CLASSIFICATION OF X-RAY SOURCES IN THE XMM-NEWTON SERENDIPITOUS SOURCE CATALOG

The 2XMMi-DR3 catalog is based on 4953 pointed observations. These observations have a variety of modes of data acquisition, exposures (>1000 s), and optical blocking filters (thick, medium, and thin). The catalog contains detections in five basic individual energy bands (0.2–0.5, 0.5–1.0, 1.0–2.0, 2.0–4.5, and 4.5–12.0 keV, numbered 1–5, respectively), for each European Photon Imaging Camera (EPIC), i.e., pn, MOS1/M1, and MOS2/M2 (Jansen et al. 2001; Strüder et al. 2001; Turner et al. 2001). Results are also given for various combinations of energy bands and cameras. Band 8 refers to the total band 0.2–12.0 keV, and EPIC/EP refers to all cameras. We also follow these notations throughout this paper.

We focused only on point sources with multiple XMM-Newton observations and at least one detection with the signal-to-noise ratio S/N ⩾ 20 in this paper. We considered only point sources because extended sources (typically Galactic supernova remnants (SNRs) and galaxy clusters) tend to be subject to complicated problems of source detection and flux measurement (Watson et al. 2009). We define a source to be point-like when its extent (EP_EXTENT in the catalog) is zero (at least in one detection). We note that in the pipeline, if the extent radius in a detection is <6'', it is set to zero, i.e., a point source is assumed. We estimated the S/N using EP_8_CTS/EP_8_CTS_ERR, where EP_8_CTS, given in the catalog, is the total counts summed over all cameras, and EP_8_CTS_ERR is its error. Our requirement of having at least one detection with S/N ⩾ 20 is to ensure at least one good spectrum for detailed analysis when needed. The requirement of having multiple observations allows us to calculate the long-term variability. It is different from the requirement of having multiple detections. The catalog includes only detections with a total likelihood (from all bands and all cameras) >6 (corresponding to about 3σ). We used the FLIX service⁴ to find the observations of a source and estimate the fluxes for the observations that have no entries in the catalog.

There are 5802 sources satisfying the above conditions. However, as the catalog was produced using an automated procedure, some of these sources suffer from various kinds of problems, and we excluded them based on visual inspection. About 16% are spurious, mostly due to single reflections caused by bright sources outside the field of view, out-of-time events, and extremely bright sources (Watson et al. 2009). We also excluded about 8% of the sources that are detected within bright extended sources, especially SNRs, though they pass the above criteria. About 2% of the sources are finally excluded due to problems such as optical loading, serious event pileup, and being too close to other bright sources.

In the catalog, each source has a unique source number (SRCID in the catalog). However, from visual inspection, we still found 42 sources assigned with multiple SRCID numbers (Table 1). Each source will be referred to using the first number in Table 1, but its detections consist of all the detections corresponding to the different SRCID numbers (Table 3). In the end, we have 4330 unique sources in our sample (Table 4).

The 2XMMi-DR3 catalog provides the count rates and fluxes of each detection for various combinations (individual and total bands/cameras). The count rates were corrected for various instrumental effects including the mirror vignetting, detector efficiency, and point-spread function losses. The fluxes in individual energy bands were calculated by dividing the count rates by the energy conversion factors (ECFs). The ECFs depend on the camera, the filter, and the source spectrum, which the catalog assumed to be an absorbed power law (PL) with a photon index of Γ_PL = 1.7 and an absorption column density of N_H = 3 × 10²⁰ cm⁻² (Watson et al. 2009). The ECFs used in the catalog were based on the calibration before 2008, except for a few observations. We applied correction factors provided on the catalog Web site to obtain fluxes corresponding to the newer calibration. In this paper, we mostly used the EPIC fluxes in 0.2–12.0 keV (band 8) and 0.2–4.5 keV (called band 14 hereafter). They were obtained by first summing the fluxes in the relevant individual bands and then averaging over the available cameras weighted by the errors. We estimated their systematic errors to be 0.107 and 0.074, respectively (Appendix A).

We also calculated four X-ray hardness ratios HR1–HR4 defined as

$$\begin{equation} {\rm HR}i=(R_{i+1}-R_i)/(R_{i+1}+R_i), \end{equation} \tag{ 1 }$$

where R_i and R_{i + 1} are the MOS1-medium-filter equivalent count rates in the energy bands i and i + 1, respectively. These count rates were obtained by multiplying the EPIC fluxes by the ECFs for the MOS1 camera with the medium filter. We note that the 2XMMi-DR3 catalog also provides the camera-specific X-ray hardness ratios, but the count rates used, and thus the hardness ratios, depend on the camera and the filter. This poses a problem to use the hardness ratios to investigate the source spectral shape uniformly, considering that the observations used to create the catalog have various filters and available cameras. Our hardness ratios are less subject to this problem, as the fluxes have been calculated to mitigate their dependence on the camera and filter by using the camera- and filter-dependent ECFs. We only observed small systematic differences between the pn and MOS hardness ratios using our definition (Appendix A).

The variability properties can provide important clues about the source type. There are many kinds of variability. For the short-term variability that can be measured within a single observation, we paid attention to stellar X-ray flares, which are good indicators of coronally active stars (Güdel 2004). They show a variety of profiles, though most of them have a fast rise and a slow decay and can last from minutes to hours. The light curves created for bright detections by the pipeline are suitable for stellar X-ray flare search. They are extracted from a circular region of radius 28'' and have bin sizes an integer multiple of 10 s (the minimum is 10 s), depending on the source intensity (Watson et al. 2009). We describe our search for stellar X-ray flares in Appendix B.

We also measured the long-term flux variability over different observations. Both bands 14 and 8 were used, but we will explore results with band 14 in more detail because the flux in band 5 (4.5–12.0 keV) tends to have large uncertainties. We defined the long-term flux variability as V_var = F_max/F_min and the significance of the difference as

$$\begin{equation} S_{\rm var}=\frac{F_{\rm max}-F_{\rm min}}{ \big(\sigma _{\rm max}^2+\sigma _{\rm min}^2+(rF_{\rm max})^2+(rF_{\rm min})^2 \big)^{1/2}}, \end{equation} \tag{ 2 }$$

where F_max and F_min are the maximum and minimum EPIC fluxes of a unique source, with the corresponding (statistical) errors σ_max and σ_min, respectively, and r is the systematic error (r = 0.107 and 0.074 for bands 8 and 14, respectively; Section 2.2). We only used detections with the flux above four times the error (σ) when calculating F_max, while we used 2σ as the flux for detections with the flux less than 2σ when calculating F_min.

We established a subsample of our source list with well-confirmed source types from the literature (Tables 2 and 4), as described below. We refer to them as identified sources hereafter. There are three main categories of X-ray sources: stars, active galactic nuclei (AGNs), and compact object systems containing white dwarfs (WDs), neutron stars (NSs), and stellar-mass black holes (BHs).

For stars, we used the General Catalog of Variable Stars (GCVS, Version 2011 January; Samus et al. 2009) and sources from SIMBAD (three from the literature) with optical spectral types available. We classified stars into the following categories: Orion variables (OrVr); pre-main-sequence stars (PrSt); variable stars (VrSt, excluding Orion variables and flaring stars, mostly eclipsing binaries, rotationally variable and pulsating variable stars); flaring stars (FlSt); and stars for the rest, typically main-sequence stars.

For AGNs, we used the catalog of quasars and active nuclei by Véron-Cetty & Véron (2010, VV10 hereafter), with an additional three from the literature (based on optical spectra). We classified them into seven main categories based on the classifications given in this catalog (Table 2): narrow-line Seyfert 1 (Sy1n), Seyfert 1 (Sy1), Seyfert 2 (Sy2), low-ionization nuclear emission-line regions (LINERs or LINs), blazars (Bla), quasi-stellar objects (QSOs, i.e., quasars), and AGNs for the rest. There are 11 Seyfert galaxies with broad polarized Balmer lines (Sp = "S1h" in VV10) or broad Paschen lines in the infrared (Sp = "S1i"). They are generally classified as Seyfert 2 galaxies in SIMBAD, and we adopt the same scheme.

The Australia Telescope National Facility Pulsar Catalog (ATNFPC, as of 2011 March; Manchester et al. 2005)⁵ was used to identify thermally cooling isolated NSs (INSs), rotation-powered pulsars (rPsr), and magnetars (MGRs). The accretion-powered X-ray pulsars (aPsr) and bursters (Bstr, believed to be weakly magnetized accreting NSs; mostly low-mass X-ray binaries) were identified from the literature, with the requirements of detections of pulsations and type-I X-ray bursts, respectively. We referred to McClintock & Remillard (2006) to identify four BH X-ray binaries (BHBs), which either have secure BH mass measurements or show X-ray properties very similar to those of BHBs with secure mass measurements (grade A in Table 4.3 in McClintock & Remillard 2006). The Catalog of Cataclysmic Binaries (CCB) from Ritter & Kolb (2003, 7th edition) was used to identify the cataclysmic variables (CVs). All these types of sources will be generally referred to as compact objects (COs) in this paper.

We also found 16 sources that are probably (Galactic or extragalactic) SNRs (or their knots) from the literature. The 19 "mixed" sources in Table 2 (see also Table 4) include two cooling WDs, three supernova, four gamma-ray bursts, four symbiotic stars, two micro-quasars, etc. The 100 ultraluminous X-ray sources (ULXs, with luminosity above 10³⁹ erg s⁻¹) are either from the literature or from this work (Section 3.3). We treated all these SNRs, "mixed" objects, and ULXs as candidate (instead of identified) sources, considering that their X-ray mechanisms are largely still unclear.

We cross-correlated our source X-ray positions with the USNO-B1.0 Catalog (Monet et al. 2003) and the Two Micron All Sky Survey Point Source Catalog (2MASS PSC; Cutri et al. 2003) to search for their optical and IR counterparts, respectively. Our sources have small positional errors, with 86% less than 05 and 99% less than 10 (statistical plus systematic). The USNO-B1.0 Catalog and the 2MASS PSC have comparable positional errors. We selected the counterpart to be the closest one within 4''. For a few sources, we did not assign the counterparts in this way. One common case is bright extended galaxies, for which the USNO-B1.0 Catalog and the 2MASS PSC often have many entries, and we chose the brightest nearby one (in terms of the R2/K_s-band magnitude) as the counterpart. The other common case is stars with large proper motions (indicated in the USNO-B1.0 Catalog). In the end we found optical and IR counterparts for 3014 (70%) and 2058 (48%) of our sources, respectively (Table 4). For very few sources, we denoted the match quality as bad due to their coincidence with the persistence artifact positions in the 2MASS,⁶ bright globular clusters, etc., and we will not explore their optical/IR properties.

We used the R2-band magnitude to define the optical flux as log (F_O) = −R2/2.5–5.37, following Maccacaro et al. (1988). In some cases when the R2-band magnitude is not available, we used the R1-band magnitude instead. For sources without optical counterparts, we assumed R2 = 21.0, which is about the minimum among the counterparts found and was taken as an upper limit. The IR flux was calculated with the K_s-band magnitude from the 2MASS PSC: log (F_IR) = −K_s/2.5–6.95, assuming the "in-band" zero-magnitude flux of the K_s band from Cohen et al. (2003). For sources without IR counterparts, we calculated the upper limit using K_s = 15.3, the 3σ limiting sensitivity of this band in the 2MASS. Throughout the paper, all fluxes are in units of erg s⁻¹ cm⁻² and correspond to apparent/absorbed values.

We also similarly cross-correlated our sources with the extended IR sources from the 2MASS Extended Source Catalog (2MASS XSC; Skrutskie et al. 2006) and the optical sources from the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009). We used them mostly to check whether our sources are coincident with the center of (extended) galaxies. To reduce the contamination, we only assumed extended IR sources from the 2MASS XSC to be galaxies when they are coincident with the center of an optical extended source, based on visual inspection of the Digital Sky Survey (DSS) images. For the SDSS extended sources, we assumed them to be galaxies if their r-band magnitudes are >20 (the separation between the point and extended sources by the SDSS pipeline is not reliable for very faint sources; see Scranton et al. 2002).

We used the Third Reference Catalog (RC3) of galaxies (de Vaucouleurs et al. 1991) to investigate the probability of our sources being non-nuclear extragalactic sources. This catalog is reasonably complete for galaxies having apparent diameters larger than 1' at the D₂₅ isophotal level and total B-band magnitudes brighter than about 15.5 and redshifts less than 0.05. The D₂₅ isophote refers to the 25 mag arcsec⁻² B-band isophote and is approximated as an ellipse. This catalog also includes some objects of special interest, resulting in 23,022 galaxies in total. It gives the apparent major and minor diameters and the position angle of the D₂₅ isophote for each galaxy. The D₂₅ isophote is roughly the domain of a galaxy as seen in the DSS images, and by comparing the source positions with this isophote we can check whether the sources are possibly associated with that galaxy. Following Liu & Bregman (2005), we calculated the angular separation α between the galaxy center and the source, which was then scaled by the elliptical radius R₂₅ of the D₂₅ isophotal ellipse in the direction from the galaxy center to the source. We assumed that only sources with α/R₂₅ < 2 and α > 4'' can possibly be non-nuclear extragalactic sources. The positions of the galaxy centers given in the RC3 have only modest accuracy. We found that the positions from NASA/IPAC Extragalactic Database (NED)⁷ are closer to the real galaxy centers (at least for galaxies related to our sources) based on visual inspection of DSS images. Thus, we chose to use the galaxy center positions from NED when possible. We also estimated the maximum 0.2–12.0 keV absorbed luminosity for each candidate non-nuclear extragalactic source. We adopted the distances to most galaxies used in Liu & Bregman (2005) and Liu (2011). For 17 other galaxies, we obtained their distances using the redshifts from NED and assuming a flat universe with the Hubble constant H₀ = 75 km s⁻¹ Mpc⁻¹ and the matter density Ω_M = 0.27 if they have recessional velocities larger than 1000 km s⁻¹ or from the literature otherwise.

We created simple energy spectra, one for each available camera for each detection, using the count rates in five basic energy bands in the 2XMMi-DR3 catalog and fitted them with an absorbed PL (Table 3). The response files corresponding to the "thin," "medium," and "thick" optical blocking filters were constructed using the observations 0112560101, 0204870101, and 0311190101, respectively, from source regions centering at the pointing direction and covering the whole field of view. SAS 11.0.0 and the calibration files of 2011 June were used. The event selection criteria for each energy band/camera used for source detection in Watson et al. (2009) were followed. The interstellar medium absorption was modeled by the WABS model in XSPEC. A systematic error of 10% on the model was assumed. Relative normalizations among different cameras were allowed to be free. We note that we used the PL model just to roughly characterize the spectral shape. The real detailed X-ray spectra of AGNs are still often described by this model when there are no strong soft excesses, but for stars, the APEC and MEKAL models in XSPEC are generally needed to describe their detailed X-ray spectra well.

3.1.1. Spatial Distribution

We show the spatial distribution of the identified sources in Galactic coordinates in Figure 1 (left panel) and their distributions with respect to the Galactic latitude b (right panel). We differentiate stars, AGNs, and compact objects. We note that in the sky map in the left panel some fields are too crowded to see the real number of sources, while the distributions on the right panel complement this information. The bin sizes in the distribution plots vary to correspond to an equal spatial area. The error bars shown were obtained by assuming Poisson statistics in each bin (this is also assumed for all other distribution plots throughout this paper). We see that there are many stars near b = −194, which is due to the Orion Nebula (about 42% of the identified stars are from this nebula). Apart from this field, the identified stars concentrate at low Galactic latitudes. Stars with high Galactic latitudes are also seen (about 31% with |b| > 20°, excluding those from the Orion Nebula). Stars are typically in the Galactic plane. The large spread of stars along the Galactic latitude in our sample indicates that they are nearby.

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The identified AGNs tend to be at high Galactic latitudes, only about 2% with |b| < 20°. Such a bias can be explained by the large absorption along the Galactic plane and the preference to target the region outside the Galactic plane in galaxy surveys, such as the SDSS. There are more identified AGNs from the northern Galactic hemisphere (about 68% with b > 20° while about 30% with b < −20°), which can be explained by the fact that many AGNs in our sample are discovered by the SDSS, whose sky access is primarily in the north.

The identified compact objects clearly concentrate near the low Galactic latitude region, about 47% with |b| < 10°. The excess of the identified compact objects in the region of −50° < |b| < −30° is due to the presence of LMC and SMC.

3.1.2. X-ray Color–Color Diagrams and Spectral Fits

Figure 2 shows the X-ray color–color diagrams for identified sources. Stars, AGNs, and compact objects are plotted in the left, middle, and right columns, respectively. Only data points with error bars less than 0.1 on both colors are plotted. Spectral tracks of absorbed PL (dotted lines) and APEC spectra (dashed lines) are overlaid for comparison. APEC is a model of the emission spectrum from collisionally ionized diffuse gas in XSPEC and is often used to model the X-ray spectra of stars. In the HR1–HR2 diagram, we see that most stars occupy a region with characteristic APEC temperatures about 0.5–1 keV. However, in the HR2–HR3 and HR3–HR4 diagrams, there are many stars in a region with APEC temperatures >1 keV, which means that these stars probably need multiple APEC components to describe them. Investigations of these sources show that a majority of them correspond to detections with flares. Stars rarely show very hard X-ray spectra. Be stars such as HD 110432 (no. 110586) and SS 397 (no. 167002) can be very hard (e.g., Lopes de Oliveira et al. 2007), with HR4 larger than −0.4 in Figure 2. The outliers in the upper-left region in the HR3–HR2 diagram consist of famous stellar systems such as η Carinae (no. 87820), γ² Velorum (no. 65891), HL TAU (no. 38943), EX Lupi (no. 248785), and FU Orionis (no. 53697) (e.g., Farnier et al. 2011; Schild et al. 2004; Giardino et al. 2006; Grosso et al. 2010; Skinner et al. 2006).

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Figure 2 shows that AGNs (middle column) are mostly in the region with Γ_PL = 1–3. The main outliers are Seyfert 2, which have HR4 larger than 0. They may have strong absorption and typically have two main components with the hard one probably due to the reflection and/or heavy absorption of Seyfert 1 nuclei (Turner et al. 1997; Awaki et al. 2006; Noguchi et al. 2009). Comparing the HR1–HR2 and HR3–HR4 diagrams, we see that most narrow-line Seyfert 1 galaxies are in a region with Γ_PL > 2 in the HR1–HR2 diagram, but in a region with Γ_PL < 2 in the HR3–HR4 diagram. This can be explained by the frequent presence of soft excesses in these sources.

Compact objects show a large spread in Figure 2 (right column). This is to a large degree due to many subclasses included. However, many types of compact objects are known to show large spectral variations. For example, some CVs (brown stars) can have spectra changing from very hard to super-soft. Some weakly magnetized accreting NSs (bursters) also have a large range of HR3 (green triangles). Accretion-powered X-ray pulsars, whose X-ray spectra are known to be hard (White et al. 1983), occupy the region with Γ_PL around 0.5, where we see few stars and AGNs. The thermally cooling isolated NSs (black filled circles) stay in the lower left corner of the (HR1–HR2 and HR2–HR3) diagrams, as expected due to their soft nature (Haberl 2007). The magnetars (purple diamonds) look very hard in the HR1–HR2 diagram, which can be explained by large absorption, but many of them occupy a soft region in the HR3–HR4 diagram, with Γ_PL ≳ 3. Many magnetars are known to show strong spectral turnover at 15 keV, with very soft and very hard spectra below and above this energy, respectively (Enoto et al. 2010; Kuiper et al. 2006), and our results are consistent with this.

The spectral differences among various classes of sources can also be seen from the simple fits with an absorbed PL to spectra created using the band count rates in the 2XMMi-DR3 catalog (Table 3). Focusing on detections with S/N ⩾14, we obtained 1374 (79%), 2271 (92%), and 364 (65%) detections with reduced χ² ⩽4 for stars, AGNs, and compact objects, respectively. Their Γ_PL distributions are shown in Figure 3, and we see that they are remarkably different for different classes. AGNs have Γ_PL concentrated near the median of 1.91, with a standard deviation of only 0.31, while stars and compact objects have Γ_PL much more scattered. The Γ_PL values for stars are generally high, with only about 13% less than 2.5. We found that a majority of detections with low Γ_PL are due to flares, while detections with Γ_PL > 6.0 (corresponding to low APEC temperatures in the color–color diagrams) are mostly (about 70%) from main-sequence stars. For compact objects, detections with Γ_PL > 6.0 are mostly from thermally cooling isolated NSs and novae (a subclass of CV). There are 31% of detections with Γ_PL < 1.0, mostly from accretion-powered X-ray pulsars. In comparison, AGNs and stars have only 1.7% and 0.5% of detections with Γ_PL < 1.0, respectively.

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3.1.3. Long-term X-ray Variability

Figure 4 plots the X-ray flux variation factor V_var versus the maximum flux in 0.2–4.5 keV and the distributions of V_var for the three main classes (i.e., stars, AGNs, and compact objects). We obtained median variation factors m = 1.79, 1.48, and 1.65 for stars, AGNs, and compact objects, respectively. There are about 95.4% of the stars, 98.4% of the AGNs, and 71.7% of the compact objects with V_var less than 10. The distributions of V_var for stars and AGNs are relatively smooth. They roughly resemble half-normal distributions for the logarithm of V_var (dotted lines, with the same median as the data). When the flux logarithm for each source follows the same normal distribution and there are only two detections for each source, the logarithm of V_var is expected to follow a half-normal distribution. In contrast, the distribution of V_var for compact objects shows a large spread and depends on the subclasses clearly, as discussed below.

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The distribution of V_var for each subclass is given in Figure 5. We see that Orion variables are more variable (with m = 2.71) than other stars (such as the main-sequence stars, which have m = 1.45). The variable stars, which are classified mostly due to their optical variability, have m = 1.51, close to that of main-sequence stars. The three subclasses of Seyfert galaxies (Sy1n, Sy1, and Sy2) overall show similar variability, with m = 1.56, 1.57, and 1.49, respectively. However, some narrow-line Seyfert 1 galaxies show very large variability (a factor of 154 for PHL 1092; see also Miniutti et al. 2009). LINERs have m = 1.16, which is much lower than those of other AGNs, but we cannot exclude the probability that it is due to contamination of steady circumnuclear diffuse emission in these systems (e.g., González-Martín et al. 2009).

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The large spread of the distribution of V_var for compact objects mostly comes from accreting compact objects (BHBs, bursters, accretion-powered X-ray pulsars, and CVs; Figures 4 and 5). They were observed to vary by factors up to a few thousands. Some of them are known to vary much more than measured here (e.g., Aql X-1). This can be explained by a selection effect because XMM-Newton cannot observe bright sources in imaging modes. For isolated NSs, the rotation-powered pulsars and thermally cooling isolated NSs have m = 1.11 and 1.15, respectively (their median values of S_var are only 0.79 and 1.35, respectively). PSR J1302-6350 (i.e., PSR B1259-63, no. 116117) is the only one with significantly large variability (a factor of 31.2). However, it is a binary system, and its X-ray emission mechanism is probably different from most rotation-powered pulsars (Chernyakova et al. 2006). Different from the above two classes of isolated NSs, the majority of magnetars are observed to be variable, with some varying by factors of a few tens.

3.1.4. Multi-wavelength Cross-correlation

We found optical counterparts from the USNO-B1.0 Catalog for about 75%, 90%, and 56% of the identified stars, AGNs, compact objects, respectively. The corresponding percentages of IR counterparts found from the 2MASS PSC are 100%, 40%, and 56%, respectively. In Figure 6, we show the X-ray-optical and X-ray-IR positional separations for the identified stars and AGNs. About 90% of the optical/IR counterparts have separations <15 from the X-ray positions. Separations are expected to follow the Rayleigh distribution if both R.A. and decl. have a constant separation error σ_sep (the quadratic sum of the X-ray and optical/IR positional errors). The value of σ_sep for each Rayleigh distribution overplotted on the distribution of the separations in Figure 6 (dotted line) was inferred from the median of the separations, which is 1.18 times σ_sep for the Rayleigh distribution. We obtained σ_sep = 042 and 052 for the optical counterparts of AGNs and stars, respectively. The corresponding values for the IR counterparts are σ_sep = 042 and 051, respectively. The optical/IR counterparts of stars on the whole have larger separations from X-ray positions than those of AGNs, probably due to stellar proper motions. The above results indicate a high astrometric accuracy of our source sample.

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The identified compact objects for which we found the optical/IR counterparts are mostly CVs and accretion-powered X-ray pulsars. We found no optical/IR counterparts for the seven thermally cooling isolated NSs. In fact, their optical counterparts are known to be very faint, with B-band magnitudes about 26 (Pires et al. 2009). Some optical/IR counterparts are found for magnetars, but they all have large separations (>19) from the X-ray positions and are mostly in the crowded fields of optical/IR sources, thus probably spurious. Indeed, magnetars generally have R-band magnitudes larger than 24 and K_s-band magnitudes around 19 (Woods & Thompson 2006), below the detection limits of the USNO-B1.0 Catalog and the 2MASS PSC. We found few optical/IR counterparts for the 21 rotation-powered pulsars in our sample either. PSR J1302-6350 (i.e., PSR B1259-63, no. 116117) and PSR J1023+0038 (no. 83189) are the only two confident cases with optical and IR counterparts, but both of them are binary systems (Johnston et al. 1992; Archibald et al. 2009).

Figure 7 plots the X-ray flux versus the optical flux for identified sources with optical counterparts. It shows that the identified stars span higher optical fluxes than AGNs and compact objects, but they all have the lowest optical fluxes around 10^−13.5 erg s⁻¹ cm⁻², about the detection limit in the USNO-B1.0 Catalog. Figure 8 plots the X-ray flux versus the IR flux for identified sources with IR counterparts. We see that the identified stars also span higher IR fluxes than AGNs and compact objects. Moreover, they all have IR fluxes ≳ 10^−12.5 erg s⁻¹ cm⁻², brighter than the 3σ detection limit, while many identified AGNs and compact objects have IR fluxes lower than this limit.

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In the IR color–color diagram in Figure 9 for sources with IR counterparts, we see that the identified AGNs concentrate within the big dashed square, which is in agreement with previous studies (e.g., Hyland & Allen 1982). The IR counterparts of the identified stars and compact objects span a larger range of colors. Compared with the locus of main-sequence stars (the green solid line in Figure 9) and the reddening vector (the arrow), their large spread in IR colors is probably due to strong extinction in some of them.

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Figure 10 plots the X-ray-to-IR versus X-ray-to-optical flux ratios for all identified sources. For sources without optical/IR counterparts, their optical/IR flux upper limits are used and they are circled in this figure. Sources with neither optical nor IR counterparts fall onto the dotted reference line. The corresponding distributions of the X-ray-to-optical and X-ray-to-IR flux ratios are shown in Figure 11. For stars and AGNs, we separate the sources with (solid line) and without (dotted line) optical/IR counterparts (there is no distribution plot for stars without IR counterparts because they all have IR counterparts). As there are not many compact objects, they are not separated but combined to create a single distribution plot. In Figures 10 and 11, we see that stars are generally separated from AGNs and compact objects in terms of the X-ray-to-IR flux ratio (refer to the dashed reference lines; see also Figure 8). Stars have log (F_X/F_IR) ≲ −0.9, AGNs have −0.9 ≲ log (F_X/F_IR)  ≲ 2.5, and compact objects have log (F_X/F_IR) ≳ 0.5. AGNs tend to have higher X-ray-to-optical flux ratios (log (F_X/F_O) ≳ −1.0) than stars (log (F_X/F_O) ≲ −1.0) for sources with optical counterparts. However, many stars, especially Orion variables, have no optical counterparts. These stars are probably subject to strong extinction so that their optical counterparts fall below the detection limit of the USNO-B1.0 Catalog, making their (apparent) X-ray-to-optical flux ratios as large as those of AGNs and compact objects.

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Figure 11 shows that, compared with AGNs with optical counterparts, AGNs without optical counterparts on the whole have slightly larger X-ray-to-optical flux ratios, which were obtained using an (assumed) optical upper limit of R2 = 21.0. This is probably due to the selection bias that AGNs without optical counterparts are far away and tend to be included by us if they have high X-ray-to-optical flux ratios and are thus bright in X-rays, and/or the selection bias that AGNs with optical counterparts include sources with strong star-forming activity in the host galaxies and thus with large star light contamination.

We were able to identify the source types from the literature for only about one-third of our sources. For the rest, we classified them as one of three candidate classes: stars, AGNs, and compact objects. We derived the following source type classification method.

Sources with log (F_X/F_IR) < −0.9 are classified as stars, except those with HR1 ⩽ 0.3 and those in the direction of centers of galaxies (from the RC3, the 2MASS XSC, the SDSS, etc.). Sources are treated as in the direction of galactic centers if the separation is <4''. Sources with log (F_X/F_IR) > −0.9 are classified as stars if they have X-ray flares detected.

The remaining sources are assumed to be either AGNs or compact objects. Sources with HR1 < − 0.4, HR2 < − 0.5, HR3 < − 0.7, or HR4 < − 0.8 (soft sources), sources with −0.1 < HR3 < 0.5 and −0.25 < HR4 < 0.1 (hard sources like accretion-powered X-ray pulsars), sources with V_var (0.2–4.5 keV) > 10, and sources with log (F_X/F_IR) > 2.5 are classified as compact objects and denoted as strong candidates. Sources with only a small fraction of detections marginally passing the above X-ray color selection criteria are not classified as compact objects using the colors. To decrease the probability of missing compact objects, remaining sources that are probably non-nuclear extragalactic sources (α/R₂₅ ⩽ 2.0 and α > 4'') or probably in the Galactic plane (|b| ⩽ 10°) are also classified as compact objects but denoted as weak candidates.

Applying the above classification scheme to the identified sources we found that it can identify about 99%, 93%, and 70% (88%) of stars, AGNs, and strong-candidate (plus weak-candidate) compact objects, respectively. The corresponding probabilities of false identification, defined as the ratio of the number of false identifications to the total number of identifications, are about 1%, 3%, and 18% (32%), respectively.

The results of applying the source type classification method outlined in Section 3.2 to the unidentified sources are given in Tables 2 and 4. For very few sources, our classification also used specific source properties (such as dips) reported in the literature. The relevant references have been included in Table 4. We obtained 644 candidate stars. For candidate AGNs, we differentiated the 84 coincident with (extended) galaxies (G) from the rest (1292). For compact objects, 202 are strong candidates ("CO" in Tables 2 and 4), 320 are candidate non-nuclear extragalactic sources (XGSs), and 151 are candidate Galactic-plane sources (GPSs). These sources do not include the 16 SNR, the 19 "Mixed" sources, and the 100 candidate ULXs in Tables 2 and 4. Among the 100 candidate ULXs, 11 were identified in this work. They were selected under the conditions of the maximum 0.2–12.0 keV luminosity above 10³⁹ erg s⁻¹ (six above 2 × 10³⁹ erg s⁻¹), no optical counterparts within 2'' of the X-ray position from the USNO-B1.0 Catalog or the SDSS, and α/R₂₅ ⩽ 1.0 (source 106200 has α/R₂₅ = 1.99 and was included considering its large variability (V_var(0.2–4.5 keV) = 10.9). In Table 4, we list the characteristics (being soft, highly variable in X-rays, etc.) of the candidate compact objects and ULXs that differentiate them from AGNs.

Figures 12–17 show the X-ray color–color diagrams, long-term X-ray variability, the X-ray versus optical fluxes, the X-ray versus IR fluxes, IR color–color diagrams, and the X-ray-to-IR versus X-ray-to-optical flux ratios, respectively, for these candidate sources. They correspond to Figures 2, 4, and 7–10 for identified sources, respectively. The candidate and the identified sources generally show similar properties in these plots. There are some subtle differences. Comparing Figures 14 and 15 with Figures 7 and 8, we see that the candidate sources on the whole are fainter, mostly with the maximum 0.2–12.0 keV flux <10⁻¹² erg s⁻¹ cm⁻². This can be explained: Brighter X-ray sources tend to have brighter optical counterparts, which makes the identification, typically through optical measurements, easier.

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Comparing Figures 10 and 17, we see that there are more candidate stars than identified ones with log (F_X/F_IR) > −0.9. This may be because some of them are faint in IR and optical, hence hard to identify, while X-ray flares are more effective at identifying these sources. Sources 173834 and 6007 are two extreme cases. We measured log (F_X/F_IR) = 0.63 for source 173834, due to a large flare lasting ∼20 ks in observation 0200450401. It was not detected in five other observations, and we obtained a long-term flux variation factor V_var (0.2–4.5 keV) >53. Our classification as a star is also supported by appearing within the Cygnus OB2 star-forming region. Source 6007 has log (F_X/F_IR) = 0.65, due to a large flare lasting ∼8 ks in observation 0505720501. It appears within M 31, and it was also classified as a foreground star by Stiele et al. (2008) due to a (much weaker) flare in an earlier observation. We measured V_var (0.2–4.5 keV) > 198. Sources with extreme properties warrant future investigation.

The 84 candidate AGNs that are coincident with the centers of the extended galaxies on the whole have brighter optical and IR counterparts than other candidate AGNs (Figures 14 and 15). They also have lower X-ray-to-IR and X-ray-to-optical flux ratios, which separate them from other candidate AGNs in Figure 17, probably indicating large contamination of IR and optical counterpart fluxes from the starlight. In the X-ray color–color diagrams in Figure 12, some of them are also separated from other candidate AGNs and are more in the region occupied by stars, indicating that their X-ray emission may be dominated by the hot gas inside the host galaxies, as often seen in nonactive early-type galaxies (Fabbiano 1989).

The 16 SNRs are remarkably similar to each other. They all have X-ray colors similar to stars (Figure 12). Their X-ray emission is probably due to expanding SNR shock heating the surrounding interstellar medium (e.g., Itoh & Masai 1989) and can be fitted with a bremsstrahlung model with temperatures <1 keV (Pannuti et al. 2000). They either (for most cases) have no IR or optical counterparts found from the USNO-B1.0 Catalog and the 2MASS PSC, or have counterparts at large separations from the X-ray positions (>2''), thus probably spurious. They are very steady, with the 0.2–4.5 keV flux variation factors all <1.8 (the median is 1.19; Figure 5) and the variability significance S_var all <4.

For the 100 candidate ULXs, most of them are in the region occupied by AGNs in the X-ray color–color diagrams in Figure 12, while nearly 30% of them have detections entering the soft regions (HR1 < − 0.4, HR2 < − 0.5, HR3 < − 0.7, or HR4 < − 0.8) where AGNs are hardly seen. The ULX samples are often contaminated by background AGNs (López-Corredoira & Gutiérrez 2006), and we expect that some of these 100 candidate ULXs are in fact AGNs. Figure 18 plots the X-ray flux variation factor (0.2–4.5 keV) versus the maximum luminosity (0.2–12.0 keV) and the distribution of the flux variation factor for these candidate ULXs. There are 13 candidates (found from the literature) with the maximum 0.2–12.0 keV luminosity slightly less than 10³⁹ erg s⁻¹, the lowest limit generally used to define ULXs. This discrepancy can be explained by various factors, such as source variability and different source distances used in the literature from us (we mostly refer the distances to Liu & Bregman 2005; Liu 2011). About 15% of these 100 candidate ULXs have V_var (0.2–4.5 keV) > 10, but most of them have the maximum 0.2–12.0 keV luminosity lower than 4 × 10³⁹ erg s⁻¹. We obtained a median of 1.73 for the 0.2–4.5 keV flux variation factors, which is slightly larger than that of AGNs but smaller than those of various types of accreting compact objects (Section 3.1.3). Although we do not have enough BHBs to obtain a meaningful value of their average variation factor, we expect it to be much larger than that of these candidate ULXs, considering that most BHBs are transients (McClintock & Remillard 2006).

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For the 202 strong candidate compact objects, they are spread across the X-ray color–color diagrams (Figure 12); they include some supersoft X-ray sources and some hard sources, which are probably accretion-powered X-ray pulsars. The weak candidate compact objects in the Galactic plane are mostly highly absorbed, occupying the upper right corner in the HR1–HR2 diagram.

Several special objects have very low X-ray-to-IR flux ratios in the right panel in Figure 17, though they probably contain compact objects. The four candidate symbiotic stars, i.e., AG Draconis (no. 143273), 4U 1700+24 (no. 152155), Z And (no. 189311), and SMC Symbiotic Star 3 (no. 194075), all have log (F_X/F_IR) < −1.0 (they are included in the "Mixed" class). One supergiant fast X-ray transient (SFXT), i.e., IGR J17544-2619 (no. 158580), has log (F_X/F_IR) = −1.0 (it is included in the "CO" class; González-Riestra et al. 2004). There is another SFXT, IGR J11215-5952 (no. 206717), which has been included in the class of accretion-powered X-ray pulsars due to the detection of the spin period (Sidoli et al. 2007) and has log (F_X/F_IR) only −0.1. We also detected flares lasting ∼1 hr from these two SFXTs. Their flares, however, show complicated structure, in contrast with the typical fast rise and slow decay of stellar X-ray flares. Observations of very hard spectra, short pulsation periods and extreme long-term variability as in IGR J11215-5952 (Sidoli et al. 2007) can help to differentiate them from stars.