The NuSTAR extragalactic surveys: Source catalogs from the Extended Chandra Deep Field-South and the Chandra Deep Field-North

1.   Introduction

Extragalactic X-ray surveys are efficient at identifying and characterizing highly reliable and fairly complete samples of active galactic nuclei (AGNs), given the following reasons (see, e.g., Brandt and Hasinger^[1], Brandt and Alexander^[2], Xue^[3], for reviews). First, X-ray emission is a nearly universal feature of luminous AGNs, which can be produced in various accretion disk (plus corona) models for AGNs (e.g., Yuan and Narayan^[4]). Second, X-ray emission, especially hard X-ray emission ($\geqslant 10 \;\text{keV}$), can penetrate through materials with hydrogen column densities even up to $N_{\rm{H}}\sim 10^{25}\,{\rm{cm}}^{-2}$, which is key to excavating the majority of the AGN family, i.e., highly obscured and even Compton-thick AGNs (e.g., Li et al.^{[5, 6]}). Third, X-ray emission is subject to minimal dilution by host-galaxy stellar emission and is powerful for probing the immediate vicinity of supermassive black holes (SMBHs) in AGNs even at high redshifts. Last, the production of the X-ray spectrum goes through numerous line and continuum emission processes, and a high-quality X-ray spectrum is effective to infer physical conditions near the central SMBH.

X-ray surveys have resolved a very large portion ($\sim 80\% - 90\%$) of the cosmic X-ray background (CXRB) up to $\sim 10\;\text{keV}$, with AGNs being the dominant contributor (e.g., Hickox and Markevitch^[7], Xue et al.^{[8, 9]}, Lehmer et al.^[10], Luo et al.^[11]), but the resolved fraction around the peak of the CXRB at $\sim 20–40\;\text{keV}$ has been very low ($< 10\%$lt; 10\%$; see, e.g., Brandt and Hasinger^[1], Brandt and Alexander^[2]; Harrison et al.^[12]). The Nuclear Spectroscopic Telescope Array (NuSTAR), the first focusing high-energy X-ray (3–79 keV) telescope in orbit, has largely broadened the window of X-ray observations^[13]. The NuSTAR surveys have resolved ~33%–39% of the 8–24 keV CXRB^[12], thereby helping us better understand the contribution of highly obscured and Compton-thick AGNs to the CXRB.

The Chandra Deep Fields (CDFs), consisting of the Chandra Deep Field-South (CDF-S, Luo et al.^[11], hereafter L17), Chandra Deep Field-North (CDF-N, Xue et al.^[14], hereafter X16), and Extended Chandra Deep Field-South (E-CDF-S, X16), are important sky areas for study, e.g., AGN demography, physics, and evolution^[3]. The Chandra X-ray observatory has accumulated ~7 Ms exposure in the CDF-S (L17), the deepest X-ray exposure ever made, which provides a large sample of AGNs at z~0–5 for powerful statistical studies. As a parallel field to the CDF-S and being the second deepest X-ray survey, the 2 Ms CDF-N (X16) effectively complements the 7 Ms CDF-S, accounting for cosmic variance and enabling comparative studies between fields. NuSTAR has also observed the CDFs for complementary studies over 10 keV, and has completed a series of additional extragalactic hard X-ray surveys^[12]. Mullaney et al.^[15] (hereafter M15) has released a source catalog from the NuSTAR E-CDF-S survey; however, the NuSTAR CDF-N catalog is still absent.

In this work, we propose a uniform and reliable method to process the NuSTAR E-CDF-S and CDF-N observations and perform source detection. Referring to the previous NuSTAR E-CDF-S cataloging work (M15), we obtain both the NuSTAR E-CDF-S and CDF-N source catalogs in a routinized and unified way. We describe the production of both catalogs in Section 2 and Section 3, where, for brevity, the data reduction and source detection are introduced in detail only for the E-CDF-S. We summarize our results in Section 4. We use J2000.0 coordinates and a cosmology of $H_0=71\;{{\rm{km}}\cdot {\rm{s}}^{-1}\cdot {\rm{Mp}}\cdot}c^{-1}$, $\varOmega_{\rm{M}}=0.27$, and $\varOmega_{\Lambda}=0.73$.

2.   Production of the NuSTAR E-CDF-S point-source catalog

2.1   Data reduction

We collect 33 valid observations from the NuSTAR E-CDF-S survey that cover a sky area of $\sim 30{'}\times 30{'}$, almost each of which has an effective exposure of $\sim 45\;\text{ks}$. The details of these observations are presented in Table 1.

Table  1.  Details of the NuSTAR E-CDF-S observations.

Obs. ID	Obs. Name	Obs. Date	RA	DEC	$t_{\rm eff}$
60022001002	ECDFS_MOS001	2012-09-28	52.93	−27.97	49.0
60022002001	ECDFS_MOS002	2012-09-29	52.93	−27.97	50.3
60022003001	ECDFS_MOS003	2012-09-30	52.93	−27.97	50.2
60022004001	ECDFS_MOS004	2012-10-01	52.93	−27.97	50.9
60022005001	ECDFS_MOS005	2012-10-02	53.06	−27.86	50.5
60022006001	ECDFS_MOS006	2012-10-04	53.06	−27.86	49.2
60022007002	ECDFS_MOS007	2012-11-30	53.06	−27.86	51.7
60022008001	ECDFS_MOS008	2012-12-01	53.06	−27.86	51.7
60022009001	ECDFS_MOS009	2012-12-03	53.18	−27.75	50.3
60022010001	ECDFS_MOS010	2012-12-04	53.18	−27.75	51.2
60022011001	ECDFS_MOS011	2012-12-05	53.18	−27.75	51.7
60022012001	ECDFS_MOS012	2012-12-06	53.18	−27.75	52.1
60022013001	ECDFS_MOS013	2012-12-07	53.31	−27.64	52.5
60022014001	ECDFS_MOS014	2012-12-08	53.31	−27.64	52.9
60022015001	ECDFS_MOS015	2012-12-09	53.31	−27.64	53.2
60022016001	ECDFS_MOS016	2012-12-10	53.31	−27.64	50.1
60022016003	ECDFS_MOS016	2013-03-15	52.93	−27.64	51.7
60022015003	ECDFS_MOS015	2013-03-17	52.93	−27.64	51.2
60022014002	ECDFS_MOS014	2013-03-18	52.93	−27.64	51.4
60022013002	ECDFS_MOS013	2013-03-19	52.93	−27.64	49.7
60022012002	ECDFS_MOS012	2013-03-20	53.06	−27.75	49.7
60022011002	ECDFS_MOS011	2013-03-21	53.06	−27.75	48.9
60022010002	ECDFS_MOS010	2013-03-22	53.06	−27.75	32.5
60022010004	ECDFS_MOS010	2013-03-23	53.06	−27.75	16.4
60022009003	ECDFS_MOS009	2013-03-24	53.18	−27.75	49.5
60022008002	ECDFS_MOS008	2013-03-25	53.18	−27.86	49.8
60022007003	ECDFS_MOS007	2013-03-26	53.18	−27.86	49.6
60022006002	ECDFS_MOS006	2013-03-27	53.18	−27.86	48.7
60022005002	ECDFS_MOS005	2013-03-28	53.31	−27.86	49.3
60022004002	ECDFS_MOS004	2013-03-29	53.31	−27.97	48.8
60022003002	ECDFS_MOS003	2013-03-30	53.31	−27.97	49.0
60022002002	ECDFS_MOS002	2013-03-31	53.31	−27.97	49.0
60022001003	ECDFS_MOS001	2013-04-01	52.93	−27.97	48.2
Obs. ID is a unique identification number specifying the NuSTAR observation; Obs. Name gives the designation of the target at which NuSTAR was pointing. Obs. Date is the start time of the observation. RA and DEC give the J2000.0 Right Ascension and the Declination of the NuSTAR pointing position. $t_{\rm eff}$ is the effective exposure time (in ks) after background filtering (see Section 2.1.1).

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2.1.1   Flaring episodes

As NuSTAR is composed of two focal plane modules (i.e., FPMA and FPMB), each of the 33 observations results in two event files. We use the program nupipeline of the NuSTAR data analysis software NuSTARDAS to generate 66 initial event files with default parameters. Following M15, full-field lightcurves in the entire energy band (i.e., 3–78 keV) with a bin size of 20 s are produced to inspect the influence of flaring events. The dmgti tool of the Chandra interactive analysis of observations (CIAO) is used to make a user-defined good-time interval (GTI) file to avoid background flaring when the average binned count rate exceeds $1.5\;{\rm{cts}} \cdot {{\rm{s}}^{ - 1}}$ in the light curves. Taking the GTI files into account, we run nupipeline again to obtain the 66 cleaned event files. Following Alexander et al.^[16], the final cleaned event files are split into three standard energy bands, 3–8 keV (soft band; S), 8–24 keV (hard band; H), and 3–24 keV (full band; F), respectively.

2.1.2   Science, exposure, and background mosaics

From the cleaned event files, we produce exposure maps with the NuSTARDAS program nuexpomap. For the effects of vignetting, the same energy correction values as those in M15 are adopted to generate the effective exposure maps, i.e., 5.42 keV, 13.02 keV, and 9.88 keV for the soft, hard, and full bands, respectively. The E-CDF-S reaches a maximum depth of $\sim 230 \;\text{ks}$ corrected for vignetting in the full band.

Due to the high count-rate backgrounds in the NuSTAR E-CDF-S observations, we generate model background maps using the IDL software nuskybgd^[17]. Following a similar strategy adopted by M15, we choose 4 large (i.e., radius of $3{'}$) circular regions centered on the 4 chips of the detector as our background regions. With the user-defined regions, the nuskybgd software can extract and fit the corresponding spectra in XSPEC with the preset models and derive the best-fit parameters. These parameters are used to generate “fake” background images of the observations. Using the FTOOLS task XIMAGE, these simulated images are collected and merged into background mosaics weighted by the corresponding exposure maps; similarly, using XIMAGE, the stacked science mosaics (see Fig. 1) are directly produced from the cleaned event files.

Figure  1.  Stacked NuSTAR E-CDF-S science mosaic in the full band, with a total of 58 sources plotted as circles. The green (47/58) and red (4/58; being less significant detections) sources have the Chandra 250 ks E-CDF-S counterparts within $r_{\rm m}=30''$. The magenta source (1/58) does not have any Chandra 250 ks E-CDF-S counterparts but can be matched to a Chandra 7 Ms CDF-S source. Among the unmatched sources (6/58), 3 yellow sources reside in the very edges of the mosaic and 3 cyan sources reside in the chip-gap areas. Numbers are source XIDs. The bottom color bar indicates the counts per pixel.

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We note that in the newest version of nuskybgd, the use of the “nuabs” XSPEC model has been phased out of nuskybgd routines. However, we find that when “nuabs” is removed, the model background counts are significantly lower than what they should be. Consequently, we turn to using the old version that includes the “nuabs” model in the spectral fitting process.

2.2   Source detection

As shown in Fig. 1, traditional source detection methods (e.g., WAVDETECT^[18] and ACIS Extract^[19] adopted in Xue et al.^{[8, 14]}, Luo et al.^[11]) are invalid due to the heavy background. Following the general strategy adopted for NuSTAR surveys (M15, Masini et al.^[20]), we use the incomplete Gamma (igamma) function (see Georgakakis et al.^[21]) in the Scipy.special package to produce false probability ($P_{\rm false}$) maps for source detection:

where $N_{\rm Sci}$ and $N_{\rm Bgd}$ represent the photon counts within one region at the same position in the science and background mosaics. The $P_{\rm false}$ value gives the probability that a signal with $N_{\rm Sci}$ counts is purely due to random fluctuation given the background of $N_{\rm Bgd}$, which means that the signal is more likely to be real as $P_{\rm false}$ decreases.

We smooth the science and background mosaics with top-hat functions of different radii, with the former ($10''$) being smaller for finer structures and the latter ($20''$) being larger to decrease the background influence. The $P_{\rm false}$ maps are produced using three methods: (ⅰ) the $P_{\rm false}$ value at the position ($x$,$y$) is directly derived by igamma(Sci($x$, $y$), Bgd($x$, $y$)), where the resulting $P_{\rm false}$ maps are called $P_{r0}$ maps. (ⅱ) At position ($x$, $y$), we perform aperture photometry with a circular region of radius $10''$ on the mosaics and then calculate the $P_{\rm false}$ value from igamma(Sci$_{10''}(x,\;y)$, Bgd$_{10''}(x,\;y))$, where the resulting $P_{\rm false}$ maps are called $P_{r10}$ maps. (ⅲ) The same procedure as method (ⅱ) but using a $20''$ radius aperture is adopted to obtain the $P_{r20}$ maps. Considering the potential signals residing in the local minima of the $P_{\rm false}$ maps, we produce the inverse $P_{\rm false}$ maps using $\log({1/P_{\rm false}})$ to identify peaks with the SExtractor source-detection algorithm^[22].

Some modifications on the default SExtractor configuration file default.sex are listed below:

(Ⅰ) DETECT_MINAREA is set to 1. Because we smooth the input maps, even one pixel in the 1/$P_{\rm false}$ maps can be considered as a potential source.

(Ⅱ) THRESH_TYPE is set to ABSOLUTE. Under this condition, DETECT_THRESH represents the detection threshold above which a signal in the maps can be considered significant.

(Ⅲ) FILTER and CLEAN are set to N(o). We do not need these processes as what we address here are not real observational images.

With proper DETECT_THRESH values, SExtractor is able to detect potential sources in the three standard bands to produce our initial catalogs.

2.2.1   Simulations

We perform a series of simulations to determine DETECT_THRESH. Because the science mosaics are smoothed with the $10''$-radius circular top-hat function (see Section 2.2), we split the background images into several square cells with a side length of $20''$. For every background image, Poisson realizations are performed on these cells to make up a “science” image from pure Poisson fluctuation. The aforementioned procedures are then performed on these Poisson realizations, and SExtractor should detect no sources in the corresponding inverse $P_{\rm false}$ maps with proper thresholds.

The simulations are repeated for 100 times, in each of which we produce inverse $P_{\rm false}$ maps with three different aperture radii (i.e., $0''$, $10''$, and $20''$) in the three standard bands. DETECT_THRESH is set to the value above which SExtractor can find no more than $N$ signals in these simulated maps per aperture radius per band, and $R=N/100$ represents the false detection rate. These thresholds are applied to the real inverse $P_{\rm false}$ maps for source detection.

2.2.2   Final catalog production

We first set $R=0.1$ for loose thresholds, with which our algorithm is run on the $P_{r0}$, $P_{r10}$, and $P_{r20}$ maps to generate three seed lists in each band. These seed lists are produced from different $P_{\rm false}$ maps; thus, there might be multiple nearby detections belonging to the same source. To identify every unique source, we merge the seed lists for each band and then run a modified friends-of-friends algorithm (hereafter FOF) on these merged lists for deduplication.

FOF is common in cosmology for identifying groups in dense fields^[23], which demands that any particle (or galaxy) that finds another one within a distance $l$ (called linking length) should be linked to it to form a group. Sources in the merged lists are split into group sources and isolated sources by FOF with a linking length of $30''$. For each group, members are ranked by their inverse $P_{r20}$ values (even if being initially detected from other $P_{\rm false}$ maps), then compete against any others within a $30''$ radius, in which a member of higher value can survive and participate in a next competition. After several rounds of competitions, the final survivals from the group sources are combined with the isolated sources to make up the deduplicated seed lists for each band.

The deduplicated seed lists from different bands are combined into one seed list and then split by FOF in the same way. For each group in the combined list, members are ranked by their inverse $P_{r20}$ values in the full band (regardless of whether being detected in this band), then participate in competitions against each other. After deduplication, the remaining sources are collected to construct our seed catalog with $R=0.1$. The details are presented in Table 2.

Table  2.  The NuSTAR E-CDF-S cataloging process.

Seed catalog ($R=0.1$)	Source # ($P_{r0}$)	Source # ($P_{r10}$)	Source # ($P_{r20}$)	Source # (Total)	Source # (After deduplication)
3–8 keV	33	35	35	103	46
8–24 keV	17	13	20	50	23
3–24 keV	42	41	55	138	66
Final catalog ($R=0.01$ & $P_{r20}$)	Source # (3–8 keV)	Source # (8–24 keV)	Source # (3–24 keV)	Source # (3–8 keV & 8–24 keV)	Source # (Total)
Before deblending	33	13	54	9	58
After deblending	33	13	50	9	54

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To produce a reliable final catalog, we then set $R=0.01$, which means only 1 false signal being detected in 100 simulations. The thresholds of the inverse $P_{r20}$ maps are 3.99, 4.36, and 4.33 in the soft, hard, and full bands, respectively, corresponding to $\sim99\%$ reliability^[24]. We remove the sources that do not meet any of our final thresholds and construct the final catalog with the remaining ones.

The E-CDF-S final catalog contains 58 sources, each of which is detected in at least one of the three standard bands. Of these 58 sources, 33, 13, and 54 are detected in the soft, hard, and full bands, respectively; 3, 1, and 21 are detected only in the soft, hard, and full bands, respectively; no source is detected in exactly the soft and hard bands, 21 in exactly the soft and full bands, and 3 in exactly the hard and full bands; and 9 are detected in all the three standard bands.

2.2.3   Photometry and deblending

The radius of the 90% encircled-energy fraction contour of the NuSTAR point spread function (PSF) is approximately $67.5''$, which is relatively large compared to the average distance among sources. We adopt a similar strategy to that of M15 to choose an aperture size of $30''$ for photometry extraction and assume that the net counts within this aperture are only contaminated by other nearby NuSTAR-detected sources within $90''$.

For each source in our catalog, the total and background counts are calculated within a circular region of radius $30''$ in the science and background mosaics, respectively, while the net counts are derived by subtracting the background counts from the total counts. Following Gehrels^[25], we estimate the upper and lower $1\sigma$ confidence limits on the total counts; for those not detected in certain bands, only the upper limits are derived, using:

where $\lambda_{\rm{u}}$ and $\lambda_{\rm{l}}$ represent the upper and lower limits, $n$ is the photon count, and CL represents the confidence level, respectively.

The background count error can be approximated by $\sigma_{\rm Bgd}=\dfrac{1+\sqrt{\text{factor} \times C_{\rm Bgd} + 3/4}}{\text{factor}}$, where $C_{\rm Bgd}$ is the background count and the $\text{factor}$ gives the ratio between the total area where the background model is defined and the area for photometry extraction (i.e., $\text{factor}=(180''/30'')^2\times 4=144$). Subsequently, the upper and lower limits on the net counts are calculated as $\sigma_{\rm Net,u}=\sqrt{\lambda_{\rm{u}}^2+\sigma_{\rm Bgd}^2}$ and $\sigma_{\rm Net,l}=\sqrt{\lambda_{\rm{l}}^2+\sigma_{\rm Bgd}^2}$, respectively.

To deblend the sources in our catalog, the FOF algorithm is applied again to split them into group sources and isolated sources with a different linking length of $90''$. For the isolated sources, we assume that they cannot be contaminated by any other sources (away beyond $90''$); for the group sources, a system of $n$ linear simultaneous equations is established:

where $C_{\rm{T}}^n$ is the total net counts of source $n$, $C_{\rm{D}}^n$ is the deblended net counts of source $n$, and $N(r_{i,j})$ is the normalized function of the separation between the sources $i$ and $j$ ($r_{i,j}$ represents the separation distance, while $N(0)=1$), in which several simplifications are proposed to avoid the complications of the nonazimuthally symmetric NuSTAR PSF.

Following the deblending procedure above, we then perform deblending with another aperture of $20''$ radius, and recalculate the $P_{\rm false}$ of each source after deblending. The postdeblending $P_{\rm false}$ values are compared with the $P_{r20}$ thresholds, and 4 of the 58 sources in our catalog become no longer significant. Additionaly, we find 1 source in the area of relatively low exposure ($<40$ ks, corresponding to $\lesssim10\%$ of the maximum survey exposure). All of these 5 sources are detected in the full band only, and we flag but do not remove them (see Fig. 1).

To validate the reliability of our catalog (a total of 58 sources), we match it to the previous NuSTAR E-CDF-S catalog (a total of 54 sources) in M15 using a matching radius $r_{\rm m}=30''$ and find a total of 36 counterpart pairs. We compare their net counts in Fig. 2 and find good consistency within $1\sigma$ errors. We also compare their aperture-corrected fluxes (see Section 2.3) and find good agreement between each other.

Figure  2.  Comparison of net counts obtained by this work and M15 in the E-CDF-S. The diagonal dashed lines indicate the 1∶1 relations.

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A significant fraction of the M15 sources are not detected by our work (and vice versa), mainly due to two facts: the detailed cataloging methodologies are different between our work and M15, and those unmatched sources generally have lower net counts such that they could be too faint to be detected by either work.

2.3   Matching to the Chandra E-CDF-S and CDF-S catalogs

We first match our catalog to the Chandra 250 ks E-CDF-S catalog (X16) using $r_{\rm m}=30''$, and find 51 of the 58 sources to have at least one Chandra counterpart. In these matches, 20, 24, 5, and 2 NuSTAR sources have 1, 2, 3, and 4 Chandra counterparts, respectively; no NuSTAR sources has more than 4 Chandra counterparts. For the flagged sources (see Section 2.2.3), all of the 4 less-significant sources (XIDs =14, 15, 25, 38; see Fig. 1) have Chandra counterparts, but the source with low exposure time (XID = 18) does not. We then match the 7 sources without Chandra 250 ks counterparts to the Chandra 7 Ms CDF-S catalog (L17) using $r_{\rm m}=30''$, only finding one further match (XID = 19).

We inspect the positions and properties of the 6 unmatched sources, finding that 3 reside in the very edge of the NuSTAR E-CDF-S survey mosaic (XIDs=18, 21, and 45; see Fig.1), which implies uncertainty in their detections. For the 3 remaining sources, one (XID = 2) is also near the edge of the mosaic and detected only in the 3–24 keV band, and the other two sources (XIDs = 37, 49) reside in the chip-gap areas (see Fig. 1) which might be spurious. Because we aim to find as many sources as possible using our algorithm alone (without manual intervention), these 6 sources are conserved and flagged in our final catalog.

To compare the fluxes of these matched sources, the observed deblended fluxes of the NuSTAR sources are derived following the same approach as Alexander et al.^[16] For the sources detected in both the soft and hard bands, we calculate their hardness ratios, HR=(H−S)/(H+S), using the Bayesian estimation of hardness ratios method^[26]; for other sources, an HR value corresponding to the power-law spectral photon index of $\varGamma=1.8$ is assumed. Using the derived HRs, the same parameters as in M15 are then adopted to convert count rates to observed fluxes (see Section 2.3.3 of M15), which reach a soft-band flux limit of $\sim {10^{ - 14}}{\rm{erg}}\cdot{{\rm{s}}^{ - 1}}\cdot{\rm{c}}{{\rm{m}}^{ - 2}}$.

Due to the different observable energy range of Chandra (0.5–7 keV), we assume the Chandra counterparts having a simple power-law spectrum (i.e., $f(E)\propto E^{-\varGamma}$), then derive the conversion factor between the fluxes in the 2–7 keV and 3–8 keV bands. The fluxes in the 2–7 keV band and photon indices ($\varGamma$) can be obtained from the Chandra catalogs (X16; L17). For the multiple Chandra counterparts within $r_{\rm m}=30''$ of the NuSTAR sources, we calculate their total 3–8 keV fluxes instead. The comparison between the NuSTAR and total Chandra 3–8 keV fluxes of the matched sources is shown in Fig. 3, which indicates general agreement within a factor of 3 for the majority of the sources. However, the NuSTAR fluxes appear to be systematically lower than the Chandra fluxes, which is mainly due to that the NuSTAR measured/assumed photon index may be different from the Chandra measured/assumed photon index (in the case of 1-to-1 match) or photon indexes (in the case of 1-to-multiple match).

Figure  3.  Comparison between the NuSTAR E-CDF-S deblended fluxes (this work) and the total Chandra E-CDF-S (X16; left panel) and CDF-S (L17; right panel) fluxes in the 3–8 keV band (all fluxes are aperture-corrected). In each panel, the green 1∶1 line is centered at the shaded area indicating a factor of $\le 3$ difference from the 1∶1 line, and the horizontal dotted line indicates the detection limit.

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3.   Production of the NuSTAR CDF-N point-source catalog

3.1   Data reduction and source detection

We collect 12 valid observations from the NuSTAR CDF-N survey that cover a sky area of $\sim 7'\times10'$, almost each of which has an effective exposure of $\sim 50 \;\text{ks}$. We summarize the information of these observations in Table 3. For data reduction, we apply the exactly same procedures as in Section 2.1, therefore the technical details are introduced briefly in this section.

Table  3.  Details of the NuSTAR CDF-N observations.

Obs. ID	Obs. Name	Obs. Date	RA	DEC	$t_{\rm eff}$
60110003002	GOODSN_MOS003	2015-04-22	12.61	+62.20	45.6
60110002001	GOODSN_MOS002	2015-04-23	12.62	+62.24	45.6
60110001001	GOODSN_MOS001	2015-04-24	12.62	+62.28	46.1
60110001003	GOODSN_MOS001	2015-08-04	12.62	+62.28	59.7
60110002003	GOODSN_MOS002	2015-08-09	12.61	+62.24	64.3
60110003003	GOODSN_MOS003	2015-08-10	12.61	+62.20	59.0
60110001005	GOODSN_MOS001	2015-10-31	12.62	+62.27	61.5
60110002004	GOODSN_MOS002	2015-11-01	12.62	+62.23	64.3
60110003004	GOODSN_MOS003	2015-11-02	12.61	+62.20	67.8
60110001007	GOODSN_MOS001	2016-01-30	12.62	+62.27	52.8
60110002005	GOODSN_MOS002	2016-01-31	12.62	+62.23	52.9
60110003005	GOODSN_MOS003	2016-02-01	12.61	+62.19	54.0
Same as those of Table 1.

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Full-field lightcurves in the entire energy band with a bin size of 20 s are produced to inspect the influence of flaring events, and a threshhold of $1.3\;{\rm{cts}}\cdot{\rm{s^{-1}}}$ is selected to reject the periods with high background flares. Following the same procedures in Section 2.1.2, the science, exposure, and background mosaics are created from the cleaned event files. The CDF-N reaches a maximum depth of ~440 ks corrected for vignetting in the full band, almost doubling that of the E-CDF-S. We present the stacked science mosaic in the full band in Fig. 4.

Figure  4.  Stacked NuSTAR CDF-N science mosaic in the 3–24 keV band (cf. Fig. 1), with a total of 42 sources plotted. The green (29/42) and red (4/42; being less significant detections) sources have the Chandra 2 Ms CDF-N counterparts within $r_{\rm m}=30''$. Among the unmatched sources (9/42), 8 yellow sources reside in or near the edges of the mosaic, and 1 cyan source is only detected in the 8–24 keV band.

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Again we set $R=0.1$ to obtain the seed list from the $P_{\rm fasle}$ maps, then refilter these seed sources with a strict threshold of $R=0.01$ for the final catalog that contains 42 CDF-N sources, each of which is detected in at least one of the three standard bands. Of the 42 sources, 26, 11, and 31 are detected in the soft, hard, and full bands, respectively; 9, 2, and 12 are detected in the soft, hard, and full bands only, respectively; no source is detected in exactly both the soft and hard bands, 10 in exactly both the soft and full bands, and 2 in exactly both the hard and full bands; 7 are detected in all the three standard bands. After deblending, 6 of the 42 sources are no longer significant, and we still flag and keep them in our final catalog. These results are listed in Table 4.

Table  4.  The NuSTAR CDF-N cataloging process.

Seed catalog ($R=0.1$)	Source # ($P_{r0}$)	Source # ($P_{r10}$)	Source # ($P_{r20}$)	Source # (Total)	Source # (After deduplication)
3–8 keV	27	19	28	74	32
8–24 keV	4	9	13	26	14
3–24 keV	42	26	30	98	38
Final catalog ($R=0.01$ & $P_{r20}$)	Source # (3–8 keV)	Source # (8–24 keV)	Source # (3–24 keV)	Source # (3–8 keV & 8–24 keV)	Source # (Total)
Before deblending	26	11	31	7	42
After deblending	22	11	27	6	36

 | Show Table

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3.2   Matching to the Chandra CDF-N catalog

We match our catalog to the Chandra 2 Ms CDF-N catalog (X16) using $r_{\rm m}=30''$, and find 33 of the 42 sources to have at least one Chandra counterpart. In these matches, 14, 11, 4, and 3 NuSTAR sources have 1, 2, 3, and 4 Chandra counterparts, respectively, and 1 NuSTAR source has more than 4 Chandra counterparts.

For the NuSTAR sources without Chandra counterparts, we inspect their positions and properties and find that almost all of them (8/9; XIDs = 2, 3, 12, 32, 34, 37, 38, 40) reside in or near the edges of the NuSTAR CDF-N field and the remaining one (XID = 25) is only detected in the hard band which might be too “hard” to be detected by Chandra (see Fig. 4).

We compare the fluxes of these matched sources in Fig. 5, which also indicates general agreement within a factor of 3 for the majority of the sources. The normalized flux histograms of the NuSTAR CDF-N and E-CDF-S sources are compared in Fig. 6: CDF-N sources generally have lower fluxes than E-CDF-S sources, being consistent with the fact that the average NuSTAR CDF-N exposure depth (reaching a soft-band flux limit of $\sim 5\times 10^{-15}\;\text{erg}\cdot \text{s}^{−1}\cdot \text{cm}^{−2}$) is almost twice that of the E-CDF-S.

Figure  5.  Same as Fig. 3, but for the comparison between the NuSTAR CDF-N deblended fluxes (this work) and the total Chandra CDF-N fluxes (X16) in the 3–8 keV band (all fluxes are aperture-corrected).

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Figure  6.  Normalized distributions of deblended NuSTAR fluxes in the CDF-N and E-CDF-S.

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4.   Conclusions

In this work, we collect the original observations from the NuSTAR E-CDF-S and CDF-N surveys and produce cleaned event files. Simulated background mosaics are generated using the IDL software nuskybgd, and then processed along with science mosaics to produce $P_{\rm false}$ maps for source detection.

For the NuSTAR E-CDF-S survey, the main results are as follows:

(Ⅰ) The E-CDF-S catalog consists of 58 sources that are detected using our algorithm without manual intervention, with 4 of them being not significant after deblending.

(Ⅱ) We compare our catalog with the previous NuSTAR E-CDF-S catalog (M15) using $r_{\rm m}=30''$ and find a total of 36 matches, the net counts of which agree well within $1\sigma$ errors.

(Ⅲ) We compare our catalog with the Chandra E-CDF-S and CDF-S catalogs (X16 and L17), and find a total of 51 matches, the fluxes of which agree well above the detection limit. All of the 4 sources being not significant after deblending have counterparts in the Chandra catalogs; and the 7 unmatched sources are flagged as being spurious but still conserved in the catalog.

For the NuSTAR CDF-N survey, the main results are as follows:

(Ⅰ) The CDF-N catalog, produced for the first time by this work, consists of 42 sources that are detected using our algorithm without manual intervention, with 6 of them being not significant after deblending.

(Ⅱ) We compare our catalog with the Chandra CDF-N catalog (X16), and find a total of 33 matches, the fluxes of which agree well above the detection limit. We flag the 9 unmatched sources as being spurious but conserve them in the catalog.

(Ⅲ) The flux limits are significantly lower in the NuSTAR CDF-N field (having deeper exposures) than that in the NuSTAR E-CDF-S field.

Our source-detection method provides a systematic approach for source cataloging in other NuSTAR extragalactic surveys. We make our NuSTAR E-CDF-S and CDF-N source catalogs publicly available (see Appendix for catalog description), which provide a uniform platform that facilitates further studies involving these two fields.