34.8% with Chandra (ACIS), 51.3% with XMM-Newton, and 92.9%
with Swift-XRT; these sources are flagged in the catalog (see Appendix A). The
reason for the non-detections could be that the observations were too shallow
to detect faint sources, or it could be attributed to variability given that
the observations are non-contemporaneous, or it could be the result of
absorption of lower-energy X-ray photons along the line-of-sight. Only
$\sim$1% (17/1274) lack any form of coverage from all of these three lower-
energy X-ray observatories (flagged as flag_softx_cov = null in the catalog).

Of the 964 NuSTAR sources with lower-energy X-ray counterparts, 142 sources
have been detected with more than one of the lower-energy X-ray observatories:
22 from Chandra+XMM-Newton; 32 from Chandra+Swift-XRT; 51 from XMM-
Newton+Swift-XRT; and 37 from all three lower-energy X-ray observatories. For
these sources we adopted the position with the highest accuracy as the ‘best’
lower-energy X-ray counterpart, which are in the following order: CSC2.0,
4XMM-DR10s, 4XMM-DR10 and 2SXPS. Hence, of the 964 lower-energy X-ray
counterparts, we have adopted the positions for 300 from CSC2.0, 317 from
4XMM-DR10s, 168 from 4XMM-DR10, 171 from 2SXPS, and 8 manually measured
positions using lower-energy X-ray imaging, i.e., one position from Chandra, 4
from XMM-Newton, and 3 from Swift-XRT; see row 4 in Table 5.999The 8 manually
measured lower-energy X-ray positions are used only to identify multi-
wavelength counterparts, but are excluded from all further X-ray analysis.

Approximately 23% (288/1274) of the NuSTAR sources have multiple CSC2.0, 4XMM-
DR10/s or 2SXPS matches within our search radius. To identify the best
counterpart for these cases, we made the assumption that the lower-energy
X-ray source with the brightest flux in the highest available energy band
(Chandra: 2-7 keV; XMM-Newton: 4.5-12 keV; Swift-XRT: 2-10 keV) is likely to
be the correct counterpart. We note that in some cases we stand the risk of
ignoring heavily obscured sources which are faint in lower energies. Three
NuSTAR sources (one Chandra and two XMM-Newton) were undetected in solely the
highest energy band of the low-energy instrument, for which we used their full
band fluxes.

The results from the lower-energy X-ray cross-matching of the primary NSS80
sources are summarized in Table 5. We provide the positions, the angular
separation between the lower-energy X-ray counterpart and the NuSTAR source,
and the number of sources with matches in each catalogue.

We show the positional offsets between the NuSTAR sources and their (a)
Chandra, (b) XMM-Newton and (c) Swift-XRT counterparts in the top panel of
Figure 8, and list the mean positional offsets for all CSC2.0, 4XMM-DR10/s and
2SXPS matches in rows 5–6 of Table 5 (as well as the mean angular offset
between the NuSTAR and lower-energy X-ray positions; see row 7). The sources
are plotted in color, coded by the source-detection significance (the minimum
false probability), and the dashed circles illustrate different search radii:
10′′ (inner), 20′′ (middle) and 30′′ (outer). Evidently, the majority of
sources for each lower-energy X-ray observatory lie within a 20′′ separation
radius (i.e., 94%, 84%, 90%, 90% for CSC2.0, 4XMM-DR10s, 4XMM-DR10 and 2SXPS,
respectively), particularly those with more significant detections (i.e.,
lower $\Delta p_{\mathrm{False,min}}$ values). The lack of significant
positional offsets (i.e., see the median astrometric offsets for each sample
in Figure 8) are indicative of consistent astrometry between the X-ray
observatories.

The bottom panel of Figure 8 shows the positional accuracy of NuSTAR as a
function of the detection significance; i.e., the angular separation between
the NuSTAR position and its best identified lower-energy X-ray counterpart
(having a higher likelihood of being correctly matched) versus the minimum
false probability of a given source. By assuming zero uncertainty in the
lower-energy X-ray position and that NSS80 sources with lower-energy
counterparts are representative of the overall population, we determine the
90% and 68% confidence limits on the NuSTAR positional uncertainty in bin
sizes of $\log$($p_{\mathrm{False,min}})=-10$, as indicated with solid and
dash-dot horizontal black lines, respectively. From this analysis we find that
the 90% confidence limit on the NuSTAR positional uncertainty varies from 23′′
to 13′′ between the least-significant and the most-significant detections.

Figure 8: The positional accuracy of NuSTAR as a function of source-detection
significance for the 956 NSS80 sources with lower-energy counterparts in
pointed archival observations; all matched lower-energy counterparts are
plotted. Top panel: Astrometric offsets between the NuSTAR source and its
matched lower-energy X-ray counterpart coordinates from (a) Chandra/CSC2.0
(circles), (b) XMM-Newton/4XMM-DR10/s (squares and diamonds), and (c) Swift
-XRT/2SXPS (stars), color-coded by source-detection significance. The
negligible mean positional offsets are shown with white markers. Bottom panel:
The radial offset between the NuSTAR source and its best lower-energy X-ray
counterpart as a function of the minimum source-detection significance
($\Delta p_{\mathrm{False,min}}$) which increases towards the right (from
green to purple color-code). The solid and dash-dot black lines indicate the
90% and 68% confidence limits, respectively, on the NuSTAR positional
uncertainty for bin sizes of $\log$($p_{\mathrm{False,min}})=-10$. The number
of sources which each bin contains is given above the solid lines. Since the
number of sources becomes small towards high $p_{\mathrm{False,min}}$ values,
we only plot bins for $\log$($p_{\mathrm{False,min}})<-50$.

We estimated the observed-frame $3-8$ keV flux ($F_{\mathrm{soft}}$) for the
lower-energy X-ray counterparts following the methodology in L17. For CSC2.0,
4XMM-DR10/s and 2SXPS sources we converted to the $3-8$ keV flux from the
$2-7$ keV, $4.5-12$ keV and $2-10$ keV101010For the 2SXPS sources we
calculated the soft-band flux using the available band 3 count rate (2–10
keV). flux using a conversion factor of 0.83, 0.92 and 0.62,
respectively.111111We estimated the conversion factors in WebPIMMS for a
Galactic absorption of $N_{\mathrm{H}}=0$ and a photon index of $\Gamma=1.8$.
We show these fluxes relative to the NuSTAR-measured fluxes for the best
identified lower-energy X-ray counterparts in Figure 9. It should be noted
that 21/300 CSC2.0 counterparts are undetected in the $2-7$ keV (ACIS) energy
band: 1/21 source are detected in the $0.5-7.0$ keV broad band
(NuSTARJ184449+7212.1), 2/21 sources (NuSTARJ095712+6904.8 &
NuSTARJ121425+2936.1) only have upper limits in the $0.5-7$ keV broad band,
while the remaining 18/21 sources only have constrained fluxes in the $0.1-10$
keV HRC wide band121212We note that some of these sources may represent the
small fraction of expected false associations between soft X-ray and NuSTAR
sources.. For these sources we used the respective bands in which they are
detected to calculate the $3-8$ keV fluxes. We see a reasonable agreement in
the flux measurements between observatories, with the majority of the sources
(80% CSC2.0, 90% 4XMM-DR10/s and 93% 2SXPS) lying within a factor of three of
the 1:1 relation (see Figure 9). At least a component of the observed scatter
is likely to be attributed to intrinsic source variability due to the non-
contemporaneous NuSTAR and lower-energy X-ray observations. In addition,
Civano et al. (2015), Mullaney et al. (2015) and Fornasini et al. (2017) have
shown that Eddington bias affects the lower NuSTAR fluxes, increasing the
spread as the flux limit is approached. Sources at the very lowest fluxes are
not commonly detected, contributing to the apparent bias with larger numbers
of sources at the lowest X-ray fluxes that are above the 3:1 relation.

Figure 9: Comparison of the $3-8$ keV NuSTAR and $<10$ keV X-ray mission
fluxes ($F_{\mathrm{soft}}$) for the best Chandra/CSC2.0 (green circles), XMM-
Newton/4XMM-DR10/s (purple squares and diamonds, respectively), or Swift-
XRT/2SXPS (blue stars) counterpart matched to the primary NSS80. The different
energy bands used to calculate the $3-8$ keV fluxes for the CSC2.0 are
indicated with different symbols, i.e., $2-7$ keV (solid green circle),
$0.1-10$ keV (white filled, green-edged circle), and $0.5-7$ keV (white
filled, green-edged star). Top panel: Distribution of NuSTAR to $<10$ keV
X-ray mission fluxes for each instrument. In both panels, the black solid line
shows the 1:1 relation, the black dash-dot lines show a factor of three from
this relation, and the red dotted line indicates a factor of 5 below the 1:1
relation. Ten sources have NuSTAR $3-8$ keV flux measurements below the 1:5
relation.

Finally, we assessed the flux contribution from all of the Chandra, XMM-Newton
and Swift-XRT sources within a radius of 30′′ from the NuSTAR source by
determining their total combined $3-8$ keV flux ($F_{\mathrm{soft}}^{30}$; see
Appendix A). We allows us to compare: (a) $F_{\mathrm{soft}}$ measured by
NuSTAR ($F_{\mathrm{soft,{\it NuSTAR}}}$), in order to assess whether a
significant amount of NuSTAR flux is coming from other sources; and (b)
$F_{\mathrm{soft}}$ from the best lower-energy counterpart
($F_{\mathrm{soft,LE}}$), to assess the contamination of low energy flux from
other sources, less affected by variation and inter-instrument differences.
Overall, 6.9% of the NSS80 sources with lower-energy X-ray counterparts have
$F_{\mathrm{soft}}^{30}>1.2\times F_{\mathrm{soft,LE}}$, and 4.9% have
$F_{\mathrm{soft}}^{30}>1.2\times F_{\mathrm{soft,{\it NuSTAR}}}$. Only 21
sources have combined fluxes that exceed $F_{\mathrm{soft,{\it NuSTAR}}}$ by a
factor of 2. Therefore, we are confident that the NuSTAR source is generally
dominated by the emission from the brightest lower-energy X-ray counterpart.

###  3.2 Finding IR & optical counterparts using Nway

Obtaining redshifts for the NuSTAR sources requires the identification of the
correct optical counterpart. The comparatively large positional uncertainty of
NuSTAR sources often leads to multiple potential optical counterparts.
Consequently, we require an approach to distinguish between true and unrelated
optical counterparts, particularly in the absence of more reliable lower-
energy X-ray positions. As discussed further in Section 4.2, MIR emission
provides a robust identification of AGN activity, particularly for hidden
luminous quasars, since the dusty AGN torus radiates predominantly at these
wavelengths, while star formation from the host galaxy peaks at FIR
wavelengths and is comparatively weak at MIR wavelengths. Therefore we should
not consider star-forming galaxies a major source of contaminants in the MIR
distributions found in Figure 11. The all-sky WISE survey therefore provides
an excellent complement to NuSTAR: the positional uncertainty of WISE sources,
particularly in the shorter wavelength $W1$ and $W2$ bands, is sufficient to
be able to reliably identify optical counterparts. Identifying WISE
counterparts for hard X-ray selected sources can therefore pave the way to
locating the correct optical counterpart even for NuSTAR sources without a
lower-energy X-ray counterpart. This section describes the process of matching
MIR and optical counterparts to NuSTAR sources both with, and without, lower-
energy X-ray counterparts.

L17 adopted a relatively simple closest neighbour approach to identify multi-
wavelength counterparts, using the more reliable positions from lower-energy
X-ray counterparts, where available, and the distinctive characteristics of
AGN with respect to galaxies in the MIR band (as traced using WISE). Here we
adopt a more sophisticated probabilistic approach using Nway (v.4.4.2; Salvato
et al., 2018) to identify IR and optical counterparts for the NSS80 sources.
Nway uses Bayesian methods to probabilistically match multi-wavelength
counterparts to X-ray sources by simultaneously matching $N$ catalogs in a
multi-dimensional parameter space, e.g., astronomical sky coordinates and
positional uncertainties, magnitude and color distributions, source density
and morphology, etc. Therefore, Nway is a powerful tool for our task of
identifying the correct optical and IR counterparts for NuSTAR detected
sources, which can include both Galactic populations, such as stars, and
extragalactic objects, such as AGN. For our Nway matching we use CatWISE20
(Marocco et al., 2021), which is a MIR all-sky catalog selected from WISE and
NEOWISE at 3.4 and 4.6 $\mu$m (i.e., $W1$ and $W2$). In addition, we use Pan-
STARRS DR2 (PS1-DR2; Flewelling, 2018) which provides coverage at declinations
$\gtrsim-30^{\circ}$ with a single epoch 5$\sigma$ depth of $r<21.8$131313For
sources at lower declinations no optical matching was performed with Nway.
Instead we performed positional cross-matching to other optical catalogues;
see case ii) for selection of principal counterparts later in this section for
details..

In what follows we summarise the main steps of our Nway matching approach to
obtain IR/optical counterparts for our spectroscopic follow-up campaign, as
outlined in Figures 10(a) and 10(b). We begin by constructing colour and
magnitude priors that are approximately representative of the population by
performing a photometrically unbiased cross-match between the NSS80 sources,
MIR, and optical catalogs, and then restricting the results from this to
secure counterparts only (i.e. high probability matches). With these expected
distributions of magnitude and color in hand we can apply them as priors to a
round of cross-matching that includes all possible counterparts (i.e. those
that had low probabilities in the first cross-match, as well as the high
probability matches) and improve the final cross-match probabilities that
inform our selection of principal counterparts.

This process and the resulting principal optical counterparts should be
understood with some basic information in mind. In general we prioritise
counterparts from the X-ray–MIR matching, as AGN are more robustly
distinguished in the MIR (see distributions in Figure 11). Selection of
optical counterparts follows using a well-defined branching procedure, with
the aim of producing the most likely counterpart candidates for the population
as a whole. The intention of this is to provide an overview of the properties
of counterparts to hard X-ray selected sources (see Sections 4.2 and 4.3). The
matches are therefore also manually checked, and in a small minority of cases
this overrides the automatic procedure (see red branch ‘VI corrected’ in
Figure 12 and Round #2 part (v)). Users are advised to consider their specific
use cases and the appropriate choice of optical counterpart for their
application.

$\star$ Preliminary round: constructing base counterpart catalogs
An optical and an IR base catalog are first created (separately) by collecting
all IR positions from CatWISE20 and optical positions from PS1-DR2 within
40′′141414This matching radius is increased to 40′′ (as compared to matching
with soft X-ray sources within 30′′) to include all potential matches to soft
X-ray counterparts, which could be offset by as much as 30′′. of the NuSTAR
position (see the green outlined boxes in Figure 10(a)).

$\star$ Round #1: defining magnitude and color priors | Figure 10(a)
Round #1 uses only astrometric and sky-density information (including
positional errors) to identify a “good” counterpart for the NSS80 sources. The
expected local sky densities of optical and WISE counterparts vary greatly
with distance from the Galactic plane, and therefore CatWISE20 and PS1 sky
densities were calculated from the actual number counts within 40′′ of each
NuSTAR source. The NuSTAR source densities were derived using the $\log
N$–$\log S$ curves reported in Harrison et al. (2016a), adopting the deblended
soft-band NuSTAR flux.

Figure 10: Flowchart illustrating our Nway matching strategy which we used to
identify CatWISE20 and PS1-DR2 counterparts to the NSS80 sources. (a) Round #1
entails the generation of the magnitude and color priors required for Round #2
(magenta outlined box; see Figure 10(b)), by using astrometric information
including source positions and their associated uncertainties, and the sky
density as a function of magnitude (green outlined boxes) to identify
counterparts to the best X-ray position (blue outlined box). Lines are dashed
or shown in different colours purely for clarity. (b) Round #2 of Nway which
utilizes the priors (magenta) from the matching to lower-energy X-ray
counterparts (blue) with $|b|>20^{\circ}$ in Round #1 and flat priors for
sources with $|b|<20^{\circ}$). All matches with probabilities $>10$% are
stored in the final post-processed catalog which include X-ray information,
multi-band positions and photometry, and key Nway information such as the
Bayesian match probabilities.  Figure 11:  Magnitude and color distributions
(integrated to unity) of the CatWISE20 (top) and PanSTARRS (bottom) matched
samples from Round #1, which are used to evaluate priors in Round #2 to
identify the “best” IR counterpart for each NuSTAR serendipitous source. WISE
magnitudes are Vega and optical magnitudes are AB. Top left panel: The
$W1$-magnitude distribution for the best matches vs. all sources (grey shaded
area), splitting the former by Galactic latitude; high Galactic latitude
sources ($|b|>20^{\circ}$) in red and low Galactic latitude sources
($|b|<20^{\circ}$) in blue. The black line is a Generalised Logistic
distribution fit to the data of the high Galactic latitude sources. The $W1$
distribution of the low Galactic latitude sources follows a similar shape to
that of the high Galactic latitude sources, with a slightly brighter $W1$
tail. Top right panel: The $W1$-$W2$ color distribution following the same
color-code as in the first panel. Here, the WISE color of the high Galactic
latitude sources, driven by the presence of AGN, is distinct from the low
Galactic latitude sources. Moreover, the peak of the distribution is around
$W1$-$W2$ $\approx$ 0.8, which is the Stern et al. (2012) criterion for
selecting MIR AGN. Therefore, the $W1$-$W2$ color distribution can be used as
a prior to identifying AGN candidates for optical/IR follow-up spectroscopy.
Bottom left panel: The $i$ magnitude distribution following the same color-
code as in the previous panels. The distribution of the low Galactic latitude
sources follows a similar shape to that of the high Galactic latitude sources,
peaking at a slightly less bright magnitude. Bottom right panel: The $g$-$i$
color distribution following the same color-code as in the previous panels.

For X-ray positions, lower-energy coordinates are used where available (see
Section 3.1), otherwise the NuSTAR position is used. In this work we use 68%
positional uncertainties appropriate for input to Nway, adapted from the
various serendipitous catalogue values for sources with soft X-ray matches.
For NuSTAR -only sources we used the 68% positional uncertainties based on
$\log$($p_{\mathrm{False,min}})$, as shown in Figure 8. These values can be
found in the catalog (column e_Xdeg).

Nway calculates the probability that each WISE or Pan-STARRS source is the
correct counterpart to a specific X-ray source ($p_{\mathrm{Cat,best}}$ and
$p_{\mathrm{PS,best}}$ for CatWISE20 and PS1-DR2,
respectively151515$p_{\mathrm{best}}$ is the relative probability that each
potential counterpart is correct; it assumes that one of the matches found is
correct. $p_{\mathrm{any}}$ provides the probability that any one of the
potential counterparts is correct. $p_{\mathrm{best}}$ is therefore equivalent
to adopting p_i (Salvato et al., 2018) as the best potential counterpart to
each NSS80 source.). For X-ray sources with large positional uncertainties
such as pure NuSTAR sources without lower-energy X-ray information,
counterpart identification is often less reliable, which will be captured in
the lower probability values returned by Nway. In addition to the best
counterpart match probability, Nway provides the probability that any of the
CatWISE/PS1-DR2 sources is the right counterpart ($p_{\mathrm{Cat,any}}$ and
$p_{\mathrm{PS,any}}$ for CatWISE20 and PS1-DR2, respectively); a higher
probability indicates a lower false-association likelihood. To ensure that we
only include sources with a high-probability of a correct match, we applied
the following constraints on the matching probabilities and discarded any
sources from Round #1 which do not comply: $p_{\mathrm{CAT/PS,any}}>0.5$ and
$p_{\mathrm{CAT/PS,best}}>0.8$. We treat sources at low Galactic latitudes
($|b|<20^{\circ}$) separately since source confusion is high closer to the
Galactic plane as a result of the high density of Galactic sources;
colour/magnitude priors appropriate to extra-galactic sources do not apply to
a population containing a large number of stellar X-ray emitters. A detailed
study focusing on Galactic and low latitude sources could improve the
counterpart matching for these sources by investigating different potential
priors (for example, the top left panel of Figure 11 implies that $W1$ may be
effective), which may be particularly valuable in these crowded regions. Only
two Galactic sources lack a soft X-ray counterpart. No sources outside of the
galactic plane that pass these probability cuts lack a soft X-ray counterpart
- these matches can therefore be considered reliable and representative of the
extra-galactic population.

The high-probability matches of the NSS80 serendipitous sources at high
Galactic latitudes are then used to generate WISE and optical magnitude
distributions in addition to color distributions which all serve as
photometric priors for the second round of Nway matching, as described in
Figure 10(b). The $W1$ magnitude and $W1$–$W2$ color distributions for the
CatWISE20 base catalog generated with Nway are shown in the top panels of
Figure 11. $W1$–$W2$ color is known to correlate with the presence of an AGN
(e.g., Stern et al., 2012; Assef et al., 2018) and $W1$ presents the deepest
observations, therefore we choose these as our color and magnitude priors.
Evidently, the WISE color distribution for sources at high Galactic latitudes
(blue distribution) provides a valuable way to distinguish between stellar
objects and AGN. A similar result holds for PS1-DR2 $i$-band magnitudes and
$g-i$ colors, where reliable counterparts are bluer in the optical compared to
the base population from PS1-DR2 (see bottom panels of Figure 11). The $g$ and
$i$ bands are both deep in PS1-DR2, and the $g-i$ color can be used to select
for reddened AGN (e.g., Klindt et al., 2019).

As an input for prior-based calculations, Nway also requires a distribution of
counterparts (WISE or optical) that are not associated with X-ray sources. For
this, we use the histograms of all sources in our 40” search fields around the
NuSTAR positions (grey histograms in the top panels of Figure 11). X-ray
source counterparts contribute to $<2$% of these histograms, so they are an
excellent representation of the background population.

At this point, we have two “good” match catalogues: X-ray–optical, and
X-ray–IR, which are used to evaluate priors for the more thorough matching in
Round 2.

$\star$ Round #2: improvement of the Nway matching using priors | Figure 10(b)
Round #2 now uses the optical and MIR priors evaluated after matching in Round
#1 ($W1$ magnitude, $W1-W2$ color, $i$-band magnitude, and $g-i$ color) to
help identify the most probable optical counterparts for the NSS80 sources.
The primary X-ray source catalog is categorized into low and high Galactic
latitude sources with the division at $|b|=20^{\circ}$. $|b|<20^{\circ}$
sources are matched geometrically (i.e., including positional errors but not
using photometric priors) to the base CatWISE20 and PS1-DR2 catalogs, as in
Round 1. Counterparts for the $|b|>20^{\circ}$ X-ray sources are identified
using the magnitude and color priors from Round #1 as inputs to Nway;
therefore these matches are weighted towards brighter sources and those with
AGN-like colors. Figure 11 compares the priors used in this round with the
distributions used to construct them. It also shows the distributions for
$|b|<20^{\circ}$ sources and all possible matches; the latter can be taken as
a reasonable indication of the ‘background’, or unmatched, distributions. We
also compare the results of Round #2 with a version of the catalogs created
using a positional offset to simulate the chances of a random association (as
advised in the Nway documentation) and assess the probability of a false
association based on these results. This informs our selection of threshold
cuts in the remainder of this section. For each NSS80 source, the highest
probability CatWISE20/PS1-DR2 match is stored in the catalog, if
$p_{\mathrm{CAT/PS,best}}>$ 10%.

We now have two “improved” match catalogues: X-ray–optical, and X-ray–IR,
which contain a potential match for each NSS80 source. These catalogues must
then be assessed to select a preferred counterpart, which we refer to as the
‘principal counterpart’. The goal of this process is to characterise the
general optical and MIR properties of the NSS80 sources (see Sections 4.2 and
4.3) and prepare for spectroscopic follow-up (see Section 3.3).

Final step: identification of principal counterpart | Figure 10(b) and Figure 12
Finally, the two catalogs are combined to form a refined catalog, with a
single Nway match in each of CatWISE20 and PS1-DR2 for each NSS80 source. This
refined catalog includes X-ray information, multi-band positions and
photometry (which can be expanded according to one’s preferences), and key
Nway information such as $p_{\mathrm{CAT/PS,best}}$ and
$p_{\mathrm{CAT/PS,any}}$ – all of these will be included in the online NSS80
catalog; see Appendix A161616Each most probable PS1 Nway match is kept in the
catalog (regardless of whether it is selected as the principal counterpart),
and are found in the columns with the suffix -PS1, columns 119-132.. The next
part of this section describes selecting the best available optical
counterpart, which is the Nway-selected source in the majority of
cases171717Counterpart information in the catalog has the suffix -cpart,
columns 134-146..

Figure 12: A flowchart of the principal adopted optical counterparts to the
NSS80 sources. The actions in green represent NSS80 sources with lower-energy
X-ray $+$ CatWISE20 counterparts with an optical match within 2.7′′ from the
WISE position. Optical matches are retrieved from PS1-DR2 (either from our
Nway matching or manually), SDSS, NSC2, DES2 or USNOB1. The purple actions
indicate lower-energy X-ray $+$ optical matches which lack a CatWISE20
association. For these sources we matched the Chandra, XMM-Newton or Swift-XRT
positions (softX $\equiv$ lower-energy X-ray) to the aforementioned optical
catalogues using characteristic positional uncertainties of 2.5′′, 5′′ or 6′′,
respectively. The blue actions represent NuSTAR-only X-ray $+$ CatWISE20
positions matched to the aforementioned optical surveys (prioritising Nway
matches where available) using a matching radius of 2.7′′; these optical
matches are only used for the purposes of spectroscopic follow-up. NSS80
sources that lack any optical association (some of which may be too
faint/distant) are indicated with grey actions. In red is shown the
contribution of objects with a visually selected optical match - these
include, for example, objects where cross-matching limits for other branches
are exceeded slightly but on visual inspection a clear match is found. This
results in an optical completeness of $\sim$86% (1098/1274) for the NSS80
catalog: 844/964 lower-energy X-ray and 254/310 NuSTAR-only X-ray
associations. This information is available in the NSS80 catalog; see Appendix
A.

When selecting the final principal optical counterparts, subsets of the NSS80
sources are dealt with in different ways, depending on the available optical
or lower-energy X-ray data and the results of the Nway matching, as outlined
below. Generally we consider the CatWISE20 match to be the primary
counterpart, with optical associations secondary; Figure 11 shows that the MIR
distribution of best Nway matches is more distinct from that of all possible
matches than the equivalent comparison using optical distributions (for extra-
galactic sources). We note that in all cases the results were visually
inspected (with imaging in all cases, and optical spectra where available; see
Section 3.3) by several of the authors, to assess the results. If multiple
convincing counterparts are seen then the match is not flagged as reliable,
although the results are not changed for a significant number of sources. We
consider the following cases, with each following a branch of Figure 12:

  1. i)

Sources with a lower-energy X-ray match, at least one CatWISE20 match, and at
least one PS1 match within 2.7′′ of the CatWISE20 position: As mentioned in
Section 3.1, 964/1274 NSS80 sources have a lower-energy X-ray counterpart and,
therefore, will have more reliable multi-wavelength counterpart associations
than those with NuSTAR-only positions. Of the 964 lower-energy X-ray sources,
850 have a CatWISE20 match to the lower-energy X-ray position,181818The
majority of these have a greater than 30% CatWISE20 match probability,
$p_{\mathrm{CAT,best}}$. of which 573 have at least one PS1 association found
by Nway (Pan-STARRS only covers declinations $\gtrsim\,-30^{\circ}$; 627/850
sources with soft X-ray and CatWISE20 matches fall in this region). However,
given that the two catalogs were independently matched to the lower-energy
X-ray positions, the PS1 position is not necessarily an exact match to the
CatWISE20 position. A maximum angular separation of 2.7′′ between the PS1 and
CatWISE20 positions removes counterparts where the probability of a correct
match is $\lesssim$0.1% based on positional uncertainty alone (with
probabilities converted from e.g., Lake et al., 2012). Hence, for the 573 with
lower-energy X-ray $+$ CatWISE20 $+$a PS1 counterpart from Nway within 2.7′′
of the CatWISE20 position, we adopt this PS1 source as the principal optical
counterpart and it is flagged as PS1-NWAY191919A PS1-NWAY match within 2.7′′
of the CatWISE20 position will be selected even if there is a closer potential
optical counterpart that is not found by Nway.. If the position from Nway is
too distant but a match can be found in PS1 by matching manually then this is
labelled PS1-MAN (31 sources202020These numbers can be found for any label by
filtering the catalog on the column OOrig_cpart.).

  2. ii)

Sources with a lower-energy X-ray match, at least one CatWISE20 match, but no
PS1 match within 2.7′′: The lower-energy X-ray $+$ CatWISE20 $+$PS1 sources
with angular separations $>$ 2.7′′ between the CatWISE20 and PS1 positions
(with a mean separation of 7.1′′) are less reliable and possibly different
sources altogether. To identify potential optical counterparts for the 34
sources with PS1 matches rejected in the previous step, as well as the 277/850
lower-energy X-ray $+$ CatWISE20 counterparts which lack a PS1 association
from Nway, we matched, in order of priority, to (1) the SDSS photometric
catalog DR12 (Alam et al., 2015), (2) the second data release of the NOIRLab
Source Catalog (NSC2; Nidever et al., 2021), (3) the Dark Energy Survey Data
Release 2 (DES-DR2; Abbott et al., 2016), and (4) the USNOB1 catalog (Monet et
al., 2003), using a 2.7′′ positional uncertainty. These matches were done
based on the closest available source and identify 228 optical counterparts.
They are labelled according to the catalog used212121The number of sources
matched to other catalogs in this step are SDSS: 2; NSC2: 200; DES2: 6;
USNOB1: 5..

  3. iii)

Sources with a lower-energy X-ray match, but no CatWISE20 match: 114/964
lower-energy X-ray counterparts lack any CatWISE20 association (i.e. a
CatWISE20 Nway match with $p_{\mathrm{Cat,best}}>0.1$); 79% (90/114) of these
sources are at low Galactic latitudes. If an Nway PS1 match is available for
these sources this is used, and if not a PS1-DR2 match based on angular
separation alone is attempted using the Chandra, XMM-Newton and Swift-XRT
positions, with positional offset limits of 2.5′′, 5′′ and 6′′, respectively.
These values are used instead of the individual source probabilities used in
Nway because the goal in this case is different; we aim to select a single
closest match and exclude distant and therefore unlikely matches, rather than
statistically assessing the probabilities. If no PS1-DR2 is found, we move to
the aforementioned optical catalogues, identifying counterparts for 86/114
sources in this category. Matches made in this way have flags with the suffix
-softX.

In total we have identified optical associations for $\sim$ 85% (824/964) of
the NSS80 sources with lower-energy X-ray counterparts. The remaining 140/964
lower-energy X-ray sources lack any optical association at this stage: i.e. we
find no optical source down to the magnitude limits of the searched optical
catalogs within a matching radius of 2.7′′ (when there is a CatWISE
counterpart), or the matching radius of the soft X-ray counterpart (when there
is no CatWISE counterpart)222222Sources which lack an optical counterpart may
do so because their counterpart is faint/distant..

  4. iv)

Sources with no lower-energy X-ray match: For the 310/1274 NSS80 sources
without lower-energy X-ray counterparts, the X-ray positional error circle
from NuSTAR is comparatively large, so unique counterparts cannot be
identified with high confidence (see Figure 13). However, from our Nway
matching we were able to secure a potential WISE association for all 310
sources with a $p_{\mathrm{Cat,best}}\gtrsim 0.1$; note that
NuSTARJ182353+0742.0 is a borderline case with $p_{\mathrm{Cat,best}}=0.095$
and $p_{\mathrm{Cat,any}}=0.53$. To search for an optical counterpart for
these sources, for the purposes of optical spectroscopic follow-up only (i.e.,
to retrieve an optical position and $r$-magnitude if detected), we cross-
matched the CatWISE20 position to the aforementioned optical surveys using a
2.7′′ search radius, starting by checking the position of the Nway PS1 match,
then moving onto a manual PS1 match, and finally working through the other
optical catalogs. In total we obtained a potential optical counterpart for
243/310 NuSTAR-only X-ray sources. Matches made in this way have flags with
the suffix -CatWISE, and should be viewed with more caution than those with
soft X-ray counterparts.

  5. v)

Visually inspected sources: Finally, as each source was visually inspected we
find a small number (21/1274) where it is appropriate to override the
procedural matching explained in this section. The majority of these are
sources that fail a matching distance criterion by only a small amount but on
visual inspection appear likely to be a correct match. For example, if a PS1
source is further than 2.7′′ from the CatWISE20 counterpart, but it is within
the match radius for the soft X-ray counterpart and in a region with few
nearby sources we may choose to manually select the optical counterpart.
Matches made in this way have flags with the suffix -VI, and should also be
treated with appropriate caution.

This step increases the optical completeness of the NSS80 catalog from
$\sim$85% (1077/1274) to $\sim$86% (1098/1274): 844/964 lower-energy X-ray and
254/310 NuSTAR-only X-ray associations; see Appendix A for an abbreviated code
indicating the origin of the adopted optical counterpart to the NuSTAR source.

Figure 13: A histogram of the distribution of match probabilities for the Nway
CatWISE20 (top panel) and PanSTARRS (bottom panel) candidates before applying
the $>$10% $p_{\mathrm{Cat/PS1,best}}$ cut at the end of Round #2, both for
NuSTAR-only (open) and improved lower-energy X-ray positions (filled). The
high quality probability cut ($p_{\mathrm{Cat/PS1,best}}\geq 0.4$) is plotted
with a dash-dotted line. Evidently, in the absence of more reliable lower-
energy X-ray positions, Nway returns low probabilities for the
CatWISE20/PS1-DR2 matches. Left panel shows all sources; middle and right
panels show high and low Galactic latitude sources respectively.

Our selection process to identify the principal adopted optical counterpart is
summarised in Figure 12. Not all Nway matches will be true counterpart
associations since the cross-matching depends on X-ray counterpart information
(i.e. positional uncertainty, which is influenced by source and background
counts), whether a soft X-ray counterpart can be found (generally these have
much smaller positional uncertainties than NuSTAR and thus improve cross-
matching), the Galactic latitude of the source (i.e., source confusion easily
occurs for high density fields usually within the Galactic plane) and the
depth of the optical/IR imaging surveys (e.g., shallow imaging can miss
counterparts that are evident in deeper surveys), to mention but a few. Figure
13 shows the distribution of Nway match probabilities
($p_{\mathrm{CAT/PS,best}}$) for the “best” CatWISE20 (top panel) and
PanSTARRS (bottom panel) candidates, both for NuSTAR-only (open) and improved
lower-energy X-ray positions (filled). Evidently, the CatWISE20/PS1-DR2
probabilities are low in the absence of more reliable lower-energy X-ray
positions.

We therefore attempted to identify a subset of our NSS80 that have high-
probability matches based on our Nway analysis to minimise false
associations—henceforth described as ‘reliable’ counterparts—and provide this
information in the catalog (NWAY_RFlag; Table 11. We first identified high-
probability CatWISE20 matches with thresholds of $p_{\mathrm{Cat,best}}>0.4$
and $p_{\mathrm{Cat,any}}>0.5$. The expected rate of false associations based
on matching with randomised catalogs (as in Salvato et al., 2018) around each
NuSTAR /soft X-ray position gives a 1.4% chance of false association if a soft
X-ray source is present, and 12.6% if there is no soft X-ray source, improving
to 0.5% and 9.6% respectively when limited to $|b|>10^{\circ}$. We supplement
the reliable CatWISE20 counterparts with reliable PS1-DR2 counterparts, if
present, for sources that fail the CatWISE20 probability criterion, by
applying the same higher probability cut on their PS1-DR2 probabilities (i.e.,
$p_{\mathrm{PS,best}}>0.4$ and $p_{\mathrm{PS,any}}>0.5$). In total, 963/1274
NSS80 sources have a reliable CatWISE20 or PS1-DR2 counterpart, of which 76%
(726) are high Galactic latitude sources. 370 of these only have a reliable
CatWISE20 counterpart and 103 only PS1-DR2; many of these do have an Nway
match that is below the 0.4/0.5 thresholds. The remaining 321 NSS80 sources
have low-probability Nway counterparts and should, therefore, be used with
caution to avoid biasing the results.

Finally, we have a single principal match catalog, checked at each stage for
the most reasonable match. All selected matches are included, and particularly
high probability matches are flagged as reliable. This subset can be selected
with the flag NWAY_RFlag; see Table 4.

Figure 14: Astrometric offsets between the lower-energy X-ray counterpart
coordinates and the WISE (top row) and the adopted optical (bottom row)
coordinates, color-coded using the NuSTAR detection likelihood
($p_{\mathrm{false,min}}$), for Nway-identified counterparts flagged as
reliable. The high Galactic latitude lower-energy X-ray counterparts are from
CSC2 (left column; circles), 4XMM-DR10/s (middle left column; squares and
diamonds, respectively), 2SXPS (middle right column; stars), and NuSTAR only
(right column; plus symbols). Low Galactic latitude sources are plotted with
color-coded crosses and sources with less reliable counterpart associations
are indicated with open grey-edged crosses. The dashed (dotted) circles
correspond to the 1$\sigma$ (2$\sigma$) search radii for each lower-energy
X-ray telescope: 1.2′′ (2.5′′), 2.4′′ (5′′), 3.4′′ (6′′), 12′′ (24′′) for
Chandra, XMM-Newton, Swift-XRT, and NuSTAR, respectively. The white circle,
square, diamond, star, and plus indicates the median astrometric offset for
each of the extragalactic samples. Note the different scale for the NuSTAR-
only section.

Figure 15: Distributions of the MIR and optical magnitudes and colors for the
high probability Nway-selected counterpart samples at high Galactic latitudes
($|b|>20^{\circ}$; green) and low Galactic latitudes ($|b|<20^{\circ}$;
peach). The median of each distribution is plotted with a dash-dotted line.
The dashed black lines indicate the distributions constructed in Nway round #1
and used as priors in round #2. Top four panels: magnitude distributions for
the four photometric WISE bands, for the sources with successful CatWISE20
matches satisfying the high probability cut. Middle three panels: the
$g$-band, $r$-band and $i$-band magnitudes (corrected for Galactic extinction)
for all the sources satisfying the Nway high probability cuts. Bottom two
panels: the $W1-W2$ and $g-i$ colors for all the sources satisfying the Nway
high probability cuts. These colors are used as as priors for Nway. The dash-
dotted, grey line indicates the Stern et al. (2012) AGN threshold of
$W1-W2>0.8$. WISE magnitudes are Vega and optical magnitudes are AB.

Figure 14 shows the distribution of astrometric offsets between the X-ray
source and the adopted CatWISE20 (top panel) and optical (Pan-STARRS, SDSS,
NSC2, DES, and USNOB1; bottom panel) counterpart, for the high probability
Nway-selected samples (filled symbols) and for sources with low Nway
probabilities (open, grey-edged crosses). Sources with Galactic latitudes
$|b|>20^{\circ}$ are plotted with circles, squares/diamonds and stars for
NSS80 sources with CSC2, 4XMMDR10/s and 2SXPS counterparts, respectively. The
low Galactic latitude sources identified with Nway based solely on geometric
information are shown with crosses.

In Figure 15 we show histograms of the WISE (top panels) and optical ($g$,$r$
and $i$; middle panels) magnitudes232323All PanSTARRS magnitudes quoted in the
NSS80 catalog are, in order of preference, Kron, PSF, or the default aperture
magnitudes. There are flagged in the columns mag_type_PS1 and mag_type_cpart
for Nway and selected counterpart magnitudes, respectively. The Kron
magnitudes are better for extended sources, which would constitute the larger
number of counterparts for the NuSTAR serendipitous survey given their
apparent redshift distributions. Thus if a Kron magnitude is available, it is
used, and if not we check for the other types. If users perform a detailed
study on individual sources we advise a check that the magnitude is
appropriate for their application. for the high probability Nway-selected
samples at high (green) and low (peach) Galactic latitudes, respectively. The
median magnitudes of the low Galactic latitude sources are on average 1-2
magnitudes brighter than the high Galactic latitude sources.

In addition the $W1-W2$ and $g-i$ colors for all the sources satisfying the
Nway high probability cuts are shown in the bottom panels of Figure 15. The
median $W1-W2$ for high Galactic latitude sources is similar to the AGN
threshold of $W1-W2=0.8$ presented in Stern et al. (2012).

###  3.3 Optical spectroscopy

To maximise the scientific impact of the NuSTAR observations and to explore
the intrinsic source properties, we carried out a major, coordinated
spectroscopic campaign using a broad range of telescopes across the globe to
obtain redshifts of the NSS80 sources. The analysis of, and classifications
obtained from, these new spectroscopic data and those from pre-existing
spectroscopy, are described in Section 3.3.3.

####  3.3.1 Dedicated Follow-up Campaign

L17 obtained spectroscopic redshifts for 276 of the 497 NuSTAR serendipitous
sources through multi-year observing programmes in both hemispheres. For NSS80
we continued the multi-year spectroscopic follow-up campaign with the
following telescopes (see Section 4.4.2):

  * •

In the Northern hemisphere we used a combination of the 5.1 m Hale Telescope
at the Palomar Observatory (Decl. $\gtrsim$ -21∘; P.I. F. A. Harrison and D.
Stern) and 10 m Keck I at the W. M. Keck Observatory (-35∘ $\lesssim$ Decl.
$\lesssim$ 75∘; P.I. F. A. Harrison), targeting brighter targets
preferentially with the former, and fainter targets with the latter;

  * •

In the Southern hemisphere we used a combination of the 8.2 m Very Large
Telescope (VLT) at the European Southern Observatory (Unit Telescope 1 (UT1);
$-70^{\circ}$ $\lesssim$ Decl. $\lesssim$ $10^{\circ}$; P.I. G. B. Lansbury
and L. Klindt), and the 11 m Southern African Large Telescope (SALT) which is
part of the South African Astronomical Observatory in Sutherland (-80∘
$\lesssim$ Decl. $\lesssim$ 20∘; PI L. Klindt).

This multi-latitude campaign resulted in spectroscopic redshifts and
classifications for 550 NSS80 sources (including those in L17, 2 galaxy and 4
AGN pairs), as summarized in Table 6. We provide the date of the observing
run, the telescope and instrument used, and the total number of sources
observed, for both visitor and service mode observations; this key observing
information is listed for each individual source in the spectroscopic catalog
(see Appendix E.1 and Table 15). This subset can be selected from the primary
catalog with the flag SpecCAT; see Table 4. The reader can refer to Table 4 in
L17 for a summary of the NSS40 spectroscopic follow-up observations.

We note that all instruments are long-slit spectrographs. A further 44 NSS80
sources were followed up, but we failed to obtain a reliable redshift
measurement: 33/44 sources are optically faint (7 undetected in the $r$-band
and 26 with $r>20$), 9/44 sources have low S/N spectra due to compromised
observations (either due to weather conditions or telescope failures), one
source is optically-undetected, but given its radio and X-ray emission it is
possibly a radio-lobe associated with the science target, and the remaining
source is a BL Lac candidate with a power-law continuum lacking spectral
features; see Table 15 and Figure B5. Hence, 680/1274 (53%) NSS80 sources have
not yet been targeted for spectroscopic follow-up.

Table 6:  Chronological list of the optical spectroscopic follow-up campaign of NSS80 sources post L17; see L17 for the details of the NSS40 spectroscopic follow-up campaign. Listed for visitor mode observations are the ID assigned to each observing run, the date of the observing run, the telescope and instrument used and the number of sources observed. For service mode observations we also provide the observing period (semester) and the observing run end date. The different telescope instruments include the Double Spectrograph (DBSP), the Low Resolution Imaging Spectrometer (LRIS), the Focal Reducer and low dispersion Spectrograph (FORS2), and the Robert Stobie Spectrograph (RSS).  Run ID | UT Start Date | Telescope | Instrument | $N_{\mathrm{src}}$
---|---|---|---|---
Visitor mode
1 | 2016 October 02 | Palomar | DBSP | 3
2 | 2016 November 27 | Keck | LRIS | 3
3 | 2017 April 28 | Keck | LRIS | 16
4 | 2017 July 21 | Keck | LRIS | 15
5 | 2017 July 27 | Palomar | DBSP | 7
6 | 2017 September 14 | Palomar | DBSP | 2
7 | 2017 September 16 | Keck | LRIS | 9
8 | 2017 November 22 | Palomar | DBSP | 2
9 | 2018 March 18 | Keck | LRIS | 8
10 | 2018 June 06 | Palomar | DBSP | 9
11 | 2018 July 16 | Keck | LRIS | 4
12 | 2018 September 09 | Palomar | DBSP | 2
13 | 2018 October 03 | Keck | LRIS | 6
14 | 2019 March 07 | Keck | LRIS | 1
15 | 2019 July 22 | Palomar | DBSP | 3
16 | 2019 July 28 | Palomar | DBSP | 1
17 | 2019 August 02 | Palomar | DBSP | 1
18 | 2019 August 23 | Palomar | DBSP | 1
19 | 2019 October 26 | Palomar | DBSP | 7
20 | 2019 December 24 | Keck | LRIS | 15
21 | 2020 June 16 | Palomar | DBSP | 5
22 | 2020 September 12 | Palomar | DBSP | 5
23 | 2020 September 25 | Palomar | DBSP | 24
24 | 2020 October 23 | Palomar | DBSP | 28
Service mode
25 | P100 | VLT | FORS2 | 13
26 | P101 | VLT | FORS2 | 12
27 | P102 | VLT | FORS2 | 9
28 | P103 | VLT | FORS2 | 17
29 | 2017-SEM1+SEM2 | SALT | RSS | 4
30 | 2018-SEM1+SEM2 | SALT | RSS | 10
31 | 2019-SEM1+SEM2 | SALT | RSS | 8
32 | 2020-SEM1 | SALT | RSS | 3

####  3.3.2 Spectroscopic observations & data reductions

Since the spectral features of the NSS80 sources are not known a priori, we
adopt a broad wavelength coverage with sufficient spectral resolution to
search for, identify and accurately measure any spectral features. Therefore,
two grating angles were selected for each target observation with
Keck,242424Keck/LRIS is a double spectrograph, consisting of a blue and red
channel. However, only the grating angle on the red side is adjustable, while
the blue side grism is fixed. Palomar and SALT, whereas a broad wavelength
coverage was achieved with a single camera station for VLT. This allowed us to
access the 3200 Å $-$ 9000 Å visible wavelength range and cover commonly known
AGN and quasar emission and absorption lines across a range of redshifts. For
example, at lower redshifts (e.g., $z=0.3$), emission lines such as Mg ii
$\lambda$2800, [Ne v] $\lambda$3346 and $\lambda$3426, [O ii] $\lambda$3728,
[Ne iii] $\lambda$3869, H$\delta$ $\lambda$4102, H$\gamma$ $\lambda$4340,
H$\beta$ $\lambda$4861, [O iii] $\lambda$4959 and $\lambda$5007, [O i]
$\lambda$6300 and $\lambda$6364, [N ii] $\lambda$6548 and $\lambda$6584,
H$\alpha$ $\lambda$6563, and [S ii] $\lambda$6716 and $\lambda$6731 are
covered, and at higher redshifts (e.g., $z=2$), lines such as Ly$\alpha$
$\lambda$1216, Si iv $\lambda$1398, C iv $\lambda$1549, He ii $\lambda$1640, C
iii] $\lambda$1909, C ii] $\lambda$2326, and Mg ii $\lambda$2800 are covered.
For all our observations we adopted a slit width of $1-1.5^{\prime\prime}$,
depending on the seeing, and configured the spectrographs to obtain low-
resolution spectra (i.e., a resolving power of $R\sim 1000$), which is
sufficient to achieve our science goals.

For the majority of observations a total of two exposures were obtained (with
the exception of very bright targets), and in the case where
dithering252525Dithering is important for fringing corrections, especially at
longer wavelengths for standard CCD arrays such as SALT/RSS and VLT/FORS2.
Keck/LRIS and Palomar/DBSP, on the other hand, have thick, red-sensitive CCDs
on their red arms which have negligible fringing. was requested, 1 horizontal
tile and 2 vertical tiles with a maximum offset size of 10′′ were obtained.
Calibration images (flat fields and arc frames) were also recorded, and
spectrophometric standard stars were observed in the different instrument
configurations for flux calibration. It should be noted that, due to the
design of SALT, the spectra cannot be absolute flux calibrated. This is due to
the moving pupil during exposures and tracking which consequently changes the
effective area of the telescope. Therefore, the standards were only used for
relative spectral (shape) calibration.

The spectroscopic data reductions included basic CCD pre-reductions, spectral
calibration, background subtraction, spectral extraction and flux calibration.
The tasks available in iraf (see Massey et al., 1992) were used to perform the
reduction and analysis processes for the Keck, Palomar and SALT spectra, and
the EsoReflex 2.9.1 pipeline was used to reduce the VLT/FORS2 spectra. For
more details see Section 4.4 of Klindt (2022). The final flux-calibrated
optical spectra described herein are available in Appendix E.1 and will be
made available on the NSS80 webpage; see Section A.2 in L17 for the NSS40
optical spectra).

####  3.3.3 Spectral Classification and Analysis

To assist in the measurement of spectroscopic redshifts, we used the open-
source Manual and Automatic Redshifting Software (Marz; Hinton et al., 2016)
by matching the observed flux calibrated input spectra (FITS file format)
against a library of stellar, galaxy and AGN templates available in the Marz
web application; see fig. 6 in Hinton et al. (2016) for a visual display of
the twelve (5 stellar + 6 galaxy + 1 AGN) current templates available in
Marz.262626Hinton et al. (2016) compiled the library of templates from runz
(originally developed for the use of the 2dF galaxy redshift survey; Colless
et al., 2001) and autoz with original templates from 2dF (Colless et al.,
2001), WiggleZ (Drinkwater et al., 2010), the Gemini Deep Survey (Abraham et
al., 2004), SDSS DR2 (SubbaRao et al., 2002) and galaxy eigenspectra from
Bolton et al. (2012). Via this manual template comparison approach, the object
type can easily be identified and the spectrum can be redshifted to align the
observed spectral lines with the template (for moderate to high S/N spectra).
From this, Marz provides a redshift solution, however, it does not assign
uncertainties to the redshifts (see Yuan et al., 2015, for more details). For
low S/N spectra where template comparison and line identification are arduous,
we identified potential spectral features and used a look-up table of
wavelength ratios based on the emission and absorption lines observed in AGN
and galaxy spectra for spectral lines. The redshift solution is then
determined by cross-matching the observed wavelength ratios of the identified
lines to the rest wavelength ratios based on the emission and absorption lines
observed in AGN. Sources with low S/N spectra or dubious redshift measurements
are flagged in the catalogue.

During the full 80-month period, including L17, we obtained redshift
measurements for 550 NuSTAR sources, of which we spectrally classified 547
(this accounts for 43% of the NSS80 primary catalog): 427 were obtained via
our optical follow-up campaign and 123 from archival data (primarily SDSS
DR16; Ahumada et al., 2020; see Table 15 for details). The source
classifications and redshift measurements for all NSS80 sources with optical
spectra are provided as supplementary material in Appendix E.1. The majority
of the sources have robust redshift measurements obtained from two or more
spectral lines, whilst 21/550 sources have a single-line measurement; these
sources are flagged as “quality B" redshift measurements. Sources were
selected for follow-up based on target visibility, chances of success given
optical magnitude and instrument characteristics, and where possible higher
probability counterparts were chosen. However, many targets were included in
telescope observing programs as filler targets and thus the selection is not
completely uniform.

Figure 16:  A pie-chart of the NSS80 source classifications obtained via our
spectroscopic follow-up campaign. In total, there are 612 source entries in
the NSS80 spectroscopic catalog: 594 unique spectroscopic entries and 18
additional entries. Of the 594 unique entries, we have classified 492 as
extragalactic sources, including 284 BL (or BL?), 194 NL (or NL?), one galaxy
cluster, 10 galaxies, and three unclassified sources with redshift
measurements from literature. We have also classified 58 Galactic sources at
$z=0$. There are a further 43 sources that lack a reliable redshift
measurement, 28 of which are unclassified due to the lack of spectral lines,
but a power-law continuum is detected in all of the cases, 14 sources have
counterpart uncertainties due to the lack of a lower-energy X-ray counterpart
or high optical source density, one source is a Fermi BL Lac candidate. The
remaining one source is a hotspot of 4C 74.26 (radio quasar), which was
targeted as the primary NuSTAR science target; see Figure 17. In addition to
the unique entries, we obtained spectra for a further 18 sources: three AGN
pairs of which one pair is a dual AGN system, two AGN-galaxy pairs, one galaxy
pair, and one unclassified pair (see Figure 18), 7 sources with photometric
redshifts, and four sources which are potentially the correct counterpart
oppose to the one selected; 3/4 are fainter lower-energy X-ray sources (2 BLs
+ 1 phot-$z$ source of unknown type) nominally closer to the NuSTAR source
than the selected (X-ray brighter) BL counterpart, and the remaining source is
an optically bright NL galaxy at a different redshift than the Nway-selected
NL counterpart (which is associated with the primary NuSTAR science target).

Based on the spectroscopic redshift measurements, 492/550 NSS80 sources are
extragalactic and 58 are Galactic. The extragalactic sources are classified
through visual inspection of the flux-calibrated spectra into the following
general classes, and subsets can be selected from the primary catalog using
the Classification column (see Table 4):

  * •

Broad line object (BL) if any permitted line is significantly broader than the
forbidden lines, or if a single line measurement for our quality “B” spectra
satisfies the standard definition of a broad-line, i.e., $FWHM\geq 1000$ km
s-1 (measured in iraf);

  * •

Narrow line object (NL) if the permitted lines are of similar width to the
narrow forbidden lines;

  * •

Galaxy (Gxy) if only absorption lines are detected.

Based on this simple classification scheme, we find that 58% (284/492) are BL
AGN, 39% (194/492) are NL objects and 2% (10/492) are galaxies (Gxy); see
Figure 16. We also classify 1/492 source as a galaxy cluster (GClstr;
NuSTARJ132535-3825.6) and 3/492 sources have redshift measurements obtained
from the literature, but lack spectroscopic classification. We append the
optical classification with a “?" symbol for 29 sources (12 BL? + 17 NL?)
where it is ambiguous whether the permitted lines are broad or not. Regardless
of the optical classification, the vast majority of the sources are expected
to be AGN due to the detection of X-ray emission at high X-ray energies of $>$
3 keV, which is further confirmed for most sources by the identification of
strong optical emission lines often superimposed on a power-law spectrum. The
58 Galactic sources are not classified here but based on the NSS40 results,
they are likely to include, for example, cataclysmic variables, X-ray
binaries, and active stars; 40% (23/58) of the Galactic sources are at low
Galactic latitudes ($|b|$ $<$ $10^{\circ}$). The number of Galactic NuSTAR
sources has increased by a factor of $\sim$3 from the NSS40 to the NSS80
catalog. These sources will be further investigated through an additional
follow-up campaign (see e.g., Tomsick et al., 2018, for a study of the L17
Galactic sources). There are also 43 NSS80 targets which we followed-up, but
failed to obtain a reliable redshift measurement. For all these cases a faint
(often red) continuum is detected, one of which is a Fermi BL Lac candidate
(NuSTARJ081003-7527.2) with a featureless power-law spectrum (Ackermann et
al., 2016). Possible reasons for the lack of spectroscopic identifications for
these sources are given in Section 3.3.4. Finally, the remaining source
(NuSTARJ204256+7503.1) is a hotspot associated with the primary NuSTAR science
target 4C 74.26, a radio quasar at $z=0.104$ (e.g., Erlund et al., 2007,
2010). Figure 17 shows multi-wavelength imaging of the NuSTAR-detected hotspot
at a projected distance of $\sim$ 580 kpc from the quasar. Hence, in total,
there are 594 unique source entries in the NSS80 spectroscopic catalog given
in Table 15.

Figure 17: Multi-wavelength imaging of the luminous X-ray hotspot in 4C 74.26
(e.g., Erlund et al., 2010), the primary NuSTAR science target. The hotspot,
which coincides with a radio-bright lobe of 4C 74.26, is detected with both
lower-energy (i.e., Chandra, XMM-Newton and Swift-XRT) and hard X-ray
observatories such as NuSTAR. Table 7:  Source information for the three AGN
pairs, two AGN-Gxy pairs, one galaxy pair, and one pair of unknown type.

NSS80 name | NSS80 field | NuSTAR | $z$ | $L_{\mathrm{10-40keV}}$ | PFlag | Pair | Angular | Physical
---|---|---|---|---|---|---|---|---
|  | detection |  |  |  | type | distance | distance
|  |  |  | (erg s-1) |  |  | (arcsec) | (kpc)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
NuSTARJ054231+6054.4 | BY_Cam | S+H+F | 0.257 | $4.07\times 10^{44}$ | 0 | NLAGN + NLAGN | 4.7 | 19.1
NuSTARJ091534+4054.6 | NGC_2785 | F | 1.298 | $6.41\times 10^{44}$ | 0 | BLAGN + BLAGN | 16.3 | 138.6
NuSTARJ120530+1649.9 | IRAS12032p1707 | S+H+F | 0.216 | $2.37\times 10^{43}$ | 1 | BLAGN + NLAGN | 45.5 | 159.4
NuSTARJ022742+3331.5 | CXOJ022727d5p333443 | S+H+F | 0.09 | $6.33\times 10^{42}$ | 0 | NLAGN + NL | 8.9 | 15.1
NuSTARJ184552+8428.2 | 1RXSJ184642d2p842506 | S+H+F | 0.233 | $4.92\times 10^{43}$ | 1 | NLAGN + Gxy | 8.1 | 30.3
NuSTARJ021454-6425.9 | RBS0295 | F | 0.068 | $1.21\times 10^{42}$ | 1 | Gxy + Gxy | 22.2 | 29.04
NuSTARJ020614+6449.3 | 3C_58 | F | – | – | – | Unknown | 1.99 | –

Note. — Columns: (1) Unique NuSTAR source name. (2) Object name for the
primary science target of the NuSTAR observation(s), i.e., the field name. (3)
The energy bands for which the source is detected: soft (S; 3-8 keV), hard (H;
8-24 keV), and full (F; 3-24 keV) bands. (4) The spectroscopic redshift of the
NuSTAR source. (5) The rest-frame 10–40 keV luminosity; see Figure 26. (6) A
binary flag indicating sources that show evidence for being associated with
the primary science target of their respective NuSTAR observations, according
to the definition $\Delta(cz)<0.05\,cz$. (7) The type of sources for each
pair: BLAGN refers to quasars, NLAGN to narrow-line AGN (from BPT
diagnostics), NL to narrow-line objects (e.g., star forming galaxies), and Gxy
to galaxies (absorption lines only). (8) The angular distance for each pair.
(9) The projected physical distance for each pair.

In addition to the unique spectroscopic entries, we obtained spectra for a
further 18 cases where two potential optical/IR counterparts were identified –
this gives a total of 612 entries in the NSS80 spectroscopic catalog (i.e., 18
NuSTAR sources have duplicate entries to capture information for both targeted
counterparts). Notably, among these there are 6 sources with companions (i.e.,
in pairs with $\Delta z<$0.1): three AGN pairs, two AGN-galaxy (AGN-Gxy)
pairs, and one galaxy pair. In Figure 18 optical spectra of the three AGN
pairs are shown (the main target spectra are plotted in black and their
companions in peach), and Figure 19 show the two AGN-galaxy pairs and the
galaxy-galaxy pair. We also show the spectra of a candidate source pair
(NuSTARJ020614+6449.3) at low Galactic latitude, for which both sources only
have a faint, red continuum detected. The source information for these systems
is provided in Table 7. For the three AGN and two AGN-galaxy-pairs the
projected physical distances are in the range $\sim$ 15–160 kpc. These
include:

  * •

NuSTARJ054231+6054.4, a dual AGN system at $z=0.257$, comprising a pair of
likely merging, obscured AGN (in X-rays, there is lower-energy X-ray coverage
with Swift-XRT but no detection; in optical, their spectra show only narrow
lines). The term dual AGN refers to a system where two AGN at the same
redshift are identified at a small separation angle. Koss et al. (2016)
reported on the first dual AGN identified with NuSTAR, i.e., SWIFTJ2028.5+2543
– a system where both nuclei are heavily obscured to Compton thick
($N_{\mathrm{H}}\approx(1-2)\times 10^{24}$ cm-2).

  * •

NuSTARJ091534+4054.6, a BL AGN pair at $z=1.298$, comprising two closely
associated quasars;

  * •

NuSTARJ120530+1649.9, an AGN pair including a BL AGN
(WISEAJ120530.63+164941.4; Ahn et al., 2012; Toba et al., 2014) and a NL AGN
at $z=0.217$. This pair is at the same redshift as the primary NuSTAR science
target (WISEAJ120547.71+165107.9; Darling & Giovanelli, 2006) and is,
therefore, associated with the luminous IR galaxy (see Table 8).

  * •

NuSTARJ022742+3331.5, an AGN-Gxy pair at $z=0.09$ which is composed of a
“borderline” NL AGN and a star-forming galaxy (confirmed by BPT diagnostics).
The NL AGN is detected in all three NuSTAR bands;

  * •

NuSTARJ184552+8428.2, an AGN-Gxy pair at $z=0.233$ comprising a NL AGN and an
early-type galaxy companion, which are in the same halo as the NuSTAR science
target (see Table 8). The NL AGN is detected in all three NuSTAR bands with a
soft band luminosity of $L_{\mathrm{3-8\,keV}}=1.91\times 10^{43}$ erg s-1,
indicating that it is indeed an X-ray AGN.

The galaxy pair (NuSTARJ021454-6425.9) is comprised of a galaxy at $z=0.068$
and a galaxy companion at $z=0.075$; the latter is associated with the primary
NuSTAR science target (RBS0295; Schwope et al., 2000); see Table 8. The pair
of sources are undetected in the NuSTAR soft and hard energy bands with a full
band luminosity of $L_{\mathrm{3-24\,keV}}=1.52\times 10^{42}$ erg s-1 which
may be a spurious detection, considering also its low NuSTAR detection
probability [$\log(P_{\mathrm{false,min}})\sim-6.2$] and lack of a lower-
energy X-ray identification.

Figure 18: Optical spectra for the three NSS80 AGN pairs: (a) a dual AGN
system of merging, obscured AGN, (b) a BL AGN (i.e., quasar) pair, and a (c)
BL AGN + NL AGN pair. For each source pair the two spectra are plotted in the
left panel and a $30^{\prime\prime}$ $\times$ $30^{\prime\prime}$ Pan-STARRS
(or DECam for sources with declinations $<-25^{\circ}$) $i$-band image centred
on the NuSTAR position is shown on the right. Spectrum panel: Shown on the top
are the unique NuSTAR ID and source name, in the upper left corner the
observing telescope and run identification number (corresponding to Table 6),
and in the upper right corner the source classification and redshift. Sky
subtraction has been performed, but some features may remain: for example the
7600 Å absorption feature. Image panel: All WISE detections are shown with ‘X’
marks, color-coded in $W1-W2$ colors: non-AGN like sources with $W1-W2<0.8$
(green), AGN-like sources with $W1-W2>0.8$ (red), and non-AGN like sources
based on the $W1-W2$ color, but with a bright $W3$ detection (peach). The
NuSTAR 25′′ and 30′′ error circles are plotted in a dash-dotted and a solid
black line, respectively. The lower energy X-ray position is marked with a
blue cross and the respective error circle, the CatWISE20 position is
indicated with a green crosshair, a WISE color-coded star and a green 2.7′′
error circle, the PS1-DR2 position is shown with a purple 2′′ error circle,
and the spectroscopically observed pair of sources are marked with a red and a
peach crosshair corresponding to the spectrum (black and peach).  Figure 19:
Optical spectra for the two AGN-Gxy pairs [(a)+(b)], one galaxy pair (c), and
one pair of sources of unknown type (d). The spectroscopically observed pair
of sources are marked with a red and a peach crosshair corresponding to the
spectrum (black and peach), or a red and a green crosshair if one of the
sources is the CatWISE20 counterpart. See Figure 18 for the symbol key.
Figure 20: Optical spectra for the NSS80 sources with two counterpart
candidates. Three of the four candidates [(a)–(c)] are fainter lower-energy
X-ray sources nominally closer to the NuSTAR source than the selected (X-ray
brighter) BL counterpart. The correct counterpart for the remaining source (d)
is either an optically bright NL AGN ($z=0.036$) associated with the BAT-
detected primary NuSTAR science target or a NL galaxy ($z=0.137$) which lacks
a lower-energy X-ray counterpart. See Figure 18 for the symbol key.

The 18 additional spectroscopic entries also include four sources that could
potentially be the correct counterparts rather than the one selected in the
unique catalog entry; see Figure 20. Three are fainter lower-energy X-ray
sources [(a)-(c)] nominally closer to the NuSTAR source than the selected
(X-ray brighter) BL counterpart. The correct counterpart for the remaining
source (d) is the choice between an optically bright NL AGN ($z=0.036$)
associated with the BAT-detected primary NuSTAR science target (LEDA178130;
Jones et al., 2004, 2009; Lansbury et al., 2017b; Koss et al., 2022), or a NL
galaxy ($z=0.137$) 12.5′′ from the Nway-selected NL AGN, which lacks a lower-
energy X-ray counterpart; the former takes preference of being the correct
counterpart to the NSS80 source since it is a confirmed AGN. These sources
will be further investigated through our multi-wavelength follow-up campaign.

In addition to the 550 spectroscopically confirmed redshifts, we also obtained
photometric redshifts from the literature for an additional 7 NSS80 sources
(from Salvato et al., 2009; Richards et al., 2009; Bilicki et al., 2014;
Masini et al., 2020); flagged as “quality C" redshift measurements in the
catalog and we append the optical classification with a “C". We exclude these
7 sources with phot-$z$ measurements from any redshift-dependent analysis
given the larger uncertainty on phot-$z$ measurements. Overall the current
spectroscopic completeness for the primary NSS80 catalog is 43% (550/1274);
this improves to 52% (508/981) for sources at high Galactic latitudes
($|b|>10^{\circ}$). Further on-going optical spectroscopic campaigns will
increase the spectroscopic completeness of the NSS80, in addition to further
lower-energy X-ray observations to improve the number of sources with reliable
lower-energy X-ray counterparts.

For all NuSTAR sources with spectroscopic identifications, we assign an
“associated” flag to those that have a velocity offset from the science target
smaller than 5% of the total science target velocity, i.e.,
$\Delta(cz)<0.05\,cz$, following L17. Based on this, 19 spec-$z$ NSS80 sources
show evidence for being associated with the primary NuSTAR science target and
are, therefore, excluded from any subsequent analysis. Table 8 provides source
information for these serendipitous sources and their associated NuSTAR
science target (of which 15 are BASS DR2 sources; see Koss et al., 2022).

Table 8:  NSS80 sources which show evidence for being associated with the
primary NuSTAR science target according to the definition
$\Delta(cz)<0.05\,cz$.

Serendip Name | Serendip Type | $z_{\mathrm{serendip}}$ | Primary Target | Primary Type | $z_{\mathrm{target}}$ | BASS
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
NuSTARJ002544+6818.8 | NL | 0.012 | LEDA136991 | Sy2 | 0.012 | 1
NuSTARJ010736-1732.3 | NL | 0.021 | IC1623 | GPair | 0.02 | 0
NuSTARJ012215+5002.2 | - | 0.021 | MCG+8-3-18 | Sy2 | 0.021 | 1
NuSTARJ021454-6425.9 | Gxy | 0.075 | RBS295 | Sy1 | 0.074 | 1
NuSTARJ024144+0512.3 | NL | 0.07 | IRAS02394+0457 | Sy2 | 0.07 | 1
NuSTARJ035902-3011.7 | NL | 0.093 | SARS059.33488-30.34397 | Sy1.9 | 0.097 | 1
NuSTARJ040702+0346.8 | NL | 0.088 | 3C105 | Sy2 | 0.088 | 1
NuSTARJ050559-2349.9 | NL | 0.036 | LEDA178130 | Sy2 | 0.035 | 1
NuSTARJ054349-5536.7 | BL | 0.272 | WISEJ054357.21-553207.5 | QSO | 0.273 | 0
NuSTARJ065805-5601.2 | NL? | 0.296 | Bullet Cluster | GxyCluster | 0.296 | 1
NuSTARJ065842-5550.2 | NL | 0.297 | Bullet Cluster | GxyCluster | 0.296 | 0
NuSTARJ071422+3523.9 | NL | 0.015 | MCG+6-16-28 | Sy2 | 0.015 | 1
NuSTARJ120530+1649.9 | BL | 0.216 | WISEAJ120547.71+165107.9 | LIRG | 0.218 | 0
NuSTARJ125442-2657.1 | Gxy | 0.058 | CTS18 | Sy1.2 | 0.059 | 1
NuSTARJ151253-8124.3 | NL | 0.069 | 2MASXJ15144217-8123377 | Sy1.2 | 0.069 | 1
NuSTARJ165105-0129.4 | NL | 0.041 | 2MASXJ16510578-0129258 | Sy2 | 0.04 | 1
NuSTARJ184552+8428.2 | NL | 0.233 | 1RXSJ184642.2+842506 | Sy1 | 0.225 | 1
NuSTARJ190813-3925.7 | Gxy | 0.075 | IGRJ19077-3925 | Sy1 | 0.075 | 1
NuSTARJ224536+3947.1 | NL | 0.081 | 3C452 | Sy2 | 0.081 | 1

Note. — Columns: (1) The unique NSS80 name for each serendipitous source. (2)
Spectroscopic classification of the NSS80 serendipitous source. (3)
Spectroscopic redshift of the NSS80 serendipitous source obtained with our
follow-up campaign. (4) The primary NuSTAR science target name. (5) Source
type of the NuSTAR science target name. (6) Redshift of the NuSTAR science
target. (7) A binary flag indicating NuSTAR science targets which are BASS DR2
sources (Koss et al., 2022).

####  3.3.4 Comparison between confirmed spectroscopic and Nway identified AGN

A significant fraction of the optical spectroscopic follow-up programme was
based on the approach outlined in L17 using closest counterparts for lower-
energy X-ray sources and/or counterparts with AGN-like MIR properties from
WISE. Here we investigate how the optical counterpart identified from that
approach compares to that found using the Nway approach described in Section
3.2. We note that a disagreement between the counterparts does not necessarily
mean that the incorrect counterpart was followed-up; due to the probabilistic
approach of Nway the ‘best’ selected counterpart will not always be the true
one (see discussion of false probabilities in Section 3.2). For example, the