The 7-year MAXI/GSC X-Ray Source Catalog in the High Galactic Latitude Sky (3MAXI)

We analyze the MAXI/GSC event data from 2009 August 13 to 2016 July 31 provided by RIKEN (rev. 1.8),¹⁴ focusing on those at high Galactic latitudes ($| b| \gt 10^\circ$). The same data-screening criteria as adopted by Hori et al. (2018; see their Section 2) are applied. We exclude the data taken with four GSCs (GSC3, GSC6, GSC9, and GSCa) out of all 12 GSCs from the analysis. GSC6, GSC9, and GSCa were operated only for <1 yr, which is too short to establish a reliable background model (see below). The GSC3 data are highly contaminated by background counts owing to defects of the veto counters (Sugizaki et al. 2011), and they are also subject to large calibration uncertainties in the position determination. Apart from them, the GSC0 data since 2013 June 15 are not used because they are affected by gas leakage. We select the 4–10 keV band for source detection by considering the high quantum efficiency and low background rate (Mihara et al. 2011).

Here we summarize main differences of the third MAXI/GSC high Galactic latitude catalog compared with the second one (Hiroi et al. 2013). A major advantage is the increased photon statistics (37 months to 84 months). Others are improved calibration of the background (the non-X-ray background plus the cosmic X-ray background) and the point-spread function (PSF), as detailed in Hori et al. (2018). These are key components in our image analysis (Section 2.2.1). It was found that the background event rates well correlate with the rates of simultaneous events in the carbon-anode cells and the tungsten-anode cells for particle veto (i.e., VC-counts; Mihara et al. 2011; Sugizaki et al. 2011). This correlation was already used to reproduce the background events in Hiroi et al. (2013). In the new background model, we also take into account the direction of movement of the ISS with respect to the Earth (to the north or south), on which the background-to-VC-count correlation is found to largely depend (see Figure 2 of Shidatsu et al. 2017b; Hori et al. 2018). In return, the 10–20 keV data can now be reliably utilized, which were not analyzed in the previous work. Also, an updated PSF database as a function of energy and detector position of each counter (see the Appendix of Hori et al. 2018) is implemented to the MAXI event simulator, "maxisim"(Eguchi et al. 2009).

Here we briefly describe the image analysis for source detection, which is essentially the same as that adopted in Hiroi et al. (2013). In the event files, each photon has information of sky position (RA and decl.), which is converted from an estimated position in the detector along the anode direction and the pointed direction of the collimator at the detected time. We first divide the all-sky image into 768 tangentially projected images of 140 × 140 size (binned by 01 × 01), whose central coordinates are determined by the HEALPix system (Górski et al. 2005). Then, we apply the processes described in the following subsections to each projected image. This consists of two steps: (1) making a tentative source-candidate list based on simple photon statistics, and (2) determining the flux, significance, and position by image fitting with a model composed of the background and PSFs. To model the background image, we produce simulated background events that have 10 times more counts than those of real data, using the MAXI/GSC background generator (Eguchi et al. 2009).

2.2.1. Source Finding

2.2.2. Image Fit

The PSFs for the source candidates are constructed from simulated photon events produced by the MAXI simulator (Eguchi et al. 2009) with exactly the same observing conditions as for the real data. We assume a point source having the same spectrum as the Crab Nebula. Throughout this paper, we assume that the Crab Nebula has a power law with a photon index of 2.1 and a normalization of 10 photons cm⁻² s⁻¹ keV⁻¹ at 1 keV, absorbed with a hydrogen column density of 2.6 × 10²¹ cm⁻². The fluxes are 3.96 × 10⁻⁹ erg cm⁻² s⁻¹, 1.21 × 10⁻⁸ erg cm⁻² s⁻¹, 8.51 × 10⁻⁹ erg cm⁻² s⁻¹, and 1.61 × 10⁻⁸ erg cm⁻² s⁻¹ in the 3–4 keV, 4–10 keV, 10–20 keV, and 3–10 keV bands, respectively, which correspond to "1 Crab."

Then, we fit the PSF and background models to the real image. Here we restrict the fitting region to an inner 110 × 110 area, because the outer region may be affected by sources located just outside the edge of the 140 × 140 region. The fluxes and peak positions of the PSFs and the normalization of the background are left as free parameters. We determine these parameters by the Poisson maximum likelihood (ML) algorithm (C-statistics), using the MINUIT software package. The likelihood function is defined as

$$\begin{eqnarray}&&C\equiv 2\displaystyle \sum _{i,j}{ \mathcal L }(i,j),\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray*}&&\begin{array}{l}{ \mathcal L }(i,j)\\ =\,\left\{\begin{array}{ll}M(i,j)-D(i,j)+D(i,j)\{\mathrm{ln}D(i,j)-\mathrm{ln}M(i,j)\} & \\ & ({D}_{i,j}\gt 0)\\ M(i,j) & ({D}_{i,j}=0).\end{array}\right.\end{array}\end{eqnarray*}$$

The observed data and model at the (i, j) bin are denoted with D(i, j) and M(i, j), respectively. The 1σ statistical error of each parameter is estimated by finding a value when the likelihood function (C) is increased from its minimum by unity. The detection significance is defined as (best-fit flux)/(its lower-side 1σ error). We confirm that the lower- and upper-side errors are generally consistent with each other. This is expected because the number of counts is large enough to follow a Gaussian distribution. Since we measure a relative count rate to that that would be expected from the Crab Nebula spectrum, the flux is given in "Crab" units.

2.2.3. Iteration of Source Finding and Image Fit

We detect 682 sources with 4–10 keV detection significances of s_{D,4–10 keV} ≥ 6.5 at high Galactic latitudes ($| b| \gt 10^\circ$). Table 1 gives our source catalog. Considering the improved calibration of the background and PSF models (Section 2.1), and following the 7-year "low" Galactic latitude catalog (Hori et al. 2018), we have decided to lower the detection threshold from s_{D,4–10 keV} ≥ 7, which was adopted in the 37-month catalog (Hiroi et al. 2013), to s_{D,4–10 keV} ≥ 6.5 in our new catalog. The number of the cataloged sources increases by a factor of ≈1.4 compared with Hiroi et al. (2013), where 500 sources were listed. If the same threshold of s_{D,4–10 keV} ≥ 7 as in Hiroi et al. (2013) is adopted, the source number of our catalog becomes 615. The counterpart candidate is listed in Table 2, as detailed in Section 4.1. The sensitivity limit achieved for 50% of the survey area is ∼0.48 mCrab, or ∼5.9 × 10⁻¹² erg cm⁻² s⁻¹ (Section 5.3). Figure 1 shows the distribution of the flux and detection significance in the 4–10 keV band, as well as their correlation. Figure 2 plots the statistical errors in the position (1σ_stat) against the detection significance. The spatial distribution in the Galactic coordinates is shown in Figure 3. The classification of sources in this figure is detailed in Section 4.1.

Table 1.  X-Ray Properties of Sources in the Third MAXI/GSC Catalog

No.	3MAXI	R.A.	Decl.	σstat	sD,4–10keV	f4–10keV	sD,3–4keV	f3–4keV	sD,10–20keV	f10–20keV	f3–10keV	HR1	HR2	HR3	TSvar	${\sigma }_{\mathrm{rms}}^{2}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)	(16)	(17)
1	J0001−684	0.251	−68.463	0.215	11.1	7.74 ± 0.70	9.8	2.19 ± 0.23	1.2	3.00 ± 2.60	9.93 ± 0.74	0.07 ± 0.07	−0.29 ± 0.40	−0.27 ± 0.40	2.29	−0.045 ± 0.037
2	J0004−348	1.037	−34.897	0.161	7.8	7.36 ± 0.94	11.2	2.87 ± 0.26	2.0	6.67 ± 3.41	10.23 ± 0.98	−0.09 ± 0.08	0.13 ± 0.26	0.10 ± 0.26	4.98	−0.047 ± 0.059
3	J0006+727	1.602	72.742	0.097	12.5	10.39 ± 0.83	16.1	4.36 ± 0.27	1.8	5.94 ± 3.25	14.75 ± 0.87	−0.12 ± 0.05	−0.10 ± 0.27	−0.14 ± 0.27	10.26	0.043 ± 0.054
4	J0009+109	2.462	10.938	0.146	9.5	8.53 ± 0.90	7.9	2.10 ± 0.27	4.5	15.75 ± 3.48	10.63 ± 0.94	0.14 ± 0.08	0.45 ± 0.10	0.47 ± 0.09	14.78	0.067 ± 0.069
5	J0010+323	2.621	32.390	0.177	7.3	7.63 ± 1.04	8.4	2.58 ± 0.31	⋯	0.39(<4.49)	10.21 ± 1.09	−0.02 ± 0.09	−0.86 ± 1.33	−0.86 ± 1.32	5.64	−0.071 ± 0.080
6	J0011−113	2.804	−11.311	0.089	12.7	10.24 ± 0.81	10.7	2.48 ± 0.23	⋯	0.58(<3.69)	12.72 ± 0.84	0.15 ± 0.06	−0.85 ± 0.74	−0.84 ± 0.78	8.93	0.009 ± 0.030
7	J0011−292	2.962	−29.231	0.137	9.6	8.02 ± 0.84	12.1	2.93 ± 0.24	2.1	6.83 ± 3.28	10.95 ± 0.87	−0.06 ± 0.07	0.10 ± 0.24	0.08 ± 0.24	9.36	0.034 ± 0.066
8	J0012−313	3.132	−31.351	0.235	7.6	6.46 ± 0.85	5.5	1.32 ± 0.24	2.6	8.49 ± 3.29	7.78 ± 0.88	0.23 ± 0.11	0.30 ± 0.19	0.35 ± 0.18	6.98	−0.020 ± 0.061
9	J0012−154	3.139	−15.433	0.177	7.2	5.60 ± 0.78	9.7	2.16 ± 0.22	1.5	4.60 ± 3.06	7.76 ± 0.81	−0.08 ± 0.09	0.08 ± 0.34	0.06 ± 0.34	6.81	−0.038 ± 0.097
10	J0016−825	4.145	−82.587	0.171	7.2	5.29 ± 0.73	3.4	0.82 ± 0.24	2.2	5.49 ± 2.48	6.11 ± 0.77	0.36 ± 0.14	0.19 ± 0.23	0.26 ± 0.22	5.02	−0.072 ± 0.087
11	J0021+286	5.319	28.601	0.119	10.1	9.92 ± 0.98	8.9	2.58 ± 0.29	2.0	7.94 ± 3.92	12.50 ± 1.02	0.11 ± 0.07	0.07 ± 0.25	0.09 ± 0.25	10.20	0.076 ± 0.075
12	J0022−193	5.733	−19.356	0.150	10.6	8.25 ± 0.78	10.5	2.39 ± 0.23	3.7	11.66 ± 3.12	10.64 ± 0.81	0.06 ± 0.07	0.34 ± 0.13	0.35 ± 0.12	5.37	−0.034 ± 0.041
13	J0027+075	6.762	7.597	0.193	7.4	6.51 ± 0.88	2.9	0.74 ± 0.25	⋯	1.00(<4.30)	7.25 ± 0.91	0.48 ± 0.14	−0.64 ± 0.97	−0.59 ± 1.08	9.65	0.024 ± 0.098
14	J0029+127	7.269	12.736	0.206	7.7	7.09 ± 0.93	5.6	1.50 ± 0.27	2.8	10.05 ± 3.58	8.59 ± 0.97	0.21 ± 0.11	0.34 ± 0.17	0.38 ± 0.16	4.48	−0.059 ± 0.075
15	J0035−791	8.974	−79.178	0.121	13.0	8.83 ± 0.68	13.4	3.03 ± 0.23	3.8	9.19 ± 2.38	11.86 ± 0.72	−0.02 ± 0.05	0.19 ± 0.13	0.19 ± 0.13	24.40	0.092 ± 0.057
16	J0039+231	9.850	23.117	0.170	6.6	6.02 ± 0.92	4.3	1.21 ± 0.27	2.4	8.45 ± 3.55	7.23 ± 0.96	0.24 ± 0.13	0.33 ± 0.20	0.38 ± 0.19	3.41	−0.090 ± 0.089
17	J0041−093	10.455	−9.318	0.026	54.1	46.94 ± 0.87	54.2	15.02 ± 0.28	7.2	22.56 ± 3.12	61.96 ± 0.91	0.01 ± 0.01	−0.19 ± 0.07	−0.18 ± 0.07	7.99	−0.000 ± 0.002
18	J0042+412	10.668	41.238	0.044	31.6	36.63 ± 1.16	32.4	11.97 ± 0.37	4.6	19.84 ± 4.30	48.60 ± 1.22	0.00 ± 0.02	−0.13 ± 0.11	−0.13 ± 0.11	6.38	−0.004 ± 0.005
19	J0048+319	12.051	31.900	0.057	20.4	21.47 ± 1.05	7.9	2.42 ± 0.31	6.0	24.01 ± 4.04	23.89 ± 1.09	0.49 ± 0.05	0.23 ± 0.08	0.31 ± 0.08	15.54	0.009 ± 0.014
20	J0048−732	12.057	−73.205	0.094	14.6	17.22 ± 1.92	13.9	3.71 ± 0.27	3.9	11.07 ± 2.83	20.93 ± 1.94	0.21 ± 0.06	−0.04 ± 0.14	−0.00 ± 0.14	47.97	0.227 ± 0.096

Note. Column (1): source number. Column (2): MAXI name determined from the source coordinates. Columns (3)–(4): R.A. and decl. in units of degrees. Column (5): 1σ statistical error of the position in units of degrees. Note that the systematic error is not taken into consideration. Columns (6)–(7), (8)–(9), and (10)–(11): detection significance and 7-year averaged flux in units of 10⁻¹² erg cm⁻² s⁻¹ for each energy band. When a 1σ error is larger than the best-fit value, the 1σ upper limit is represented. The conversion factor from Crab units into erg cm⁻² s⁻¹ units in the 4–10 keV, 3–4 keV, and 10–20 keV bands is 1.21 × 10⁻¹¹ erg cm⁻² s⁻¹ mCrab⁻¹, 3.96 × 10⁻¹² erg cm⁻² s⁻¹ mCrab⁻¹, and 8.51 × 10⁻¹² erg cm⁻² s⁻¹ mCrab⁻¹, respectively. Column (12): the flux in the 3–10 keV band. Note that the factor of 1.61 × 10⁻¹¹ erg cm⁻² s⁻¹ mCrab⁻¹ is usable for the conversion. Column (13): hardness ratios calculated from the fluxes in the 3–4 keV and 4–10 keV bands. Note that they are derived from the flux in units of Crab. Columns (14)–(15): same as Column (13), but for the 4–10 keV and 10–20 keV bands and the 3–10 keV and 10–20 keV bands. Column (16): time variability index (see the text for the definition). The hypothesis that the flux does not vary can be ruled out for TS_var > 18.48 at the 99% confidence level. Column (17): excess variance.

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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2.3.1. Spurious Source Fraction

2.3.2. Hardness Ratios

To calculate HRs of the detected sources, we determine the fluxes in the 3–4 keV and 10–20 keV bands in the following way. Tangentially projected images in these bands are produced from the event files. We prepare the input source list for the image fit from our catalog produced above. For completeness, here we also include the source candidates whose detection significances were less than 6.5σ in the 4–10 keV band. We then perform an image fit to the image in the 3–4 keV or 10–20 keV band using this source list. During the fitting process, the positions are fixed at those determined in the 4–10 keV band. This process is repeated by adding new source candidates found in the smoothed residual map with nominal significances (see Section 2.2.1) above 5.5σ. Eventually, we find no new sources detected with significances above 6.5σ in the 3–4 keV or 10–20 keV band but not included in the above catalog based on the 4–10 keV band survey. The 3–10 keV fluxes are also calculated from the 3–4 keV and 4–10 keV fluxes obtained above by assuming the Crab-like spectrum. We define the HR as

$$\begin{eqnarray}&&\mathrm{HR}=\displaystyle \frac{{f}_{{\rm{H}}}-{f}_{{\rm{S}}}}{{f}_{{\rm{H}}}+{f}_{{\rm{S}}}},\end{eqnarray} \tag{ 2 }$$

where f_H and f_S correspond to the hard- and soft-band fluxes, respectively, in Crab units. The catalog lists three HRs: HR1 (3–4 keV, 4–10 keV), HR2 (4–10 keV, 10–20 keV), and HR3 (3–10 keV, 10–20 keV).

To deduce the spectral shape from the HRs, we calculate the relation between the HRs and spectra parameters by assuming an absorbed power-law model. The parameters are a photon index (Γ) and an intrinsic hydrogen column density (N_H). We also take into account a representative Galactic absorption of ${N}_{{\rm{H}}}^{\mathrm{Gal}}=2.5\,\times {10}^{20}$ cm⁻² in addition to the intrinsic one. This column density roughly corresponds to the minimum value over the high Galactic latitude sky ($| b| \gt 10^\circ ;$ Daltabuit & Meyer 1972) and should be considered as a lower limit for extragalactic objects. We confirmed, however, that the spatial variation in the total Galactic column (${N}_{{\rm{H}}}^{\mathrm{Gal}}\lt 2\times {10}^{21}$ cm⁻² for $| b| \gt 10^\circ$) has little effect on the following results. The source redshift is not considered for simplicity. We generate, through the MAXI on-demand tool,¹⁵ the 7-year averaged MAXI/GSC response file and calculate the predicted count rates in these bands for given spectral parameters. We consider two cases: a power-law model with and without an intrinsic absorption. The Galactic absorption is taken into account in both cases. In the former case, we fix Γ = 1.8 and vary log N_H/cm⁻² in a range of 20–24, whereas in the latter case, we fix N_H = 0 and vary Γ in a range of 1–3. The results are plotted in the left panels of Figure 4. We also calculate the conversion factors from the flux in Crab units to that in the CGS system (erg cm⁻² s⁻¹), which are presented in the right panels of Figure 4. For an unabsorbed power law with Γ = 1.8, HR1 = 0.0749, HR2 = 0.115, and HR3 = 0.136, and the conversion factors are 4.00 × 10⁻¹² erg cm⁻² s⁻¹ mCrab⁻¹, 1.24 × 10⁻¹¹ erg cm⁻² s⁻¹ mCrab⁻¹, 1.65 × 10⁻¹¹ erg cm⁻² s⁻¹ mCrab⁻¹, and 8.74 × 10⁻¹² erg cm⁻² s⁻¹ mCrab⁻¹ in the 3–4 keV, 4–10 keV, 10–20 keV, and 3–10 keV bands, respectively.

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Flux variability provides us with a key to deduce the nature of X-ray sources; for example, we can use the fact that many compact objects (e.g., X-ray binaries and AGNs) are transients, whereas extended sources like galaxy clusters are more persistent.

Here we produce the 4–10 keV light curves in 1-year binning. We split the real, background, and PSF data used in the catalog construction into each year and perform image fitting for each time-sliced data set. We adopt the same observation period as those in the catalog construction, and therefore the time bins in 2009 and 2016 have smaller sizes than the other bins. In addition to the cataloged sources, there may be transient sources that can be detected at significances above 6.5σ in a 1-year image but not in the 7-year accumulated data. Thus, we systematically search for such sources (see Section 3.2) and incorporate their PSFs in the image fitting. The positions of the cataloged sources are fixed at those determined from the whole 7-year data, while the positions of the newly detected transients are at those determined in the time bin where their detection significances are the highest. Then, we construct the light curves of the individual sources by fitting the normalizations of their PSFs and the background model.

In addition to the statistical flux errors, we derive the systematic error, which may remain because we do not consider possible time variation of the PSF profile in our PSF database. We simply determine the systematic error so that the Crab light curve is consistent with 1 Crab over the 7 years. This is a conservative way to estimate the systematic errors, since the X-ray flux of Crab is not perfectly constant (Wilson-Hodge et al. 2011) and its variability is included in the estimation. As shown in the left panel of Figure 5, adding 1.4% error is found to be sufficient. This value is taken into account in all the light curves as the systematic errors. This systematic uncertainty is comparable to that derived in Hori et al. (2018), 1.6%, and much reduced compared with that in the 37-month data (∼10%; Hiroi et al. 2013; Kawamuro et al. 2016a). This improvement can be ascribed to the sophisticated PSF model. Among the light curves (Figure 6), we present, as an interesting case, the NGC 1365 (AGN) one in the right panel of Figure 5, which shows the strong variability by a factor of ∼5 within the 7-year. Individual light-curve plots and full light-curve data are published in an online tar.gz supplement.

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We characterize the light curves in two steps. First, to statistically examine whether a light curve is constant or varies, we adopt a likelihood-based method as used in Nolan et al. (2012). This is more appropriate than the simple least chi-squared method when the photon statistics follow the Poisson distribution, and therefore it can be used for faint sources as well as for bright ones. We calculate a test statistic defined as

$$\begin{eqnarray}&&{\mathrm{TS}}_{\mathrm{var}}=2\displaystyle \sum _{i}\displaystyle \frac{{\rm{\Delta }}{F}_{i}^{2}}{{\rm{\Delta }}{F}_{i}^{2}+{f}^{2}{F}_{\mathrm{const}}^{2}}[\mathrm{log}{{ \mathcal L }}_{i}^{{\prime} }({F}_{i})-\mathrm{log}{{ \mathcal L }}_{i}^{{\prime} }({F}_{\mathrm{const}})],\end{eqnarray} \tag{ 3 }$$

where F_i, ΔF_i, F_const, and f denote the best-fit flux, statistical uncertainty, 7-year averaged flux, and systematic error (i.e., 1.4%), respectively, at the ith time bin. TS_var follows the chi-squared distribution when the number of bins is large. If TS_var > 18.48, we can reject the null hypothesis that the flux is constant at the 99% confidence level for 7 degrees of freedom. Next, we derive the excess variance (${\sigma }_{\mathrm{rms}}^{2}$) following Vaughan et al. (2003), or Equations (3) and (4) in Hori et al. (2018), to investigate the strength of flux variations. TS_var and σ_rms are listed in Table 1.

We systematically search for transient events that are missed in the catalog based on the 7-year integrated images. First, we create the significance maps in the individual years in the same manner as described in Section 2.2.1, using the best-fit model only including the cataloged sources. We then identify residuals with nominal significances above 5.5σ as the candidates of transients. Then, we perform the image fitting by including their PSFs in the model in addition to those of the catalog sources. Four transient sources are found to show significances of s_{D,4–10 keV} ≥ 6.5 in a time bin. Table 3 and Figure 7 present their X-ray properties and the light curves, respectively. Their coordinates are estimated from a period where the source shows the highest significance among all the time bins. Note that circular regions with a 3° radius around the very bright sources Sco X-1, Cyg X-2, and the Crab Nebula are excluded from this analysis to avoid fake source detection due to systematic errors in the PSF calibration.

Table 3.  Properties of Transient Events

	MAXI								Counterpart
No.	3MAXIt	R.A.	Decl.	σstat	sD,4–10keV	f4–10keV	TSvar	${\sigma }_{\mathrm{rms}}^{2}$	Name	R.A.	Decl.	z	Type
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)
1	J0051−735	12.954	−73.562	0.080	11.7	48.4 ± 2.8	1721.87	5.395 ± 0.782	RX J0052.1−7319	13.058	−73.322	⋯	HMXB
2	J0912−649	138.047	−64.911	0.060	20.8	72.3 ± 3.5	3486.07	5.652 ± 0.329	MAXI J0911−655	138.010	−64.868	⋯	millisecond X-ray pulsar
3	J1257+014	194.471	1.489	0.118	9.4	18.6 ± 1.9	367.453	3.253 ± 0.849	NGC 4845	194.505	1.576	0.004110	Sy2/tidal disruption event
4	J1357−095	209.257	−9.509	0.139	13.6	25.5 ± 1.8	758.631	5.708 ± 0.835	Swift J1357.2−0933	209.320	−9.544	⋯	LMXB

Note. Column (1): source number. Column (2): MAXI transient source name. Columns (3)–(4): R.A. and decl. in units of degrees. Column (5): 1σ statistical error of the position in units of degrees. Note that the systematic error is not taken into consideration. Columns (6)–(7): detection significance and flux in units of 10⁻¹² erg cm⁻² s⁻¹. Column (8): time variability index (see the text for the definition). Column (9): excess variance. Columns (10)–(14): available information of the counterpart (name, R.A. and decl. in units of degrees, redshift, and source type), which is based on the Swift/BAT Hard X-ray Transient Monitor catalog (https://swift.gsfc.nasa.gov/results/transients/). The data file of the light curves is available from the online supplementary tar.gz file.

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Identification of the X-ray sources is an important task for the statistical use of the catalog. To find possible counterparts of our catalog sources including the transients (hereafter we call them "the third MAXI sources"), we spatially cross-match them to those in other X-ray catalogs in the following order: the Swift/BAT 105-month catalog (BAT105; Oh et al. 2018), the Uhuru fourth catalog (4U; Forman et al. 1978), the RXTE All-Sky Monitor long-term observed source table (XTEASMLONG¹⁶ ), Meta-Catalog of X-Ray Detected Clusters of Galaxies (MCXC; Piffaretti et al. 2011), the XMM-Newton slew survey catalog (XMMSL2¹⁷ ), and the ROSAT all-sky survey bright source catalog (1RXS; Voges et al. 1999). To reduce false identifications, we only take account of XMMSL2 and 1RXS sources brighter than >1.0 × 10⁻¹² erg cm⁻¹ s⁻¹ and >0.30 counts s⁻¹, respectively. This is a flux corresponding to 0.3 mCrab when the Crab spectrum is assumed. The statistical positional errors of the third MAXI sources (σ_stat) are evaluated as $\sqrt{{{dx}}^{2}+{{dy}}^{2}}$, where dx and dy are one-dimensional spatial errors in perpendicular directions at the 1σ level. A systematic error (σ_sys) is further added to the statistical ones as ${\sigma }_{\mathrm{pos}}=\sqrt{{\sigma }_{\mathrm{stat}}^{2}+{\sigma }_{\mathrm{sys}}^{2}}$. We adopt σ_sys = 003, determined to self-consistently match the cross-matching result (see Section 4.3 and Figure 8). Here, we identify a counterpart if its position falls within 2.5σ_pos of a third MAXI source. Using several representative sources, we have verified that the radius of 2.5σ_stat typically corresponds to that of the 95% confidence contour for the source positions where the C value in Equation (1) is increased from the best value by 6.0. The positional errors in the reference catalogs are ignored. Note that if we find more than one source as counterpart candidates, we list the object nearest to the MAXI position. The cross-matching result is summarized in Table 2, and the numbers of the positionally matched MAXI sources are listed in Table 4. The breakdown of the source types is seen in Table 5. The counterparts of the transients (Section 3.2) are also identified from the Swift/BAT Hard X-ray Transient Monitor catalog¹⁸ in the same manner, but with the 3.0σ positional errors, because the probability of false matching is much lower than in the other cases (see Section 4.2).

In some cases, we suspect that a matched counterpart is likely incorrect, judging from the X-ray properties (i.e., the time variability, HRs, and observed fluxes). Also, some bright galaxy clusters are not identified from the automatic cross-matching. This could be because our PSF model is developed so that it reproduces a point source and would not properly fit such extended sources. More plausible counterparts for them are listed in the catalog, with the associated comments in Column (9).

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The above cross-matching is based only on the separation angles between the MAXI and other reference sources, and some counterparts are incorrectly identified because they just coincidentally fall within the positional error of a third MAXI source. We derive the expected number of such events by combining integrated positional errors of the MAXI sources used for each cross-matching and source number densities (i.e., source number divided by our survey area) of the reference catalogs. We find that 10, 1, 2, 11, 11, and 7 MAXI sources may be misidentified in referring to BAT105, 4U, XTEASMLONG, MCXC, XMMSL2, and 1RXS, respectively. Note that due to the incomplete all-sky survey of XMMSL2, its derived value should be regarded as a lower limit. If we use only MCXC and Swift/BAT 105-month catalogs, similarly to the case of Hiroi et al. (2013), who used MCXC and the Swift/BAT 70-month catalog (Baumgartner et al. 2013), the expected fraction of the false identification is ∼0.03. This remains at the same level as in the 37-month catalog, in spite of the increased source number in the 7-year MAXI and Swift/BAT 105-month catalogs. This small value is likely because the systematic errors of the PSF model are reduced in our catalog.

Using the results in Section 4.1, we examine the separation angles between the MAXI sources and their possible counterparts as a function of the detection significance (s_{D,4–10 keV}). Figure 8 plots the 90% confidence limit of the separation angles, estimated in each significance bin. For consistency, we fit the data with the same equation as that in Hiroi et al. (2013), $\sqrt{{(A/{s}_{{\rm{D}},4\mbox{--}10\mathrm{keV}})}^{B}+{C}^{2}}$. The best-fit parameters are A = 2.27 ± 0.05, B = 1.74 ± 0.02, and C = 0.047 ± 0.001, suggesting the systematic error at a 90% confidence limit of ≈0047. The corresponding 1σ error is ∼003. The systematic error is successfully reduced from the previous works (≈005; Hiroi et al. 2011, 2013).

In this section, we describe basic properties of our catalog based on the parameters constrained so far: the fluxes, the HRs, and the time variability index (TS_var). Here, we simply categorize the third MAXI sources into four types: AGN (i.e., Seyfert galaxies and blazars), galaxy cluster, Galactic/Small/Large Magellanic Cloud (SMC/LMC) source (i.e., cataclysmic variables/stars, X-ray binaries, and pulsars), and the others. The HR distributions are shown in Figure 9, and the scatter plots between the HRs and the 4–10 keV fluxes are shown in Figure 10. A noticeable point is that the HRs of AGNs are typically harder than those of the galaxy clusters. The difference is more clearly seen in the HRs using the 10–20 keV band. This is likely to be a natural consequence of the difference in their typical spectra; galaxy clusters are bright in soft X-ray bands by optically thin thermal emission, whereas AGNs exhibit harder spectral profiles, roughly described with a power-law component with a photon index of ∼1.4–2.4 (e.g., Ueda et al. 2014; Kawamuro et al. 2016b). Strong absorption, often seen in AGNs, hardens their spectrum even more, and thereby higher HRs are expected. A more detailed view can be obtained from X-ray color–color plots in Figure 11, which overplots HR tracks predicted from a single (absorbed) power-law model based on Figure 4.

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Figure 12 shows the histogram of the time variability index (TS_var) and its scatter plot against the 4–10 keV flux. Also, Figure 13 plots the HRs with respect to TS_var. Most of the galaxy clusters have no significant flux variation, with TS_var < 18.48, but there are two exceptions showing moderate TS_var values of ≈30. One is 3MAXI J1231+122, identified as the Virgo Cluster, and this apparent variability may be due to uncertainties associated with our PSF model, which assumes a point source, and/or the presence of an AGN in M87 (Wong et al. 2017). The other source, 3MAXI J1702+339, is located near the bright, variable source Her X-1, and part of its flux could be contaminated by Her X-1, causing the fake variability.

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Here we briefly view the nature of the third MAXI sources that have a single counterpart in the BAT105. Figure 14 plots the correlation between the 4–10 keV and 14–195 keV fluxes, together with the flux ratios predicted from unabsorbed power-law models with three different photon indices (Γ = 1.7, 2.0, and 2.5). Note that we use the 4–10 keV fluxes estimated through the conversion factor of 1.21 × 10⁻¹¹ erg cm⁻² s⁻¹ mCrab⁻¹, while the 14–195 keV fluxes are retrieved from Oh et al. (2018). As seen in Figure 14, most of the MAXI sources have soft spectra, corresponding to photon indices larger than 1.7.

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We present the log N–log S relation, the cumulative flux distributions of the sources detected at s_{D,4–10 keV} ≥ 6.5. To derive it, we estimate the sensitivity at every sky position by combining the background counts and the effective exposure map, given in Figure 1 of Hori et al. (2018). The effective exposure map, in units of cm² s, is estimated via simulation of the cosmic X-ray background, with uniform brightness (see Hori et al. 2018, for more details). The survey area as a function of the sensitivity (i.e., the area curve) is displayed in the top panel of Figure 15. From this curve, we can find that our survey is complete, in half of the high Galactic latitude sky ($| b| \gt 10^\circ$), down to 5.9 × 10⁻¹² erg cm⁻² s⁻¹, superior to the 37-month catalog (i.e., 7.5 × 10⁻¹² erg cm⁻² s⁻¹; Hiroi et al. 2013). The deepest sensitivity of ∼4 × 10⁻¹² erg cm⁻² s⁻¹ is consistent with the lowest flux among the actually detected sources.

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We divide the number of sources with fluxes of S ∼ S + dS by the survey area at S and obtain the log N–log S relation in the differential form. By integrating it, we obtain the number density N (>S) of total sources having fluxes above S (bottom panel of Figure 15). At fluxes lower than 8 × 10⁻¹¹ ergs cm⁻² s⁻¹, the log N–log S relation has a slightly steeper slope than that expected for sources uniformly distributed in a static Euclidean universe (i.e., N (>S) ∝ S^−1.5). This may be partially caused by the Eddington bias (i.e., fainter sources than the sensitivity limit emerge owing to statistical fluctuation).