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

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

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

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For each of the 12 cycle 6 observations, summed FPMA+B mosaics were created in five energy bands: 3–24, 3–8, 8–24, 8–16, and 16–24 keV. The five bands were separated using the HEASoft Xselect tool. Each band was then merged into a full-exposure mosaic using the Ximage tool. Loss of spatial resolution due to the resampling is negligible because the pixel angular resolution (245) of the standard NuSTAR sky binning by NuSTARDAS is much smaller than the ∼18'' FWHM of NuSTAR. The cycle 6 mosaic was also merged with the cycle 5 mosaic to achieve the deepest sensitivity. The astrometric offsets of the NuSTAR NEP-TDF survey could not be measured reliably due to the limited number of bright sources in the field, but the previous NuSTAR COSMOS survey (Civano et al. 2015) found a NuSTAR astrometric offset of 1''–7'', small compared to the NuSTAR FWHM. Therefore, astrometric offsets should only marginally affect our results (Civano et al. 2015), and we did not apply any astrometric correction when merging the observations. (In any case, there is only one bright source in the field of view, FoV, that could have been used for astrometric correction.) Figure 2 shows the 3–24 keV FPMA+B merged mosaics.

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The background map was used for both source detection and simulation. The background of NuSTAR is spatially nonuniform across the FoV and variable among different observations, adding complexities when producing the background maps. We used the nuskybgd ³⁰ package (Wik et al. 2014), which was used for all previous NuSTAR extragalactic surveys, to produce background maps of each cycle 6 observation following the same method as Z21. We merged the cycle 6 background maps into an FPMA+B mosaic, which was then merged with the cycle 5 mosaic into a cycles 5+6 mosaic.

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

We generated simulated observations in the five energy bands following Z21's procedure. To summarize, each iteration randomly places mock sources on the background maps described in Section 2.4. The fluxes of the mock sources were randomly assigned following the X-ray source flux distribution ($\mathrm{log}N$–$\mathrm{log}S$) measured by Treister et al. (2009). The minimum fluxes in the 3–24 keV bands were 3 × 10⁻¹⁵ erg cm⁻² s⁻¹ for cycle 6 and 2 × 10⁻¹⁵ erg cm⁻² s⁻¹ for cycles 5+6, about 10 times fainter than the expected limits of each survey. Adopting a much fainter flux limit than the sensitivity of the survey would result in many mismatched measured and input sources and produce an incorrect reliability curve of source detection. The fluxes of the input sources in each energy band were extrapolated from their 3–24 keV fluxes assuming an absorbed power-law model with photon index Γ = 1.80 and Galactic absorption N_H = 3.4 × 10²⁰ cm⁻² (HI4PI Collaboration et al. 2016). The fluxes were converted to count rates using conversion factors (CFs) of 4.86, 3.39, 7.08, 5.17, and 16.2 × 10⁻¹¹ erg cm⁻² count⁻¹ in the 3–24, 3–8, 8–24, 8–16, and 16–24 keV bands, respectively. The CF was computed using WebPIMMS ³¹ assuming the above spectral model. The simulated observations of each exposure were then merged into mosaics in five energy bands for both FPMA and FPMB, which were then combined into FPMA+B mosaics. We used 1200 simulations for the NuSTAR NEP-TDF cycle 6 survey and 2400 for the combined cycles 5+6 survey.

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

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

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

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

$$\begin{eqnarray}&&\mathrm{Rel}(\mathrm{DET}\_\mathrm{ML})=\frac{{N}_{\mathrm{matched}}(\geqslant \mathrm{DET}\_\mathrm{ML})}{{N}_{\mathrm{detected}}(\geqslant \mathrm{DET}\_\mathrm{ML})}.\end{eqnarray} \tag{ 1 }$$

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

$$\begin{eqnarray}\mathrm{Completeness}\ (\mathrm{flux})=\displaystyle \frac{{N}_{\mathrm{matched}\&\geqslant \mathrm{Rel}\_(\mathrm{flux})}}{{N}_{\mathrm{input}(\mathrm{flux})}}.\end{eqnarray} \tag{ 2 }$$

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

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

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

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

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The simulations described in Section 3.1 can quantify the positional uncertainties of the sources detected. Figure 7 shows the separations between the detected and input-catalog positions in the cycles 5+6 survey simulations as an example. The separation histograms follow a Rayleigh distribution (Pineau et al. 2017). The best-fit Rayleigh scale parameters for all matched sources are σ_all,C6 = 95 and σ_all,C56 = 92 for the cycle 6 and cycles 5+6 surveys, respectively. Eliminating the faintest sources by limiting the sample to sources detected above the 95% reliability level gives smaller separations of σ_95%,C6 = 66 and σ_95%,C56 = 65. The separations are even smaller for sources with 3–24 keV flux >10⁻¹³ erg cm⁻² s⁻¹, σ_{95%,bright,C6} = 38 and σ_{95%,bright,C56} = 37. The measured separations are consistent with the previous cycle 5 survey and other NuSTAR extragalactic surveys; therefore, we used these distributions as the expected positional uncertainty of real detections. The simulations did not include the astrometric offsets; therefore, they do not reflect the full positional uncertainty, but the effect is likely minimal.

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The fluxes of the simulated sources detected in each energy band were measured and compared with the input fluxes to quantify the accuracy of the flux measurement technique. We extracted the source counts and deblended background counts of each matched source using the CIAO (Fruscione et al. 2006) tool dmextract. The effective exposure of each source was measured from the exposure maps (Section 2.2). The net counts were then converted to in-band fluxes using the CF (Section 3.1). The counts were extracted in a 20'' circular region, and we converted this aperture flux to total flux using an aperture correction factor of F(20'')/F_tot = 0.32, as calculated from the NuSTAR PSF. ³² Figure 8 shows the ratio of measured to input 3–24 keV fluxes. Flux measurements for faint sources are overestimated, as expected from Eddington bias, which favors the detection of faint sources with positive noise deflections. This excess corresponds to the detection limits of the survey and is also exposure-dependent (Figure 4). Therefore, the fluxes of the fainter sources can be better measured with deeper exposures.

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Z21 found an underestimate of the measured fluxes for bright (F₃₋₂₄ > 10⁻¹² erg cm⁻² s⁻¹) sources. This was due to a computing error when generating false-probability maps where the false probability in the center pixel of the bright sources was saturated. The bug led to an incorrect measurement of the source position and therefore underestimated its flux. This error did not affect the flux measurement of the real observations in the NEP-TDF because all detected sources are much fainter than 10⁻¹² erg cm⁻² s⁻¹. The error is fixed in this work.

The XMM-Newton data were reduced following Brunner et al. (2008), Cappelluti et al. (2009), LaMassa et al. (2016), and Z21. Details of the XMM-Newton Science Analysis System (SAS) packages are described in the XMM-Newton data analysis threads. ³³ The observational data files of MOS1, MOS2, and pn were generated using the SAS version 20.0.0 tasks emproc and epproc. High-background time intervals of the three instruments were excluded using >10 keV count-rate thresholds of 0.2 and 0.3 counts s⁻¹ for MOS and pn, respectively. We also excluded data in energy bands that might be contaminated by fluorescent emission lines, i.e., the Al Kα line at 1.48 keV in both MOS and pn and two Cu lines at ∼7.4 and 8.0 keV in pn only. The specific energy intervals removed were 1.45–1.54 keV in both MOS and pn data and 7.2–7.6 and 7.8–8.2 keV in pn. We then used the clean event files to generate the images of MOS1, MOS2, and pn in the 0.5–2 and 2–10 keV bands.

To generate exposure maps, we used the SAS task eexpmap. The maps were weighted by each instrument's energy conversion factor (ECF), which converts count rate to flux. ECFs were calculated using WebPIMMs assuming an absorbed power-law model with Γ = 1.80 and Galactic column density N_H = 3.4 × 10²⁰ cm⁻², as for the NuSTAR observations (Section 3.1). The ECFs used for MOS and pn are 0.54 and 0.15 × 10⁻¹¹ erg cm⁻² count⁻¹ in the 0.5–2 keV band and 2.22 and 0.85 × 10⁻¹¹ erg cm⁻² count⁻¹ in the 2–10 keV band, respectively.

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

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

Before merging the three epochs of observations into mosaics to maximize the sensitivity of the survey, we estimated the astrometric offsets of the three observations. The astrometric offset of an XMM-Newton observation is typically less than 3'' and on average is 10–15 (e.g., Cappelluti et al. 2007; Ni et al. 2021). To determine the astrometric offset of our three epochs, we matched >6σ (mlmin > 20) XMM-Newton sources to optical sources from the Sloan Digital Sky Survey (SDSS) DR16. ³⁴ Only Type=Star sources were used, and the matching radius was 45. XMM-Newton epochs 1, 2, and 4 had 13, 22, and 15 matched SDSS counterparts, respectively. The median offsets in R.A. and decl. are (Δα, Δδ) = (397, 095) for epoch 1, (088, 113) for epoch 2, and (006, 146) for epoch 4. We applied these offsets to the event and attitude files in each observation and remade the images, background maps, and exposure maps with the corrected files.

To test the astrometric corrections, we performed the source detection again and measured the offsets of the same sources from their optical counterparts. The average XMM-Newton to SDSS separations were reduced by 30% for epoch 1, 45% for epoch 2, and 41% for epoch 4 after the astrometric correction. Furthermore, the median XMM-Newton offsets among different epochs decreased by 84%–96%, suggesting that the three epochs became better aligned. The resulting images, background maps, and exposure maps of the three epochs were then merged into mosaics. The new images have more high-count pixels than the old images, again suggesting that the alignment is better corrected. The new average X-ray-to-optical offset is 122, and we take this to be the systematic position uncertainty of the XMM-Newton NEP-TDF survey.

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

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

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We cross-matched the XMM-Newton sources with the 60 sources detected in the NuSTAR cycles 5+6 survey using a simple position match. The match radius was the 20'' NuSTAR position uncertainty combined in quadrature with the position uncertainty of individual XMM-Newton sources (σ_XMM from the emldetect best-fit results) and the 122 XMM-Newton systematic uncertainty. The 20'' NuSTAR uncertainty is 3 times the best-fit Rayleigh scale parameter (σ_95%,C56 = 65) of the simulated position errors (Section 3.5). In all, 36 NuSTAR sources match at least one XMM-Newton counterpart. Thirty of these have a single XMM-Newton counterpart, and six (ID 11/13/23/31/41/46) have two XMM-Newton counterparts within the search radius. In all six cases, one of the XMM-Newton sources is both brighter and closer to the NuSTAR position than the other, and we took this to be the primary counterpart. One NuSTAR source (ID 51) has two XMM-Newton sources (ID 134/181) just outside the search radius (228 and 233, respectively). The two are in opposite directions and were both detected in the 2–10 keV band with similar flux F(2–10 keV) ∼ 9 × 10⁻¹⁵ erg cm⁻² s⁻¹. This looks like a case of source confusion where both XMM-Newton sources contribute to the NuSTAR detection.

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

For comparison between NuSTAR and XMM-Newton, the XMM-Newton 2–10 keV fluxes were converted to 3–8 keV assuming an absorbed power-law intrinsic spectral energy distribution with photon index Γ = 1.80 and Galactic absorption N_H = 3.4 × 10²⁰ cm⁻². This gives a CF of 0.62, and Figure 13 shows the comparison. Most sources have comparable fluxes measured by the two observatories. The tendency for NuSTAR fluxes to be higher than XMM-Newton fluxes at the faint end is due to the Eddington bias, as demonstrated by Figure 8. Other offsets could arise from variability in the last 3 yr or different spectral shapes of the sources than assumed for converting the XMM-Newton fluxes to the NuSTAR energy band.

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

The SDSS catalog covers the entire field, and data were downloaded from the public database. ³⁵ The HSC images were reduced by S. Kikuta, and the HSC NEP-TDF catalog was generated by C. N. A. Willmer (Willmer et al. 2023). Sources with m_i < 17.5 are saturated in the HSC observations, and we replaced their magnitudes with the magnitudes in the SDSS catalog. The J-NEP was performed with the single-CCD Pathfinder camera on the 2.55 m Javalambre Survey Telescope at the Javalambre Astrophysical Observatory with 56 narrow filters and used the SDSS u, g, r, and i filters. J-NEP covered about 80% of the XMM-Newton field. We applied magnitude cuts at S/N > 3 (corresponding to i-band magnitudes m_i ≲ 22.5, 25.8, and 24.5 for SDSS, HSC, and J-PAS, respectively) to the three catalogs to ensure reliable detections and accurate measurements of the source fluxes.

We used two near-IR catalogs covering the NEP-TDF: the YJHK catalog (Willmer et al. 2023), made with the MMT–Magellan Infrared Imager and Spectrometer (MMIRS; McLeod et al. 2012) on the MMT, and the unWISE catalog (Schlafly et al. 2019), made from 5 yr of Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) observations. The unWISE wavelengths are 3.4 (W1) and 4.6 μm (W2).

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

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

$$\begin{eqnarray}&&\mathrm{LR}=\displaystyle \frac{q(m)f(r)}{n(m)},\end{eqnarray} \tag{ 3 }$$

where m is the catalog magnitude of the candidate, n(m) is the local magnitude distribution of background sources, q(m) is the expected magnitude distribution of the real multiwavelength counterparts, and r is the position offset between the X-ray source and the candidate. In practice, n(m) was measured in an annulus between 5'' and 30'' from the X-ray source. The function q(m) is the normalization of $q^{\prime} (m)$, where $q^{\prime} (m)$ is the magnitude distribution of catalog objects within 5'' of the X-ray source after subtracting n(m) and rescaling to the 5'' circular area. Civano et al. (2012, their Figure 1) gave an example of q(m). The function f(r) is the probability distribution of the positional uncertainties, assumed to be a 2D Gaussian $f(r)=1/(2\pi {\sigma }^{2})\times \exp (-{r}^{2}/2{\sigma }^{2})$, where σ is the quadrature combination of the position uncertainty of the XMM-Newton source (Section 5.6) and the ancillary object (02). The choice of 02 was validated by cross-matching our ancillary table with the extragalactic sources (proper motion pm < 10 mas yr⁻¹) in the Gaia DR3 catalog (Gaia Collaboration et al. 2016, 2021). Table 8 lists the number of sources matched by each survey.

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

$$\begin{eqnarray}&&{R}_{i}=\displaystyle \frac{{\mathrm{LR}}_{i}}{\displaystyle \sum _{i}{(\mathrm{LR})}_{i}+(1-Q)},\end{eqnarray} \tag{ 4 }$$

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

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

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

• 1.  
  Secure. These are sources with a single counterpart with LR > LR_th or with more than one candidate counterpart but the LR of the primary counterpart is 4 times higher than the LR of the secondary counterpart. (For there to be more than one candidate, both primary and secondary counterparts must have LR > LR_th.)
• 2.  
  Ambiguous. These are sources with multiple candidate counterparts with the LR of the primary counterpart being less than 4 times higher than the LR of the secondary counterpart or the secure optical counterpart being different from the IR counterpart.
• 3.  
  Unidentified. These are sources with no optical or IR counterpart with LR > LR_th within the search radius.

The NEP-TDF also has Chandra coverage, which provides better localization of some of the X-ray sources. Therefore, we utilized the Chandra NEP-TDF source catalog (W. P. Maksym et al. 2024, in preparation) to help identify the ancillary counterparts of the XMM-Newton sources with ambiguous counterparts. In ambiguous cases, we selected the ancillary counterpart that is closer to the Chandra measured position (which is also the primary counterpart of the XMM-Newton source in most cases) as the secure ancillary counterpart of the XMM-Newton source. We also visually inspected all identifications on the XMM-Newton, HSC, and MMIRS images. Figure 14 shows three XMM-Newton sources with secure, ambiguous, and unidentified ancillary counterparts.

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The source XMM ID 17 ( = NuSTAR ID 58 = J172241+6542.6, z = 0.1791) shown in Figure 14 is a heavily obscured Seyfert galaxy with column density N_H ∼ 10²³ cm⁻² measured by NuSTAR and N_H ≥ 10²³ cm⁻² by XMM-Newton. (See Section 7.2 for more discussion.) This heavily obscured scenario is also supported by the JWST and Hubble Space Telescope (HST) imaging. The strong red spikes seen on the JWST images suggest that the nucleus is a dusty point source. The clear host-galaxy feature in yellow shown on the HST image also implies a significantly obscured core.

A total of 214 XMM-Newton sources have secure ancillary counterparts. Nineteen XMM-Newton sources have ambiguous ancillary counterparts, out of which 14, 3, 1, and 1 have two, three, four, and five candidate ancillary counterparts within the search radius and with LR > LR_th. The coordinates and fluxes of the optical and IR counterparts of the XMM-Newton sources are listed in Tables 9 and 10. The distribution of the separations between XMM-Newton sources and their secure ancillary counterparts is shown in Figure 15; the median separation is 169.

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The NEP-TDF was observed in the radio "S band" (ν = 3 GHz) by the Karl G. Jansky VLA (PIs: R. A. Windhorst & W. Cotton). The 48 hr VLA survey (Hyun et al. 2023) covered an area of ∼0.126 deg² (24' in diameter) centered at the bright (in both radio and X-ray) blazar (NuSTAR ID 29, z = 1.441). Therefore, only about 55% of the XMM-Newton area was covered by VLA. The Hyun et al. (2023) source list comprises 756 sources at S/N > 5. The 1σ noise is 1 μJy beam⁻¹ at the primary-beam center. As the angular resolution is FWHM 07, we matched the VLA catalog with the ancillary counterparts of the XMM-Newton-detected sources using 07 as the matching radius and did not consider the unidentified sources. With this procedure, 55 out of the 171 XMM-Newton sources covered by the VLA have VLA counterparts. This fraction is consistent with what was discovered in COSMOS, where ∼40% of the X-ray sources have VLA counterparts (Marchesi et al. 2016; Smolčić et al. 2017). The radio-brightest source in the XMM-Newton sample is the blazar (NuSTAR ID 29) with a 3 GHz flux of 0.2 Jy. The median flux of the XMM-Newton-matched VLA sample is 23 μJy. Both the NuSTAR and XMM-Newton catalogs report the VLA ID and fluxes from Hyun et al. (2023).

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

HST observations of the JWST NEP-TDF (GO15278, PI: R. Jansen; GO16252/16793, PIs: R. Jansen & N. Grogin) were taken between 2020 September 25 and 2022 October 31. These observations include imaging with WFC3/UVIS in the F275W (272 nm) filter and with the Advanced Camera for Surveys (ACS)/WFC in the F435W (433 nm) and F606W (592 nm) filters (O'Brien et al. 2024, R. A. Jansen et al. 2024, in preparation). The 2σ limiting depths are mag_AB ≃28.0, 28.6, and 29.5 mag in F275W, F435W, and F606W, respectively, and the ACS/WFC observations cover a total area of ∼194 arcmin².

The JWST observations of the NEP-TDF (PI: R. A. Windhorst & H. B. Hammel; PID 2738) were taken in four epochs between 2022 August 26 and 2023 May 21 (Windhorst et al. 2023). The survey includes eight NIRCam filters with 5σ point-source AB limits for each epoch of observation, ≃28.6, 28.8, 28.9, 29.1, 28.8, 28.8, 28.1, and 28.3 mag in F090W, F115W, F150W, F200W, F277W, F356W, F410W, and F444W, respectively. Each NIRCam epoch of observation covers an area of 215 × 636 with the four epochs together (Figure 10) covering ∼55 arcmin². The survey also includes NIRISS grism data with 1σ continuum sensitivity of 25.9. Each NIRISS epoch covers an area of 222 × 490.

The HST and JWST NEP-TDF surveys are much deeper than the HSC and MMIRS/WISE catalogs, but they cover only the center 26% and 7% of the XMM-Newton survey area, respectively. Therefore, we did not use the HST and JWST catalogs to identify the multiwavelength counterparts of the XMM-Newton sources. Instead we used the coordinates of the counterparts of the XMM-Newton sources (Section 6.3) to match the HST (R. A. Jansen et al. 2024, in preparation) and JWST catalogs (R. A. Windhorst et al. 2023; R. A. Windhorst et al. 2024, in preparation). We used the F606W HST catalog and F444W JWST catalog when matching, as they have the deepest sensitivities. In all, 102 XMM-Newton sources have HST counterparts, and 32 XMM-Newton sources have JWST counterparts. The NuSTAR and XMM-Newton catalogs report the F606W and F444W fluxes.

Some of the NEP-TDF X-ray sources have redshifts measured from optical spectra. Spectra came from Hectospec ³⁶ (Fabricant et al. 2005) and Binospec ³⁷ (Fabricant et al. 2019), both of which are mounted on the 6.5 m MMT.

Hectospec is a multiobject spectrograph with 300 optical fibers. Its 1° diameter FoV makes it an efficient instrument to survey the NEP-TDF X-ray sources because of their relatively low areal density. Therefore, we observed (PI: Zhao) the XMM-Newton-selected sources with Hectospec on 2022 September 1 and with a different fiber configuration on 2023 May 20. Each exposure was 2 hr split into six 1200 s exposures to avoid saturation of bright targets, remove cosmic rays, and improve pipeline reduction. The 270 line mm⁻¹ grating provided spectral resolution R ∼ 1000–2000 over the wavelength range 3800–9200 Å, and each exposure allows measuring redshifts of sources with m_i ≤ 22 AB. A limitation of Hectospec is that adjacent fibers cannot be placed within 20'' of each other. In all, we obtained 41 spectra with good enough S/N to measure the redshifts of XMM-Newton targets in the 2022 run and 37 spectra in the 2023 run. Those include spectra of both possible counterparts of XMM-Newton ID 187. Besides the XMM-Newton targets, we also observed 40 (i ≤ 21 mag) targets selected from the VLA (Hyun et al. 2023) and Chandra-detected (W. P. Maksym et al. 2024, in preparation) sources. Table 11 in Appendix C reports their redshifts and spectral types.

The Hectospec data were reduced using the IDL script HSRED ³⁸ v2.0 (originally written by Richard Cool) developed by the Telescope Data Center at SAO (Mink et al. 2007). This pipeline provides fine-tuned wavelength-calibrated, improved cosmic-ray-rejected, and sky-subtracted 1D spectra. The redshifts were measured using a semiautomated and interactive Java toolkit, A Spectrum Eye Recognition Assistant ³⁹ (ASERA; Yuan et al. 2013), which was developed to classify the spectra observed by the Large Sky Area Multi-object Fiber Spectroscopic Telescope (Wang et al. 1996). The spectroscopic redshifts were measured by cross-correlating the observed Hectospec spectra against a library of quasar, galaxy, and star template spectra ⁴⁰ from SDSS integrated into ASERA.

Binospec is an imaging spectrograph covering 3900–10000 Å(Fabricant et al. 2019). C. N. A. Willmer obtained more than 1378 optical spectra with Binospec and successfully measured more than 1000 redshifts of the sources in NEP-TDF (C. N. A. Willmer et al. 2024, in preparation). These include five additional XMM-Newton sources. Therefore, a total of 82 XMM-Newton sources have spectroscopic redshifts. We categorized the sources into quasars (presenting broad emission lines), galaxies (including type 2 AGN, which have only narrow emission lines), and stars. Future efforts to identify type 2 AGN can include methods such as the Baldwin, Philips, & Terlevich diagram (e.g., Kewley et al. 2001; Kauffmann et al. 2003).

Photometric redshifts of the X-ray source counterparts were adopted from the SDSS DR17 catalog (Abdurro'uf et al. 2022). Only photometric redshifts with low rms uncertainties, specifically photoErrorClass flag = −1, 1, 2, or 3, were considered. That added two XMM-Newton sources without spectroscopic redshifts for a total of 84 XMM-Newton sources with redshifts, reported in Tables 9 and 10. The distributions of the spectroscoptic redshifts of the XMM and NuSTAR detected sources are plotted in Figure 16.

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

$$\begin{eqnarray}&&X/O\equiv \mathrm{log}({f}_{{\rm{X}}}/{f}_{\mathrm{opt}})=\mathrm{log}({f}_{{\rm{X}}})+{m}_{\mathrm{opt}}/2.5+C,\end{eqnarray} \tag{ 5 }$$

where f_X is the X-ray flux in a given band in units of erg cm⁻² s⁻¹, m_opt is the optical AB magnitude in a given filter, and C is a constant depending on the bands chosen in X-ray and optical. Figure 17 shows the i-band (HSC) magnitudes as a function of the soft (0.5–2 keV) and hard (2–10 keV) X-ray fluxes of the XMM-Newton-detected sources. The constants used to calculate X/O are C_0.5−2 = 5.91 and C_0.5−2 = 5.44 for the soft and hard bands, respectively (Marchesi et al. 2016).

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

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

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

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

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

$$\begin{eqnarray}&&N(\gt S)\equiv \displaystyle \sum _{i=1}^{{N}_{S}}\displaystyle \frac{1}{{{\rm{\Omega }}}_{i}}\,{\deg }^{-2},\end{eqnarray} \tag{ 6 }$$

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

$$\begin{eqnarray}&&{\sigma }_{S}^{2}=\displaystyle \sum _{i=1}^{{N}_{S}}{\left(\displaystyle \frac{1}{{{\rm{\Omega }}}_{i}}\right)}^{2}.\end{eqnarray} \tag{ 7 }$$

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

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

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

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HR is useful to characterize the spectral shape of the XMM-Newton and NuSTAR NEP-TDF sources. The HRs of different column densities were estimated using a physical model that is typically used for modeling AGN X-ray spectra. The model includes a line-of-sight component (modeled by an absorbed power law), a reflection component (modeled by borus02; Baloković et al. 2018), and scattered emission of soft X-rays (modeled by a fractional power law). The model was calculated with XSPEC as phabs×(zphabs×powerlw+borus+constant×powerlw). phabs models the Galactic absorption. We assumed a photon index Γ = 1.8 in both powerlw and borus02 and a torus column density N_H,Tor = 1.4 × 10²⁴ cm⁻², a covering factor of f_c = 0.67 in borus02, and an inclination angle θ_inc = 60° following the torus properties measured by Zhao et al. (2021b). We assumed a constant = 1% fraction of the intrinsic emission being scattered (Ricci et al. 2017).

Table 10 reports the HRs of XMM-Newton sources. They are defined as (H − S)/(H + S) with 0.5–2 keV flux as the soft-band flux S and 2–10 keV flux as the hard-band flux H. Table 10 also reports S and H, which were calculated with the SAS emldetect tool. Figure 21 shows the HR distribution of the 286 XMM-Newton sources. The expected HR for a given obscuration depends on the source redshift as shown in Figure 21. About half (48%) of the XMM-Newton-detected sources have HR larger than expected for column density N_H = 10²² cm⁻² or have a lower limit of HR that implies an obscured source. For the 85 XMM-Newton sources that have redshift measurements, 38% are obscured. That lower percentage might be due to the bias from m_i ≤ 22 mag selection for the Hectospec observation: obscured sources are typically fainter in the visible light than unobscured ones.

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

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Unlike XMM-Newton, NuSTAR is sensitive to obscurations N_H > 10²³ cm⁻² (e.g., Masini et al. 2018a). A total of 47% of the NuSTAR-detected sources are obscured above that level, and 23% are CT (N_H > 10²⁴ cm⁻²) assuming z = 0.734 (median redshift of the NuSTAR sources). CT candidates include sources that have lower limits on their HR. Figure 22 shows HR as a function of redshift for the 22 NuSTAR sources with redshift measurements. Of these, 23% are heavily obscured, and 14% are CT.

The HRs of the XMM-Newton sources and the model predictions used to compare with the NuSTAR HRs were calculated assuming particular spectral shapes when converting the count rates into fluxes. Different assumed column densities and photon indices lead to different ECFs. The ECF changes by about 70% in the 0.5–2 keV band and about 20% in the 8–24 keV band assuming no intrinsic absorption compared to a CT absorption. This might explain the discrepancy of the column densities estimated using NuSTAR and XMM-Newton. Changing the photon index has little effect: only ∼5% for photon indices Γ = 1.40 or 2.20 rather than the assumed Γ = 1.80. Therefore, a broadband spectral analysis is needed to accurately measure the obscuration of these sources. Full spectral analysis of the NuSTAR and XMM-Newton sources will be presented by S. Creech et al. 2024, in preparation.

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

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

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In addition to the bright blazar mentioned in Section 6.8, there is another prominent Seyfert galaxy (and radio source; Willner et al. 2023) in the TDF field. The source XMM ID 17 (shown in Figure 14; NuSTAR ID 58) has XMM-Newton HR ≥ 0.99 suggesting N_H > 10²³ cm⁻² (Figure 21). The NuSTAR $\mathrm{HR}={0.00}_{-0.07}^{+0.05}$ also suggests N_H ∼ 10²³ cm⁻² (Figure 22). The bright core seen in the JWST long-wave imaging but not at shorter wavelengths supports the interpretation of high but not CT obscuration. The source's 2–10 keV luminosity L(2–10 keV) = 4.5 ± 0.5 × 10⁴² erg s⁻¹ and 10–40 keV luminosity L(10–40 keV) = 1.36 ± 0.08 × 10⁴³ erg s⁻¹ suggest a type 2 AGN. More intriguing, this source is variable at 3σ in the 3–24 keV band and at 2.9σ in the 3–8 keV band but is not significantly variable in the 8–24 keV band, suggesting a variable spectral shape. Its count rates increased by 115% in the 3–24 keV and 230% in the 3–8 keV bands from 2019 October to 2022 January (Figure 26). We did not find obvious variability of this source in either visible (Zwicky Transient Facility; Bellm et al. 2019; Masci et al. 2019) or IR (NEOWISE; Mainzer et al. 2014). This suggests that the X-ray variability of the source might be caused by the decreasing of the line-of-sight obscuration rather than the variability of the intrinsic accretion rate. However, further investigation is needed.