The NuSTAR Serendipitous Survey: The 80 Month Catalog and Source Properties of the High-energy Emitting Active Galactic Nucleus and Quasar Population

The NSS80 comprises 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–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 the following:

• 1.  
  Dedicated extragalactic survey fields: COSMOS (Civano et al. 2015), ECDFS (Mullaney et al. 2015), EGS (J. Aird et al. 2024, in preparation), GOODS-N (J. Aird et al. 2024, in preparation), and UDS (Masini et al. 2018).
• 2.  
  Galactic surveys (Mori et al. 2015; Hong et al. 2016), i.e., all fields within a 2° radius of the Galactic center.
• 3.  
  The Norma Arm survey (Fornasini et al. 2017).
• 4.  
  Fields where the total counts exceed 10⁶ 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 ∼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 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 2013 January–August, and spike 2 (bin 10) includes 193 Cycle 3 GO observations performed during the period 2017 August–2018 February. These spikes coincide with a decrease in the average exposure time, indicating that more shallow observations were scheduled in these periods.

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Table 2 lists the individual exposures in alphabetical order for the first five unique fields (i.e., comprising nonoverlapping pointings) in NSS80 (the full table is 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 ∼100 s to 1 Ms).

Table 2. Details of the Individual NSS80 NuSTAR Observations for the First Five Unique Fields

ID	Science Target	NSS40	Nobs	Obs. ID	Obs. Start Date	R.A.	Decl.	b		Nserendips
						(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 Dec 26	...	...	...	0.2	...
1b	...	...	...	90401371002	2018 Dec 27	...	...	...	0.7	...
2	1E1048d1m5937	...	5	...	...	162.53	−59.89	−0.52	397.9	9
2a	...	...	...	30001024003	2013 Jul 17	...	...	...	25.7	...
2b	...	...	...	30001024002	2013 Jul 17	...	...	...	26.6	...
2 c	...	...	...	30001024005	2013 Jul 19	...	...	...	167.7	...
2d	...	...	...	30001024007	2013 Jul 25	...	...	...	119.1	...
2e	...	...	...	90202032002	2016 Aug 05	...	...	...	58.9	...
3	1E1530m085	303	1	60061265002	2015 Aug 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 Jun 25	...	...	...	70.7	...
4b	...	...	...	30301017002	2017 Jun 02	...	...	...	70.3	...
4 c	...	...	...	30301013002	2018 Apr 29	...	...	...	142.3	...
5	1E1841m045	...	6	...	...	280.33	−4.94	−0.01	346.3	7
5a	...	29a	...	30001025002	2012 Nov 09	...	...	...	52.4	...
5b	...	29b	...	30001025004	2013 Sep 05	...	...	...	37.8	...
5 c	...	29 c	...	30001025006	2013 Sep 07	...	...	...	70.9	...
5d	...	29d	...	30001025008	2013 Sep 12	...	...	...	41.6	...
5e	...	29e	...	30001025010	2013 Sep 14	...	...	...	35.4	...
5f	...	29f	...	30001025012	2013 Sep 21	...	...	...	108.2	...

Notes. Columns: (1): ID assigned to each field. For fields with multiple NuSTAR exposures (i.e., N_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): R.A. and decl. (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, in kiloseconds), 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.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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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 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 NSS40, the number of post-NSS40 fields has increased by ≈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∣ ≤ 10°: 174 of the 894 NSS80 fields (19%) lie within the Galactic plane, also a factor of ∼3 increase over that of NSS40.

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The reduction of the new (i.e., post-40 months) 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 (Aird et al. 2015; Mullaney et al. 2015; Harrison et al. 2016). 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 the differences between the final NSS80 and the prior NSS40 catalogs).

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Briefly, the raw event files were processed using the nupipeline procedure from the NuSTAR Data Analysis Software (NuSTARDAS) v1.9.2 (incorporated within the HEASoft v6.24 software suite) and CIAO v4.7.0 to produce calibrated event files. ⁴⁵ 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 246. 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 optimize the depth of our data sets, we coadded the images and exposure maps from the FPMA and FPMB detectors. This resulted in a total of nine images and nine exposure maps per field (three energy bands for FPMA, FPMB, and FPMA+B). ⁴⁶ 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 reanalyzed 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, which gives the probability that the observed counts within a circular aperture of 20″ radius (justified by the tight core of the NuSTAR point-spread function, PSF; see Civano et al. 2015; Mullaney et al. 2015) were produced purely by a fluctuation of the background. ⁴⁷ The expected background is estimated by convolving the image counts with an annular aperture of inner radius 45″ and outer radius 90″ and rescaling 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 ∼5σ; 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 description. ⁴⁸

Once the master source list was created, we visually inspected all the postprocessed 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 background, and/or emission from the science target (illustrated in the lower panel of Figure 3). ⁴⁹ 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 postprocessing 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 reassessed 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 pointlike.

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 ∼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 region (Zhao et al. 2021b). The NSS80 catalog 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 ∼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.

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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 ≈370,000 independent 20″ radius regions, which with our strict (i.e., low) false-probability threshold of 10⁻⁶ (see the higher thresholds adopted in Mullaney et al. 2015 and 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.

The master source list comprises 1488 serendipitous NuSTAR sources that are significantly detected in at least one energy band, independently of any prior multiwavelength information. Based on findings in L17, the majority of the X-ray-detected sources in NSS80 are expected to be AGNs 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 nonnegligible 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 AGNs 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 AGNs in field galaxies. To identify NuSTAR sources in highly extended optical galaxies or nearby galaxy clusters, we selected sources that lay within

• 1.  
  the isophotal radius (D₂₅) of RC3 galaxies (Third Reference Catalog of Bright Galaxies; de Vaucouleurs et al. 1995) where the R-band surface brightness μ_R = 25 mag arcsec⁻², including the SMC and LMC; or
• 2.  
  the radii of Abell clusters obtained from Abell (1958) or, if unavailable, a median value of 05 as a radius; or
• 3.  
  the 2 × 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.

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Table 3 provides the numbers of sources in the primary NSS80 catalog that are detected in different energy bands as well as statistics regarding optical counterparts, spectroscopic follow-up, and successful redshift measurements. The total numbers 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	Nspec	Nz	Nz,failed		Nr < 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

Notes. 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 and 3.3). (5): the number of sources for which spectroscopic observations were undertaken, but which lack a reliable redshift measurement (the majority of which have faint, red continuum spectra); see Table 14 and Figure E5. (6): the number of sources with an associated optical counterpart detected in the r band; magnitudes are obtained from SDSS, Pan-STARRS, USNOB1, and the NOAO Source Catalog (NSC). (7): the number of sources with an associated optical counterpart brighter than r = 22 (detectable with current ground-based telescopes).

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Both the primary and secondary source catalogs are provided as machine-readable 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 online, and in Figure 7 we show an example of one of these fields. ⁵⁰ In Table 4, we give a summary of the subsets of this primary catalog, as discussed in future sections.

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 summarized below:

• 1.  
  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.
• 2.  
  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.
• 3.  
  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 postprocessing 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 catalogs. Of the 331 NSS40 unique fields, we reprocessed 50 fields—six which include only NSS40 observations, while 44 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. Thirty-six NSS40 sources were not detected in our coadded fields; we summarize potential reasons to explain these undetected sources in Table 13. Thirty-two of the 36 undetected NSS40 sources have updated false probabilities, based on the deeper coadded 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 four undetected NSS40 sources, one lies in an excess background region and three 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.

To search for lower-energy (soft) X-ray counterparts, we used Chandra, XMM-Newton, and Swift-XRT observations. We crossmatched the NuSTAR sources to (i) the Chandra Source Catalog Release 2.0 (CSC2.0; Evans et al. 2019), (ii) 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 Catalog (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 crossmatching between different surveys, and thus here and in Section 3.2 we select crossmatching 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 ∼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 eight sources which have faint lower-energy X-ray emission (yet not statistically significant) in the vicinity of the NuSTAR position (one Chandra, four XMM-Newton, and three 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 nondetections could be that the observations were too shallow to detect faint sources, or it could be attributed to variability given that the observations are noncontemporaneous, or it could be the result of absorption of lower-energy X-ray photons along the line of sight. Only ∼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 eight manually measured positions using lower-energy X-ray imaging, i.e., one position from Chandra, four from XMM-Newton, and three from Swift-XRT; see row 4 in Table 5. ⁵¹

Table 5. The Number of NuSTAR Serendipitous Sources with Lower-energy X-Ray Counterparts

		CSC2.0	4XMM-DR10s	4XMM-DR10	2SXPS	Any
(1)	NTotal/NCoverage	300/408	492/651	394/553	661/949	956/1249
(2)	NSingle	211	382	349	617	907
(3)	NMultiple	89	110	45	44	214
(4)	NBest	300	317	168	171	956 a
(5)	〈Δ R.A.	−050 ± 060	055 ± 052	020 ± 061	−028 ± 049	…
(6)	〈Δdecl.〉	036 ± 049	−013 ± 040	020 ± 051	071 ± 034	…
(7)	〈θ〉	107	112	126	109	…

Notes. Row (1): the total number of NuSTAR sources in the primary catalog with a lower-energy X-ray counterpart within a search radius of 30″ (N_Total) compared to the total number of primary NuSTAR sources with Chandra, XMM-Newton, and/or Swift-XRT coverage (N_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 nonzero exposure times at the NuSTAR coordinates. The final column enumerates the number of unique NuSTAR sources with a match in any catalog. Row (2): the number of NuSTAR sources with a single match within 30″ to the specific lower-energy X-ray catalog. Row (3): the number of NuSTAR sources with multiple matches within 30″ to the specific lower-energy X-ray catalog. Row (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. Rows (5) and (6): the mean positional offsets in R.A. (5) and decl. (6) of the NuSTAR position relative to the lower-energy X-ray counterpart (see Figure 8, top panel). Row (7): the mean angular offset between the NuSTAR and lower-energy X-ray positions in arcseconds. These values are computed for all CSC2.0, 4XMM-DR10/s, and 2SXPS matches.

^a In addition to the 956 unique sources with automatically matched counterparts described in the table, a further eight sources (one Chandra, four XMM-Newton, and three Swift-XRT) were manually identified, resulting in a total of 964 NSS80 sources with a lower-energy X-ray counterpart.

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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 crossmatching 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 catalog.

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%, and 90% for CSC2.0, 4XMM-DR10s, 4XMM-DR10, and 2SXPS, respectively), particularly those with more significant detections (i.e., lower 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.

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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 , as indicated with solid and dashed–dotted 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.

We estimated the observed-frame 3−8 keV flux (F_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 keV flux using a conversion factor of 0.83, 0.92, and 0.62, respectively. ^{52 , 53} 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 band. ⁵⁴ 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 3 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 noncontemporaneous 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.

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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 ( see Appendix A). This allows us to compare (a) F_soft measured by NuSTAR (F_soft,NuSTAR), in order to assess whether a significant amount of NuSTAR flux is coming from other sources, and (b) F_soft from the best lower-energy counterpart (F_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 , and 4.9% have . Only 21 sources have combined fluxes that exceed F_soft,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.

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 far-IR (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-neighbor approach to identify multiwavelength counterparts, using the more reliable positions from lower-energy X-ray counterparts, where available, and the distinctive characteristics of AGNs with respect to galaxies in the MIR band (as traced using WISE). Here we adopt a more sophisticated probabilistic approach using Nway (v4.4.2; Salvato et al. 2018) to identify IR and optical counterparts for the NSS80 sources. Nway uses Bayesian methods to probabilistically match multiwavelength counterparts to X-ray sources by simultaneously matching N catalogs in a multidimensional 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 AGNs. 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 μm (i.e., W1 and W2). In addition, we use Pan-STARRS Data Release 2 (PS1-DR2; Flewelling 2018), which provides coverage at decl. ≳ −30° with a single-epoch 5σ depth of r < 21.8. ⁵⁵

In what follows we summarize 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 (b). We begin by constructing color and magnitude priors that are approximately representative of the population by performing a photometrically unbiased crossmatch 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 crossmatching that includes all possible counterparts (i.e., those that had low probabilities in the first crossmatch, as well as the high-probability matches) and improve the final crossmatch probabilities that inform our selection of principal counterparts.

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This process and the resulting principal optical counterparts should be understood with some basic information in mind. In general, we prioritize counterparts from the X-ray–MIR matching, as AGNs 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.

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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″ of the NuSTAR position (see the green outlined boxes in Figure 10(a)). ⁵⁶

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 – curves reported in Harrison et al. (2016), adopting the deblended soft-band NuSTAR flux.

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 catalog values for sources with soft X-ray matches. For NuSTAR-only sources, we used the 68% positional uncertainties based on , 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_Cat,best and p_PS,best for CatWISE20 and PS1-DR2, respectively). ⁵⁷ 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_Cat,any and p_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_CAT/PS,any > 0.5 and p_CAT/PS,best > 0.8. We treat sources at low Galactic latitudes (∣b∣ < 20°) separately since source confusion is high closer to the Galactic plane as a result of the high density of Galactic sources; color/magnitude priors appropriate to extragalactic 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 extragalactic 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 AGNs. 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 AGNs (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 (gray 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 catalogs: X-ray–optical and X-ray–IR, which are used to evaluate priors for the more thorough matching in Round 2.

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°. ∣b∣ < 20° 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° X-ray sources are identified using the magnitude and color priors from Round #1 as inputs to Nway; therefore, these matches are weighted toward 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° 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_CAT/PS,best > 10%.

We now have two “improved” match catalogs: X-ray–optical and X-ray–IR, which contain a potential match for each NSS80 source. These catalogs must then be assessed to select a preferred counterpart, which we refer to as the “principal counterpart.” The goal of this process is to characterize 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 / Figures 10(b) and 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, multiband positions and photometry (which can be expanded according to one’s preferences), and key Nway information such as p_CAT/PS,best and p_CAT/PS,any—all of these will be included in the online NSS80 catalog; see Appendix A. ⁵⁸ The next part of this section describes selecting the best available optical counterpart, which is the Nway-selected source in the majority of cases. ⁵⁹

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 extragalactic 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:

• (i)  
  Sources with a lower-energy X-ray match, at least one CatWISE20 match, and at least one PS1 match within 27 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 multiwavelength 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, of which 573 have at least one PS1 association found by Nway (Pan-STARRS only covers decl. ≳ −30°; 627/850 sources with soft X-ray and CatWISE20 matches fall in this region). ⁶⁰ 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 27 between the PS1 and CatWISE20 positions removes counterparts where the probability of a correct match is ≲0.1% based on positional uncertainty alone (with probabilities converted from, for example, Lake et al. 2012). Hence, for the 573 with lower-energy X-ray + CatWISE20 + a PS1 counterpart from Nway within 27 of the CatWISE20 position, we adopt this PS1 source as the principal optical counterpart, and it is flagged as “PS1-NWAY.” ⁶¹ If the position from Nway is too distant but a match can be found in PS1 by matching manually, then this is labeled “PS1-MAN” (31 sources). ⁶²
• (ii)  
  Sources with a lower-energy X-ray match, at least one CatWISE20 match, but no PS1 match within 27. The lower-energy X-ray + CatWISE20 + PS1 sources with angular separations >27 between the CatWISE20 and PS1 positions (with a mean separation of 71) 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 Sloan Digital Sky Survey (SDSS) photometric catalog Data Release 12 (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 27 positional uncertainty. These matches were done based on the closest available source, and identify 228 optical counterparts. They are labeled according to the catalog used. ⁶³
• (iii)  
  Sources with a lower-energy X-ray match, but no CatWISE20 match. From lower-energy X-ray counterparts that lack any CatWISE20 association (i.e., a CatWISE20 Nway match with p_Cat,best > 0.1; 114/964); 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 25, 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 catalogs, 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 ∼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 27 (when there is a CatWISE counterpart), or the matching radius of the soft X-ray counterpart (when there is no CatWISE counterpart). ⁶⁴
• (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_Cat,best ≳ 0.1; note that NuSTARJ182353+0742.0 is a borderline case with p_Cat,best = 0.095 and p_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 crossmatched the CatWISE20 position to the aforementioned optical surveys using a 27 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.
• (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 27 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 ∼85% (1077/1274) to ∼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.

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Our selection process to identify the principal adopted optical counterpart is summarized in Figure 12. Not all Nway matches will be true counterpart associations since the crossmatching 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 crossmatching), 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_CAT/PS,best) for the “best” CatWISE20 (top panel) and Pan-STARRS (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 minimize 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_Cat,best > 0.4 and p_Cat,any > 0.5. The expected rate of false associations based on matching with randomized 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°. 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_PS,best > 0.4 and p_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. Of these 370 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 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, gray-edged crosses). Sources with Galactic latitudes ∣b∣ > 20° are plotted with circles, squares/diamonds, and stars for NSS80 sources with CSC2, 4XMM-DR10/s, and 2SXPS counterparts, respectively. The low-Galactic-latitude sources identified with Nway based solely on geometric information are shown with crosses.

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In Figure 15, we show histograms of the WISE (top panels) and optical (g,r and i; middle panels) magnitudes for the high-probability Nway-selected samples at high (green) and low (peach) Galactic latitudes, respectively. ⁶⁵ The median magnitudes of the low-Galactic-latitude sources are on average 1–2 mag brighter than the high-Galactic-latitude sources.

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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).

To maximize 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 preexisting spectroscopy are described in Section 3.3.3.

3.3.1. Dedicated Follow-up Campaign

3.3.2. Spectroscopic Observations and Data Reductions

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 Figure 6 in Hinton et al. (2016) for a visual display of the 12 (five stellar + six galaxy + one AGN) current templates available in Marz. ⁶⁹ 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 crossmatching the observed wavelength ratios of the identified lines to the rest-wavelength ratios based on the emission and absorption lines observed in AGNs. Sources with low-S/N spectra or dubious redshift measurements are flagged in the catalog.

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 Data Release 16, DR16; Ahumada et al. 2020; see Table 14 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, while 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.

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):

• 1.  
  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 ≥ 1000 km s⁻¹ (measured in iraf).
• 2.  
  Narrow-line object (NL) if the permitted lines are of similar width to the narrow forbidden lines.
• 3.  
  Galaxy (Gxy) if only absorption lines are detected.

Based on this simple classification scheme, we find that 58% (284/492) are BL AGNs, 39% (194/492) are NL objects, and 2% (10/492) are 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 AGNs 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°). The number of Galactic NuSTAR sources has increased by a factor of ∼3 from the NSS40 catalog 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 multiwavelength imaging of the NuSTAR-detected hotspot at a projected distance of ∼580 kpc from the quasar. Hence, in total there are 594 unique source entries in the NSS80 spectroscopic catalog given in Table 14.

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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 six sources with companions (i.e., in pairs with Δz < 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 shows 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 ∼15–160 kpc. These include the following:

• 1.  
  NuSTARJ054231+6054.4: a dual AGN system at z = 0.257, comprising a pair of likely merging, obscured AGNs (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 AGNs 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 (CT; N_H ≈ (1−2) × 10²⁴ cm⁻²).
• 2.  
  NuSTARJ091534+4054.6: a BL AGN pair at z = 1.298, comprising two closely associated quasars.
• 3.  
  NuSTARJ120530+1649.9: an AGN pair including a BL AGN (WISEAJ120530.63+164941.4; Ahn et al. 2012; Toba et al. 2014) and an 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).
• 4.  
  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 Baldwin, Phillips & Telervich (BPT) diagnostics. The NL AGN is detected in all three NuSTAR bands.
• 5.  
  NuSTARJ184552+8428.2: an AGN-Gxy pair at z = 0.233 comprising an 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_{3−8 keV} = 1.91 × 10⁴³ erg s⁻¹, indicating that it is indeed an X-ray AGN.

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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	L10−40keV	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 × 1044	0	NL AGN + NL AGN	4.7	19.1
NuSTARJ091534+4054.6	NGC_2785	F	1.298	6.41 × 1044	0	BL AGN + BL AGN	16.3	138.6
NuSTARJ120530+1649.9	IRAS12032p1707	S + H + F	0.216	2.37 × 1043	1	BL AGN + NL AGN	45.5	159.4
NuSTARJ022742+3331.5	CXOJ022727d5p333443	S + H + F	0.09	6.33 × 1042	0	NL AGN + NL	8.9	15.1
NuSTARJ184552+8428.2	1RXSJ184642d2p842506	S + H + F	0.233	4.92 × 1043	1	NL AGN + Gxy	8.1	30.3
NuSTARJ021454–6425.9	RBS0295	F	0.068	1.21 × 1042	1	Gxy + Gxy	22.2	29.04
NuSTARJ020614+6449.3	3C_58	F	⋯	⋯	⋯	Unknown	1.99	⋯

Notes. 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 Δ(cz) < 0.05 cz. (7): the type of sources for each pair: BL AGN refers to quasars, NL AGN to narrow-line AGNs (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.

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Table 8. NSS80 Sources that Show Evidence for Being Associated with the Primary NuSTAR Science Target according to the Definition Δ(cz) < 0.05 cz

Serendip Name	Serendip Type	zserendip	Primary Target	Primary Type	ztarget	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	IC 1623	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	SARS 059.33488–30.34397	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

Notes. 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).

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The galaxy pair (NuSTARJ021454–6425.9) is composed 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_{3−24 keV} = 1.52 × 10⁴² erg s⁻¹, which may be a spurious detection, considering also its low NuSTAR detection probability and lack of a lower-energy X-ray identification.

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 an NL galaxy (z = 0.137) 125 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 multiwavelength follow-up campaign.

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In addition to the 550 spectroscopically confirmed redshifts, we also obtained photometric redshifts from the literature for an additional seven NSS80 sources (from Salvato et al. 2009, Richards et al. 2009, Bilicki et al. 1996, and Masini et al. 2020), flagged as “quality C” redshift measurements in the catalog, and for which we append the optical classification with a “C.” We exclude these seven 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°). Further ongoing optical spectroscopic campaigns will increase the spectroscopic completeness of the NSS80 catalog, 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., Δ(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 Swift-BAT AGN Spectroscopic Survey (BASS) Data Release 2 sources (DR2; see Koss et al. 2022).

3.3.4. Comparison between Confirmed Spectroscopic and Nway-identified AGNs

A significant fraction of the optical spectroscopic follow-up program 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 clear identification of AGN signatures in the optical spectrum provides compelling evidence that the correct optical source was followed up, given the low probability of selecting a clear optical AGN by chance. Therefore, to provide easy access to the IR/optical counterpart information (i.e., magnitudes), we include binary flags in the catalog (“NWAY_CatWISE,” “NWAY_PS1”) indicating whether the spectroscopic target position matches to the Nway-identified CatWISE20 and PS1-DR2 counterparts. In total, 515/594 unique spectroscopic targets (Section 3.3.3) coincide with the CatWISE20 positions, and 388/594 with the Nway-identified PS1-DR2 positions.

To assist in the interpretation of our results in Section 4, we classify the spectroscopically classified sources as either reliable or uncertain (see “Cpart_RFlag” in Appendix A). The majority of the reliable sources will have positional offsets of < 5″, mostly assisted by the identification of lower-energy X-ray counterparts, while the majority of the uncertain sources will have larger positional offsets (see Appendix D). However, as our previous analysis was limited to using cataloged data it will not take into account potential anomalies such as the presence of nearby bright sources, close-separation systems, and image artifacts. We therefore supplemented our analyses with a visual inspection of all spectroscopically targeted NSS80 sources using the detailed optical finding charts; see Appendix E.1 for the post-NSS40 finding charts (and optical spectra) and Appendix E.2 for the NSS40 finding charts. ⁷⁰

Overall, on the basis of the combination of these analyses, we determined 91% (449/492) of the spectroscopically classified extragalactic sources to be reliable (274 BLs + 166 NLs); only 13/449 sources fail our high-probability cut defined in Section 3.2, mostly due to the lack of lower-energy X-ray or MIR information. The remaining 43 sources are flagged as uncertain (13 of which do not have any Nway matches satisfying our high-probability cut), either due to source confusion as a result of high source density, multiple potential counterpart associations, or shallow IR/optical coverage. Of the 58 spectroscopically classified Galactic objects, we identify 30 as reliable spectroscopic counterparts (28 of which satisfy the Nway high-probability cut) and flagged the other 28 as uncertain. We note that counterpart identification is more challenging in these cases (see, e.g., Tomsick et al. 2018). We use this reliable spectroscopic sample for our science analysis in Section 4, unless otherwise indicated.

In Figure 21, we show r-band magnitude distributions for the reliable optical NSS80 sources (i.e., those satisfying our Nway high-probability cut; light purple), overlaid with the NSS80 sources with reliable spectroscopic classifications (purple). Of the 958 high-probability counterparts, 721 sources have available constrained r-band magnitudes with a mean magnitude of 〈r_Nway〉 = 19.73. Of the 492 extragalactic NSS80 sources, 399 are flagged as reliable (based on our visual comparison between the Nway identified counterpart and the spectroscopic target) and have available constrained r-band magnitudes (excluding 19 sources with evidence for being associated with the NuSTAR targets for their respective observations): 261 BLs, 132 NLs, and six other sources (four galaxies and two unclassified), with average magnitudes of 〈r_BL〉 = 19.53, 〈r_NL〉 = 19.3, and 〈r_Other〉 = 16.58, respectively. Overall, our spectroscopic campaign is targetting the majority of the sources (in terms of r-band magnitude) but misses the faintest sources.

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4.1.1.  NuSTAR Source Counts, Count Rates, and Fluxes

Altogether, there are 1274 NSS80 sources with significant detections in at least one NuSTAR energy band—a factor of 3 improvement over that of NSS40 reported in L17. Similarly to other NuSTAR surveys (e.g., Civano et al. 2015; Mullaney et al. 2015; Lansbury et al. 2017b; Masini et al. 2020), 32% (412/1274) of the sample is detected in the 8–24 keV band, which is unique to NuSTAR among focusing X-ray observatories.

The basic properties of the NSS80 sources are given in Table 9. We find a large range (∼6–1700 ks) in the net exposure time per source for the combined telescopes FPMA+B (cleaned and vignetting corrected; t_net), with a median of ∼80 ks. For the sources with detections in the 3−8 keV, 8−24 keV, and 3−24 keV bands the lowest (deblended) net source counts (S_net) are 12, 11, and 19, respectively. The source with the highest S_net in all three energy bands is still NuSTAR J043727–4711.5, a BL AGN at z = 0.051, as reported in L17, with S_net values of 11,337, 6653, and 17,943 counts, respectively. The median S_net values in the respective bands are 62, 67, and 82, respectively. Finally, we find a range in the net count rates of 0.09–37.1, 0.07–44.3, and 0.12–72.2 ks⁻¹, and median values of 0.8, 0.8, and 1.04 ks⁻¹ for the soft-, hard-, and full-band energies, respectively.

Table 9. X-Ray Characteristics of the NSS80 Sources with Significant Detections in the Soft (3−8 keV), Hard (8−24 keV), and Full (3−24 keV) Bands, Respectively

NuSTAR Energy Band			〈tnet〉
	(ks)	(ks)	(ks)
3−8 keV	7.6	1657.4	79.8
8−24 keV	6.1	1617.9	76.4
3−24 keV	8.9	1656.4	78.3
	(counts)	(counts)	〈Snet〉 (counts)
3−8 keV	12 ± 7	11,337 ± 114	62 ± 45
8−24 keV	11 ± 5	6653 ± 88	67 ± 48
3−24 keV	19 ± 29	17,943 ± 143	82 ± 55
	CTRT (ks−1)	CTRT (ks−1)	〈CTRTnet〉 (ks−1)
3−8 keV	0.09 ± 0.04	37.1 ± 0.4	0.8 ± 0.5
8−24 keV	0.07 ± 0.03	44.3 ± 1.3	0.8 ± 0.6
3−24 keV	0.12 ± 0.05	72.2 ± 1.6	1.04 ± 0.7
	Flux (erg s−1 cm−2)	Flux (erg s−1 cm−2)	〈FluxX〉 (erg s−1 cm−2)
3−8 keV	(6.65 ± 2.68)× 10−15	(2.49 ± 0.025)× 10−12	(5.18 ± 3.56)× 10−14
8−24 keV	(9.93 ± 4.07)× 10−15	(6.15 ± 0.17)× 10−12	(11.31 ± 7.86)× 10−14
3−24 keV	(11.55 ± 4.43)× 10−15	(6.79 ± 0.15)× 10−12	(9.82 ± 6.83)× 10−14

Notes. The listed data include the minimum, maximum, and median values for the net exposure times (t_net; in kiloseconds), the net source counts (S_net counts), the net count rates (CTRT_net; ks⁻¹), and the X-ray fluxes. The median absolute deviation (MAD) is taken as the uncertainty on the median values.

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The flux distributions of detected and undetected NSS80 sources for a given band are shown in Figure 22 in comparison to the NSS40 flux distributions. The faintest fluxes are 6.65 and 9.93 × 10⁻¹⁵ erg s⁻¹ cm⁻² for detected sources in the 3−8 keV and 8−24 keV bands, respectively, and 1.15 × 10⁻¹⁴erg s⁻¹ cm⁻² for full-band source detections. The brightest fluxes in the NSS80 catalog correspond to two sources: NuSTARJ043727–4711.5, a BL AGN at z = 0.051, with a soft-band flux of 2.49 × 10⁻¹² erg s⁻¹ cm⁻², and NuSTARJ153602–5749.0, a Galactic source (z = 0), with hard- and full-band fluxes of 6.15 and 6.79 × 10⁻¹² erg s⁻¹ cm⁻², respectively. The source with the brightest flux in L17, NuSTARJ075800+3920.4 (BL AGN at z = 0.095) is recorded in our secondary NSS80 catalog, with soft-, hard-, and full-band fluxes of 3.50, 4.99, and 8.8 × 10⁻¹² erg s⁻¹ cm⁻²; the median fluxes in the NSS80 catalog are (5.18 ± 3.56), (11.31 ± 7.86), and (9.82 ± 6.83) ×10⁻¹⁴ erg s⁻¹ cm⁻², respectively. ⁷¹ The serendipitous survey pushes to fluxes ∼2 orders of magnitude fainter than those achieved by previous-generation hard X-ray observatories such as INTEGRAL (e.g., Malizia et al. 2012) and Swift-BAT (Oh et al. 2018); see Section 4.1.3.

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4.1.2. Band Ratios

In obscured objects, as optical depth increases with decreasing energy, relatively larger numbers of hard X-ray photons are detected in comparison to soft X-rays due to the preferential obscuration of lower-energy X-ray emission due to photoelectric absorption. With its capability of focusing high-energy photons, NuSTAR is well suited to categorize the obscured population of AGNs and to search for heavily obscured sources of up to CT (N_H ≳ 1.5 × 10²⁴ cm⁻²) levels of obscuration (e.g., Marchesi et al. 2018, 2019; Torres-Albà et al. 2021; Zhao et al. 2021a). The ratio in count rates between the hard and soft X-ray bands, defined as the band ratio, is indicative of the amount of intrinsic obscuration along the line of sight to the nucleus of an X-ray emitting source and can, therefore, be used as a basic estimate of the amount of obscuration to (crudely) identify CT sources from their extreme band ratios. This technique has been successfully demonstrated in several previous NuSTAR studies (e.g., Gandhi et al. 2014; Baloković et al. 2014; Lansbury et al. 2017a; Torres-Albà et al. 2021), and we use this definition in this work for consistency with the literature.

Figure 23 shows the 8−24 keV to 3−8 keV band ratios (BR_Nu) for the NSS80 sample as a function of the 3−24 keV (full-band) count rate (CTRT). ⁷² In order to examine the results for extragalactic sources only, we remove sources which are spectroscopically confirmed as having z = 0 and exclude sources with Galactic latitudes below ∣b∣ = 10°, for which there is significant contamination to the nonspectroscopically identified sample from Galactic sources. A large variation in BR_Nu is observed across the sample corresponding to spectral slopes (applying to a single absorbed power-law model with fixed Galactic N_H) ranging from Γ_eff ≈ 3 (at the softest values) to Γ_eff ≈ −0.5 (at the hardest values). To include weak and nondetections in the NSS80 catalog, we also calculate “stacked” medians in BR_Nu per count rate (in bins of 1 × 10⁻³ s⁻¹) by summing the net count rates of all NSS40 (blue-edged diamonds) and NSS80 (green-edged circles) sources. The results are consistent with a flat relation in the average band ratio versus count rate, and a constant average effective photon index of Γ_eff ≈ 1.5, suggesting at least modest amounts of obscuration on average within the sample (compared to Γ_eff ∼ 1.8 for typical unobscured sources; see, e.g., Ricci et al. 2017). Furthermore, we find no evidence of a relationship between band ratio and count rate in the higher-energy 3–24 keV band, as found by previous studies at <10 keV (e.g., Della Ceca et al. 1999; Mushotzky et al. 2000; Alexander et al. 2003). The absence of such a trend may partly be attributed to the fact that X-ray spectra of AGNs are less strongly affected by absorption in the high-energy NuSTAR band.

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When using the BR_Nu alone to identify obscured AGNs, additional knowledge of the source is required to estimate the absorbing column density (N_H), as key spectral features (e.g., the photoelectric absorption cutoff) are shifted across the observed energy band for sources at different redshifts. Therefore, potentially highly obscured AGNs can be identified using the BR_Nu values complemented by the source’s redshift information, as demonstrated in Lansbury et al. (2017a). The BR_Nu values as a function of redshift are plotted for the spectroscopically identified NSS80 sample in Figure 24. We plot tracks for a range of column densities (N_H = 10²³⁻²⁴ cm⁻²) to provide an estimate of the absorbing columns giving rise to the observed band ratios of the NSS80 sources. We find that the majority of extragalactic NSS80 sources (z > 0) have BR_Nu values in the range of 0.4–1.4, with a median of 0.8 ± 0.3, which breaks down into a median of 0.7 ± 0.2 for the BLs and a slightly higher value of 0.9 ± 0.2 for the NLs (as illustrated with the blue and green histograms, respectively). In comparison to the column density tracks, the majority of the extragalactic NSS80 serendipitous sources have N_H values of <3 × 10²³ cm⁻², with only a minority (14/82 BL and 13/55 NL constrained sources), predominantly at low redshift, with significantly higher absorbing column densities.

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We apply the same basic approach to that used in Lansbury et al. (2017a) to identify potentially heavily obscured sources, i.e., a BR_Nu > 1.7 cut (red dotted line in Figure 24), which corresponds to an effective (i.e., observed) photon index of Γ_eff ≲ 0.6 (motivated by observed CT AGNs in other NuSTAR programs; e.g., Baloković et al. 2014; Gandhi et al. 2014; Civano et al. 2015; Lansbury et al. 2015). The sample is limited to NSS80 sources with spectroscopic redshifts and constrained BR_Nu values (or lower limits). Based on this analysis, 22 sources stand out as CT candidates: 10 sources detected in all three NuSTAR bands, eight with hard- and full-band detections, and four only detected in the hard band. Of these, seven are reported in Lansbury et al. (2017a), increasing the number of NSS-selected candidate CT AGNs by a factor of ∼3; however, the eighth source in Lansbury et al. (2017a), NuSTAR J165346+3953.7, is undetected in the NSS80 catalog. Note that 3/22 sources show evidence for being associated with the primary NuSTAR science target based on Δ(cz) < 0.05 cz (see Table 8). The basic properties of these candidate CT AGNs are provided in Table 10. The majority (18/22) are spectroscopically classified as NL systems, consistent with expectations for obscured AGNs; the other systems are classified as either low-redshift galaxies or BL AGNs. We note that BR_Nu provides a crude estimate of the absorbing columns, and a more detailed investigation of the NuSTAR spectra and multiwavelength properties of the 15 newly identified CT candidates is required to strengthen the interpretation of these high-BR_Nu sources as highly absorbed systems and provide significantly improved constraints on the space density of CT AGNs (see, e.g., Yan et al. 2019). However, based on the X-ray spectral analysis presented in Lansbury et al. (2017a), we expect at least 50% of these candidates to be CT AGNs (i.e., at least four of the eight CT candidates). Importantly, three of these four systems would not have been identified as candidate CT AGNs without NuSTAR data.

Table 10. Candidate Obscured NSS80 AGNs with BR_Nu > 1.7

NuSTAR Object Name	Short Name	R.A.	Decl.	Det.	BRNu	zspec	Type	L10−40keV
		(deg)	(deg)					(erg s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
NuSTARJ010739–1139.1	J010739	16.914801	−11.65257	F S H	2.2 ± 0.5	0.048	NL	7.99 × 1042
NuSTARJ022951–0856.4	J022951	37.46319	−8.94133	F H	> 1.8	0.300	NL	1.63 × 1043
NuSTARJ035951–3009.9	J035951	59.96408	−30.16580	H	> 2.4	0.685	NL	2.85 × 1044
⋆NuSTARJ050559–2349.9	J050559	76.49839	−23.83168	F H	> 3.8	0.036	NL	8.97 × 1041
NuSTARJ082303–0502.7	J082303	125.76385	−5.04649	F H	> 2.0	0.313	NL	9.81 × 1043
NuSTARJ094910+0022.9	J094910	147.29356	0.38186	F H	> 3.7	0.093	NL	1.63 × 1042
NuSTARJ103456+3939.6	J103456	158.73575	39.66031	F S H	3.3 ± 0.6	0.151	NL	2.41 × 1043
NuSTARJ115658+5508.2	J115658	179.24379	55.13830	F H	> 3.3	0.080	NL	7.03 × 1042
NuSTARJ141056–4230.0	J141056	212.73727	−42.50139	F S H	1.9 ± 0.8	0.067	NL	2.48 × 1042
NuSTARJ144406+2506.3	J144406	221.02819	25.10514	F H	> 2.3	1.539	NL?	1.05 × 1045
NuSTARJ150225–4208.3	J150225	225.60725	−42.13960	F S H	5.4 ± 1.2	0.054	Gxy	6.18 × 1042
NuSTARJ150646+0346.2	J150646	226.69512	3.77105	F S H	3.6 ± 0.6	0.034	NL	1.37 × 1042
⋆NuSTARJ151253–8124.3	J151253	228.22496	−81.40501	F S H	1.8 ± 0.6	0.069	NL	9.26 × 1042
NuSTARJ153445+2331.5	J153445	233.68763	23.52592	H	> 3.5	0.160	NL	4.82 × 1042
NuSTARJ160817+1221.4	J160817	242.07274	12.35752	H	> 1.9	0.181	NL	1.34 × 1043
NuSTARJ163126+2357.0	J163126	247.85845	23.95061	F H	> 1.7	0.751	BL	3.97 × 1044
⋆NuSTARJ190813–3925.7	J190813	287.05529	−39.42912	H	> 3.1	0.075	Gxy	2.46 × 1042
NuSTARJ194234–1011.9	J194234	295.64177	−10.19846	F S H	3.2 ± 1.6	0.849	NL?	4.58 × 1044
NuSTARJ214320+4334.8	J214320	325.83368	43.58032	F S H	1.8 ± 0.2	0.013	NL	5.86 × 1041
NuSTARJ224225+2942.0	J224225	340.60580	29.70105	F S H	2.1 ± 0.7	0.304	BL	1.57 × 1043
NuSTARJ224925–1917.5	J224925	342.35456	−19.29294	F S H	1.7 ± 0.9	0.445	NL	3.32 × 1043
NuSTARJ231840–4223.0	J231840	349.66942	−42.38454	F H	> 1.9	0.464	NL	9.68 × 1043

Notes. The sources are listed in order of increasing R.A. The bold rows mark the extremely hard NSS40 sources reported in Lansbury et al. (2017a). Note that J150646 is now detected in all three bands, while in the 40 month catalog it was only detected in the hard band. Column (1): NuSTAR serendipitous source name. Asterisks indicate sources that show evidence for being associated with the primary NuSTAR science target according to the definition Δ(cz) < 0.05 cz; see Table 8. Column (2): abbreviated NuSTAR source name adopted here. Columns (3) and (4): NuSTAR R.A. and decl. J2000 coordinates in decimal degrees. Column (5): the NuSTAR energy bands for which the source is independently detected. F, S, and H correspond to the full (3−24 keV), soft (3−8 keV), and hard (8−24 keV) bands, respectively. Column (6): NuSTAR photometric band ratio. Column (7): source spectroscopic redshift obtained from emission-line fitting in iraf or 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 Section 3.3.3. All redshifts are robust, except for J144406 and J194234, where fewer lines (or low-S/N lines) are identified, and J050559, which has two candidate soft X-ray and WISE counterparts. Column (8): source spectroscopic classification. Column (9): non-absorption-corrected, rest-frame 10−40 keV luminosity.

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4.1.3. Redshift–Luminosity Plane

Overall, on the basis of our optical spectroscopic campaign (described in Section 3.3) we have classified 492 NSS80 sources as extragalactic, 449 of which have reliable counterpart identifications and 43 sources with uncertain counterpart associations based on our Nway assessment in Section 3.3.4 (which are indicated with white filled symbols in all figures). We exclude from our analysis the seven additional sources with photometric redshift measurements from the literature and those with reliable counterparts closely associated with the targets of the NuSTAR observations, leaving 433 sources.

The redshift distribution for the 433 extragalactic NSS80 sources with reliable counterpart associations is shown in Figure 25, excluding sources with evidence for being associated with the NuSTAR targets for their respective observations (see Table 8). The redshifts cover a large range, z = 0.012–3.43, with a median of 〈z〉 = 0.56. For the 166 extragalactic objects with independent detections in the high-energy band (8−24 keV), to which NuSTAR is uniquely sensitive, the median redshift is 〈z〉 = 0.34. Roughly comparable numbers of NL and BL objects are identified for z < 1 (132 and 147, respectively) but comparison of redshift distributions shows a significant difference, with a larger fraction of BL sources found at higher redshifts. This is supported by a larger median redshift for BL sources of 〈z〉 = 0.80. This result is not unexpected since BL AGNs at a given redshift are typically brighter in the optical band than NL AGNs of the same intrinsic luminosity (i.e., the BL AGNs are less obscured in the optical); see Figures 21 and 25.

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In Figure 26, we show the redshift–luminosity plane for the rest-frame 10−40 keV band, calculated from the observed-frame NuSTAR fluxes (following the same approach as in L17), assuming an effective photon index of Γ_eff = 1.8 (typical of AGNs detected by NuSTAR; see Alexander et al. 2013). ⁷³ For comparison, the BASS DR2 (Koss et al. 2022) is plotted with gray crosses. The Swift-BAT 14−150 keV fluxes were used to calculate L_{10−40 keV} values assuming an effective photon index of Γ_eff = 2.0 for the K-correction factor (using the median slope of 2). As can be seen, the NSS80 sources span the knee of the X-ray luminosity function out to z ≈ 1 (Aird et al. 2015), as opposed to z ≈ 0.1 for the Swift-BAT AGNs.

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Of the 433 extragalactic NSS80 sources with reliable counterpart associations, 99% (427/433) are within the luminosity range of L_{10−40 keV} ≈ 10⁴²−10⁴⁶ erg s⁻¹, with a median luminosity of 1.2 × 10⁴⁴ erg s⁻¹. These values are consistent with the NSS40 catalog. The faintest source in the L17 sample, however, with L_{10−40 keV} = 1.0 × 10³⁹ erg s⁻¹, is recorded in the secondary NSS80 catalog (see Section 2.3 and Appendix B), since the NL AGN at z = 0.002 is hosted by the galaxy IC750. Hence, the least luminous source in the primary NSS80 catalog is NuSTARJ010736–1732.3 (NL AGN at z = 0.021) with L_{10−40 keV} = 2.6 × 10⁴⁰ erg s⁻¹. As in L17, the source at the other extreme end in luminosity is NuSTARJ052531–4557.8, a radio-bright BL AGN at z = 1.479 with L_{10−40 keV} = 8.8 × 10⁴⁵ erg s⁻¹, also classified as a blazar in the literature (e.g., Massaro et al. 2009), which means that the X-ray luminosity may be inflated by beaming effects. The most distant source detected is still the optically unobscured quasar NuSTARJ232728+0849.3, at z = 3.43, reported in the NSS40 catalog.

We also compare to the luminosity–redshift plane of BASS, as shown in Figure 26. The Swift-BAT and NuSTAR serendipitous survey are complementary to one another, with the former providing a statistical sample of AGNs in the nearby Universe (z < 0.1) selected in hard X-rays, and the latter providing its counterpart for the distant Universe. Consequently, there is little overlap between the two surveys, which sample different regions of the L_x – z parameter space, with the exception of four NuSTAR sources outlying in Figure 26 which have very high fluxes at the detection threshold of Swift-BAT (all BASS detected):

• 1.  
  NuSTARJ043727–4711.5: a BL AGN at z = 0.051; L_{10−40 keV} = 2.5 × 10⁴³ erg s⁻¹.
• 2.  
  NuSTARJ091912+5527.8: an NL AGN at z = 0.049; L_{10−40 keV} = 2.0 × 10⁴³ erg s⁻¹.
• 3.  
  NuSTARJ103135–4206.0: an NL AGN at z = 0.061; L_{10−40 keV} = 2.2 × 10⁴³ erg s⁻¹.
• 4.  
  NuSTARJ180958–4552.6: a (beamed) BL AGN at z = 0.07; L_{10−40 keV} = 2.8 × 10⁴³ erg s⁻¹.

Overall, the NuSTAR serendipitous survey provides the higher-redshift component of Swift-BAT and fills out the broadest range of luminosities and redshifts in comparison to other NuSTAR surveys, e.g., the NuSTAR-ECDFS survey (Mullaney et al. 2015), NuSTAR-COSMOS survey (Civano et al. 2015), and NuSTAR-UDS (Masini et al. 2018).

In the following sections, we further explore the optical and MIR properties of the extragalactic NSS80 sources.

The MIR emission from AGNs is typically due to the reprocessing of accretion-disk radiation by circumnuclear dust, and suffers little extinction relative to other wavelengths (e.g., Nishiyama et al. 2008; Netzer 2015; Hickox & Alexander 2018); however, a nonnegligible fraction can also be produced by star formation in the host galaxy (e.g., Stern et al. 2005; Hickox & Alexander 2018). Color selections using the WISE telescope bands (3.4, 4.6, 12, and 22 μm; e.g., Assef et al. 2010; Jarrett et al. 2011; Stern et al. 2012; Mateos et al. 2012, 2013; Assef et al. 2013) can separate bright AGNs from host-galaxy light (from stars and the interstellar medium) through the identification of a red MIR spectral slope, and have thus become widely applied. These selections have the potential to identify large samples of AGNs with less bias against heavily obscured systems. However, their effectiveness worsens toward lower AGN luminosities, where the AGN component of the MIR spectrum can be swamped by the emission from the host galaxy. For example, Cardamone et al. (2008) and LaMassa et al. (2019) found that most X-ray-selected AGNs in the (deep) GOODS field and Stripe 82X, respectively, would not have been found by standard MIR color selection. Lyu et al. (2022) show similar results for spectral-energy-distribution (SED)-selected AGNs in the GOODS-S/HUDF region. Notably, the MIR host emission contribution increases with redshift due to the increase in cosmic star formation rate density, too, thus it is progressively harder to select AGNs at the same luminosity at higher redshifts. By comparison, NuSTAR selects AGNs almost irrespective of the relative strength of the AGN to the host galaxy since the X-ray emission from galaxy processes is weak in comparison to the AGN, particularly at the 3−24 keV energies probed by NuSTAR. Here we investigate the MIR properties of our NSS80 sources, and consider the results with respect to the AGN selection criteria.

As CatWISE20 contains only W1 and W2 photometry, for the purposes of examining the further properties of the sample we match all sources with an Nway CatWISE20 counterpart to their nearest AllWISE (Wright et al. 2010; Mainzer et al. 2011) source within a maximum radius of 4 ⁷⁴ This results in 865 matches, including 312/523 upper limits for W3/W4, respectively. W1 and W2 magnitudes are roughly consistent between CatWISE20 and AllWISE values except in a small minority of sources, implying that the W3 and W4 can be used for comparison with the caveat that there may be additional uncertainty due to the different photometric pipelines. In Figure 27, we plot the WISE colors (W1 − W2 versus W2 − W3) of the spectroscopically confirmed extragalactic NSS80 sample with reliable counterpart associations and W3 detections, i.e., well-defined WISE colors (see Section 3.2), and compare to the selection “wedge” defined by Mateos et al. (2012) to identify AGNs with red MIR power-law SEDs. In this comparison, we further limit our analysis to the sources with significant detections in all three of the relevant, shorter-wavelength WISE bands (W1, W2, and W3; centered at 3.4 μm, 4.6 μm, and 12 μm, respectively). Considering sources with optical spectroscopic classifications, the fractions for the overall BL AGN (top panel) and NL AGN (bottom panel) samples are = 80% (148/185) and = 42% (36/86), respectively. Therefore, NL AGNs are less likely to be identified as AGNs based on MIR colors alone. If we use the “X-ray quasar” threshold of 10⁴⁴ erg s⁻¹ in the 10−40 keV band to distinguish between faint and luminous X-ray BLs/NLs, we find that this is largely driven by the lower-luminosity objects with L_X below the X-ray quasar threshold: only 35% (23/66) low L_X lie inside the wedge, while 80% (16/20) of the high-L_X NL AGNs have AGN-like MIR colors. ⁷⁵ On the other hand, the bulk of the BL AGNs with L_X > 10⁴⁴ erg s⁻¹ lie within the wedge (95%; 117/123 high L_X). Of the L_X < 10⁴⁴ erg s⁻¹ BL AGNs, 65% (40/62) have AGN-like MIR colors.

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If we subdivide the BL AGN sample on the basis of their g − i optical color (selecting the reddest 10%, as in Klindt et al. 2019; see Section 4.3 and Figure 29), we find a lower fraction of red BL AGNs (Nu-rQSOs) lie within the wedge than found for the control BL AGNs (Nu-cQSOs): 67% (49/73) versus 98% (101/103). Of the 49 Nu-rQSOs with AGN-like MIR colors, 33 sources have L_X > 10⁴⁴ erg s⁻¹ (85% of the overall high-L_X Nu-rQSOs) and the remaining 16 have L_X values below the X-ray quasar threshold (47% of the overall low-L_X Nu-rQSOs). Hence, we can deduce from the MIR colors that the majority of Nu-rQSOs (especially at low L_X) are more host-galaxy dominated than the Nu-cQSOs. This is broadly consistent with our finding on the basis of optical analyses in the following section.

Optical selection of quasars, using for example SDSS photometry, will miss the most reddened quasars due to their colors overlapping the stellar loci in most SDSS color–color diagrams, and a comparatively shallow optical survey flux limit (e.g., Richards et al. 2003). However, since X-rays penetrate circumnuclear obscuration with minimal contribution from the host galaxy, they provide the potential to construct a more complete census of the full quasar population, ranging from heavily obscured sources (e.g., extremely red quasars, ERQs; Goulding et al. 2018), thinly veiled red quasars (e.g., rQSOs; Klindt et al. 2019, hereafter K19), and host-galaxy-dominated systems. Here we focus on the optical photometric and spectroscopic properties of the NSS80 sources subdivided on the basis of X-ray luminosity and optical spectroscopic classification.

The NSS80 is the largest-area NuSTAR survey and picks up the most X-ray-luminous AGNs over ∼36 deg². However, the NSS80 region is a factor ∼300× smaller than the SDSS and consequently will miss the most luminous systems. To place the NSS80 survey into context, and to further motivate our following analyses that make use of SDSS Data Release 7 (DR7) quasars, in Figure 28 we compare the bolometric luminosity–redshift plane of both surveys. For the NSS80 sources, we calculate bolometric luminosities from the rest-frame 10−40 keV luminosity, assuming that the 10−40 keV luminosity makes up 4% of the total luminosity (see, e.g., Lansbury et al. 2017a). The SDSS bolometric luminosities are available in Shen et al. (2011); however, they are inferred from rest-frame UV-optical continuum measurements and have not been corrected for dust extinction. Consequently, the L_bol values are likely to be significantly underestimated in the SDSS rQSOs (which makes up 10% or more of typical quasar samples; see, e.g., Richards et al. 2003). Overall, there is good overlap between NSS80 and SDSS at the lower-luminosity end, although, as expected, NSS80 misses the most luminous systems. The median L_bol for the extragalactic NSS80 sample is 7.62 × 10⁴⁴ erg s⁻¹ at the median redshift of the NLs (〈z_NL〉 = 0.30), and 5.93 × 10⁴⁵ erg s⁻¹ at the BL median redshift (〈z_BL〉 = 0.80). By comparison, the SDSS sample has median bolometric luminosities of 1.73 × 10⁴⁵ erg s⁻¹ (0.38 dex higher) and 1.07 × 10⁴⁶ erg s⁻¹ (0.26 dex higher) at redshifts equal to 〈z_NL〉 and 〈z_BL〉, respectively.

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To provide a basic characterization of the optical properties of the extragalactic NSS80 sources with reliable optical counterpart associations, in Figure 29 we show the g − i color versus redshift of the 371 extragalactic sources with constrained g − i colors and compare to the SDSS DR7 uniformly selected quasar sample and the rQSOs identified in K19; we note that the optical colors are corrected for Galactic extinction following K19. For quasar-dominated systems, g − i color provides a basic measurement of the amount of optical reddening due to dust (e.g., Fawcett et al. 2020), although emission from the host galaxy can have a significant impact on the optical colors for lower-luminosity and/or heavily obscured AGNs. At a given redshift, a range in g − i color is observed for the BLs and NLs. ⁷⁶

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We use the g − i color threshold from K19 to identify red quasars (corresponding to the 10% most reddened in SDSS; threshold is shown as the bottom edge of rQSOs in Figure 29), finding that 42% (106/251) of the NSS80 BL AGNs with reliable counterpart associations and detections in the g and i bands have red g − i colors (we coin these sources as Nu-rQSOs); we note that in this basic comparison, we reasonably assume no significant differences in the g-band and i-band passbands between the various different optical photometric surveys. ⁷⁷ Among these is the higher-redshift AGN pair (NuSTARJ091534+4054.6) at z = 1.298, with both BL AGNs identified as red quasars based on their g − i color. The remaining 145/251 BLs we use as a control sample which represents “normal” unobscured quasars (Nu-cQSOs). Of the 114 NLs with reliable counterpart associations and constrained g and i magnitudes, 105 are found to lie within the rQSO g − i region, meaning that 92% of the NLs appear red in their optical colors. Since no clear broad emission lines are seen in these sources, we expect the optical emission to be dominated by the host galaxy, a result also suggested from the optical spectroscopy (see Section 4.4). As the Nu-rQSOs have identified broad emission lines, to first order we would expect the optical colors to be typically due to dust reddening. Overall, the g − i optical color threshold adopted in Figure 29 corresponds to 10% of the SDSS quasars in K19, while 42% of the NuSTAR BL AGNs exceed this threshold. This larger fraction of rQSOs in NSS80 compared to the SDSS could be due to a greater contribution from dust-reddened quasars; however, since SDSS probes more luminous quasars than NSS80, we should keep in mind that a larger fraction could be optically red due to emission from the host galaxy. A combination of template fitting to the UV–MIR photometry, guided by the optical spectroscopic features (e.g., continuum shape, emission, and absorption lines) would be able to constrain the relative contributions to the reddening from the host galaxy and dust extinction, but is beyond the scope of the current study.

To provide more direct constraints on the origin of the optical colors of the NSS80 sources, we utilize the spectroscopic data. In this analysis, we construct composite spectra for subsets of the NSS80 spectroscopic sample, divided on the basis of spectral type, optical color, and X-ray luminosity. These composite spectra allow us to search for subtle signatures missed in individual source spectra, such as the absorption features from the host galaxy (e.g., rest-frame Ca ii H+K, G band, Mg i, and Na i-d). The overall continuum shape of the spectra can provide insights on the relative contributions from dust reddening and host-galaxy emission/absorption: in comparison to typical quasars, a drop in continuum flux at blue wavelengths can indicate reddening due to dust, whereas an increase in flux at longer wavelengths can indicate reddening due to host-galaxy contamination.

In Figure 30, we show rest-frame composite spectra for the extragalactic NSS80 sources subdivided into 274 BLs (dark blue solid line; top panel) and 166 NLs (green solid line; middle panel). We compare these composites to the high-quality X-Shooter composite spectra of a subsample of the K19 rQSOs at 1.45 < z < 1.65, which are luminosity matched in rest-frame 6 μm luminosity and redshift to the K19 control quasars (cQSOs). The X-Shooter composite spectra are produced in Fawcett et al. (2022) using geometric mean stacks, and have a continuous spectral coverage from ∼3000−25000 Å. To stack the NSS80 spectra, we followed the same approach as Fawcett et al. (2022): the spectra were first corrected for Galactic extinction, using the Schlegel et al. (1998) map and the Fitzpatrick (1999) Milky Way extinction law, and shifted to rest-frame wavelengths. Each spectrum was then rebinned to a common wavelength grid and normalized at 4000 Å. It is worth noting that the spectra contributing to these stacks were obtained via different instruments and therefore will have different spectral resolutions. Therefore, any interpretation should be mainly limited to the spectral shape, with analysis of emission or absorption lines limited to broad comparisons. To ensure reasonably representative composite spectra, we only include data when at least 15 sources contribute at a given rest-frame wavelength. The scatter within each stack subset varies, e.g., the cQSOs have a lower scatter than rQSOs due to the nature of their populations. However, the scatter is not large enough in any subset to make the comparison of their average properties invalid.

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The BL composite (dark blue) shows strikingly similar permitted lines to the SDSS quasar X-Shooter composites. However, the NuSTAR composite has stronger forbidden lines (e.g., [Ne v], [O ii], and [Ne iii]) and has a different overall continuum shape with a sharper decrease to UV-blue wavelengths and a rise to red wavelengths. These differences are consistent with that expected by a modest host-galaxy contribution not present in the more luminous SDSS quasars with a light screen of dust reddening suppressing the UV-blue emission. The NL composite (green) is distinctly different from the cQSO and rQSO SDSS composites, with weak UV-blue emission and strong red emission. It shows a continuum shape more consistent with a composite of Type-2 SDSS quasars (purple; Yuan et al. 2016). Furthermore, numerous strong forbidden lines, including [Ne v], [O ii], [Ne iii], [O iii], [O i], and [S ii], and narrow permitted lines are evident. The strong [Ne v] and [O iii], in particular, indicate the presence of an optical NL AGN. The spectral shape of the NL composite is consistent with that expected for a host-galaxy-dominated spectrum due to the AGN emission being completely obscured in the optical waveband, as expected given the lack of broad permitted lines. Direct evidence for a dominant host-galaxy component is vividly seen from the strong host-galaxy absorption features, i.e., Ca ii H+K, G band, Mg i, and Na i-d. Further differences are seen in the BL composite when we split it into Nu-rQSOs (peach) and Nu-cQSOs (light blue); see Figure 29. Both the Nu-rQSOs and Nu-cQSOs show evidence for modest dust reddening due to suppressed UV-blue emission: The weaker shorter-wavelength broad lines relative to Hα (Hβ, Mg ii, and C iii]) for the Nu-rQSOs suggest greater dust reddening than that seen in the Nu-cQSOs. These characteristics are qualitatively consistent with those seen in the SDSS X-Shooter composites. However, in stark constrast to the X-Shooter composites, the Nu-rQSOs and Nu-cQSOs show a rise in the continuum emission to red wavelengths, which is most prominent in the Nu-rQSOs, likely due to an increasing contribution from the host galaxy.

Given the evidence for host-galaxy contributions to the NSS80 composites and the lower overall bolometric luminosties of the NSS80 sources in comparison to the SDSS quasars, we subdivided the NSS80 AGNs according to their luminosities using the quasar X-ray threshold of L_{10−40 keV} = 10⁴⁴ erg s⁻¹. Figure 31 shows the composites for the NL systems, Nu-cQSOs, and Nu-rQSOs split into low-L_X (L_{10−40 keV} < 10⁴⁴ erg s⁻¹) and high-L_X (L_{10−40 keV} > 10⁴⁴ erg s⁻¹) subsamples, with 3300–5300 Å zoom ins plotted in Figure 32 to emphasize the prominent AGNs and any host-galaxy absorption features. The rest-wavelength coverage for each composite is now more limited since the X-ray luminosity selection corresponds broadly to a redshift selection and hence effectively narrower redshift ranges than the overall composites in Figure 30. Despite this limitation, some similarities and differences are apparent across each of the composite pairs. Overall, the low-L_X and high-L_X systems within each spectral class have similar emission-line features and UV-blue continuum shapes. However, the low-L_X systems all have increased emission at red wavelengths in comparison to the high-L_X systems, consistent with a relative increase in the host-galaxy contribution for a decrease in the luminosity of the AGN. This result is qualitatively similar to that seen in the WISE MIR color analyses (see Figure 27 and Section 4.2). As for the overall composites, more direct evidence for a host-galaxy component is seen from the identification of strong host-galaxy absorption, most strikingly in the low-L_X NL systems, but also evident from the sometimes weak identification of Ca ii H + K in all of the composites. Greater insight on the host-galaxy and AGN properties, including constraints on the stellar mass and populations, can be gained from detailed fitting of the composite spectra and SEDs using AGN and stellar population models. However, that goes beyond the scope of this study.

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In K19, we showed that the red optical colors of SDSS rQSOs are predominantly due to reddening of a normal blue quasar, results which have been subsequently confirmed via detailed broadband UV-FIR SED fitting (Calistro Rivera et al. 2021) and broadband UV-near-IR spectral analysis (Fawcett et al. 2022). It is worth bearing in mind that these thinly veiled, dust-obscured optical quasars may represent the detectable end of a more heavily extinguished luminous AGN population which will be missed by SDSS because of their colors (e.g., Glikman et al. 2004; Banerji et al. 2012; Eisenhardt et al. 2012; Ross et al. 2015; Hamann et al. 2017; see Table 2.1 in Klindt 2022 for a summary of dust-reddened quasars). By comparison, our analyses of the Nu-rQSOs have shown that a substantial contribution of the red optical emission is due to a host-galaxy component rather than dust reddening of the quasar in the lower-luminosity objects. On the other hand, dust obscuration (which dominates the shape at the blue end of the spectrum) plays a key role in the excess red colors for the more luminous BL objects. Hence, it is important to keep in mind the differences in the typical luminosities between the SDSS quasars and the NSS80 sources (see Figure 28). Indeed, in their broadband SED fitting of SDSS quasars, Calistro Rivera et al. (2021) found that the host galaxy is likely to dominate in the lower-luminosity rQSOs (and to make a significant contribution in cQSOs), corresponding broadly to the luminosities of the NSS80 sources (see Figure 5 of Calistro Rivera et al. 2021). Consequently, caution must be applied when adopting a simple g − i optical color cut for lower-luminosity quasars and AGNs.

Here we provide details of the optical spectroscopic properties of individual sources from the NuSTAR serendipitous survey. As described in Section 3.3.1, these largely result from our dedicated follow-up campaign using the Keck, Palomar, VLT, and SALT facilities, and also from existing publicly available spectroscopy (primarily SDSS spectroscopy).

Details for individual sources are tabulated in Table 14, the columns of which are as follows:

• (1)  
  Unique NuSTAR source identification number, in order of increasing R.A.
• (2)  
  Unique NuSTAR source name as listed in source catalog.
• (3)  
  The unique observing run identification number, as defined in Table 6 (“S” and “Lit” mark spectra obtained from the SDSS and from elsewhere in the literature, respectively).
• (4)  
  Source redshift (mainly from spectroscopic data).
• (5)  
  Source classification as described in Section 3.3.3 (sources with photometric redshift measurements are appended with a “C” symbol and sources with a level of ambiguity in the optical classification are appended with a ”?” symbol).
• (6)  
  Quality flag of spectroscopic redshift. Single-line measurements are annotated with “B” and photometric redshift measurements with “C”; “F” annotates sources which lack a reliable redshift measurement (usually faint, red continuum spectra).
• (7)  
  Nway association flag: 0 = mismatch between spectroscopic target and Nway source; 1 = match between spectroscopic target and Nway source; –99 = secondary post-NSS40 objects.
• (8)  
  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 Δ(cz) < 0.05 cz.
• (9)  
  An abbreviated flag indicating a Nway CatWISE20 (“C”) and/or PS1-DR2 (“P”) counterpart match to the spectroscopic target.
• (10)  
  Notes based on our visual assessment of the spectra.