A CATALOG OF X-RAY POINT SOURCES FROM TWO MEGASECONDS OF CHANDRA OBSERVATIONS OF THE GALACTIC CENTER

Source detection and localization were approached iteratively. We first searched for point sources in each observation separately. The locations of the point sources found in the first stage were used to refine the astrometry. Second, the astrometrically corrected images were combined to search for fainter point sources. Finally, the source lists from the individual observations were merged with those from the combined images.

We searched each observation individually for point sources using the wavelet decomposition algorithm wavdetect (Freeman et al. 2002). We employed the default "Mexican Hat" wavelet, and used a sensitivity threshold of 10⁻⁷. This threshold roughly corresponds to the chance of detecting a spurious source in an area corresponding to the PSF, if the local background is spatially uniform. For the earlier data, taken before 2006, we used images at three different resolutions: one at 05 resolution covering the inner 1024 × 1024 pixels, one at 1'' resolution covering the inner 2048 × 2048 pixels, and one at 2'' resolution covering the entire field. For later observations, we simplified the process and used only two resolutions: 05 covering the inner 2048 × 2048 pixels, and 2'' covering the entire field. Using a test field, we confirmed that there was no difference in the number of sources detected using the two techniques; the only difference is that the technique that used three, smaller images was computationally faster. We used wavelet scales that increased by a factor of $\sqrt{2}$, over the range of 1–4 pixels for the 05 image, 1–8 pixels for the 1'' image, and 1–16 pixels for the 2'' image. For each resolution, we made images in three energy bands: 0.5–8.0 keV to cover the full bandpass, 0.5–2.0 keV to provide sensitivity to foreground sources, and 4–8 keV to provide sensitivity to highly absorbed sources. For each image, a matching exposure map was generated for photons with an energy of 4 keV, so that the wavelet algorithm could keep track of regions with rapidly varying exposure, such as bad columns and the edges of the CCDs.

The lists derived from each image resolution were combined to form master source lists for each energy band. We found that the positions would be most accurate from the sources identified in the image with the finest resolution. Therefore, we discarded sources from the lower resolution images if their separations from sources identified at high resolution were smaller than the radii of the 90% contour of the PSF. In this way, we produced three lists for each observation, one for each energy band.

Next, we used the point sources detected so far to register the absolute astrometry to the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006). The 2MASS frame is consistent with the International Celestrial Reference System to within 15 mas. We compared the positions of 2MASS sources to those of X-ray sources detected in the 0.5–2.0 keV band that were identified by wavdetect as having > 3σ significance, and identified matches as those with offsets < 1''. The offsets between the 2MASS and Chandra frames were computed using a least-chi-squared algorithm. The X-ray sources that we used for astrometry are flagged in Table 2 (see Section 2.6).

For observations longer than 20 ks, we found between 3 and 36 X-ray sources in the soft band that could be associated unambiguously with stars in the 2MASS catalog, and so we used the average offsets between the X-ray and the infrared sources to correct the astrometry of the X-ray observations. We evaluated the accuracy of the registration based on the standard deviation in the mean of the offsets of the individual stars. The registration was accurate to 006 for the deepest exposures, and to 02 for the shallower ones (1σ). Unfortunately, for exposures shorter than 20 ks, too few X-ray sources were found with 2MASS counterparts to correct the astrometry to better than the default value, 05 (1σ).

Once the deepest observation at each point was registered to the 2MASS frame, the shallower observations were registered using the offsets of X-ray sources detected in the 0.5–8.0 keV band in pairs of observations. Between 2 and 759 X-ray sources matched between the deepest and the shallower observations, depending upon the exposure time of the shallower observation. The uncertainty in the astrometry of each observation is listed in the last column of Table 1. The composite image and exposure map for our survey are displayed in Figure 1.

Having corrected the astrometry for fields that included deep observations, we then combined subsets of the images in order to perform a deeper search for point sources. Two wavelet algorithms were used, on the series of images listed below. First, the tool wavdetect (Freeman et al. 2002) was used to identify point sources in the following.

• 1.  
  Composite images made from all of the observations of Sgr A*. Twelve 1024 × 1024 images were made, in four resolutions (025, 05, 1'', and 2'') and using three energy bands for each resolution (0.5–8.0 keV, 0.5–2.0 keV, and 4–8 keV).
• 2.  
  Three sets of composite images made from observations of Sgr A* in 2002, 2004, and 2005. These images were designed to be sensitive to faint, variable sources. The same image resolutions and energy bands were used as for the composite image of all of the Sgr A* data.
• 3.  
  Composite images made from three pointings that were taken with same roll angle, because the original 40 ks exposure had to be split up to accommodate scheduling constraints (ObsIDs 7038, 7041, and 7042). Three images were made for each aim point, one for each of the 0.5–8.0 keV, 0.5–2.0 keV, and 4–8 keV energy bands. Each image was made at 05 resolution, and had 2048 × 2048 pixels.

The parameters used with wavdetect were the same as for the individual observations.

Second, we used the tools wvdecomp and findpeak in the zhtools package written by A. Vikhlinin²⁴ to search for faint sources that fell below the wavdetect threshold. We searched on wavelet scales of 1–3 pixels, and required that a candidate source be identified with a minimum signal-to-noise of 4.5, corresponding to 16 spurious sources per 2048 × 2048 pixel image. Five iterations of the search procedure were performed. The tool wvdecomp iteratively cleans the image of point sources identified in previous passes through the data, so it is more efficient at separating close pairs of sources. Moreover, unlike wavdetect, wvdecomp does not use any information about the shape of the PSF in searching for sources, so it is better at identifying point sources when observations with very different aim points have been combined. Therefore, we used wvdecomp on composite images generated from all data covering the positions at which deep observations were obtained (i.e., ObsIDs 3392, 4500, 5892, 7034–7048, and 944). Each image was produced with 2048 × 2048 pixels at 05 resolution for the 0.5–8.0 keV band.

We then generated a list containing the unique sources, by merging the lists generated by wavdetect from individual observations and from combined images, and from the lists generated by wvdecomp. We found that almost all the duplicates could be removed by identifying sources with separations smaller than the prescription for positional uncertainties in Brandt et al. (2001): for sources offset from the center of each image by θ< 5', the separation was cut at 06, whereas for larger offsets it was cut at 06 + (θ − 5.0)/8.75 (θ is in arcminutes).²⁵ For each image, we gave preference to positions from the full-band sources, then from the soft sources, and finally from the hard sources. Across observations, the priority was given to the deeper observations, and to the sources detected with wavdetect over those detected with wvdecomp. We examined the final list visually by comparing it to images of the survey fields, and we removed several hundred sources that were portions of extended, diffuse features (from Muno et al. 2007), and a couple dozen duplicates that were not identified automatically. Finally, two sources were not picked up by the detection algorithms because they were blended with nearby, brighter sources. We added these to our catalog by hand (CXOUGC J174502.8 − 282505 and J174617.4 − 281246).

At this stage, we considered our source lists to be provisional, both because the search algorithms used nonuniform parameters, and because the large, spatially variable background was likely to cause our wavelet algorithms to generate a significant number of spurious sources. In order to confirm their validity, we next computed photometry for each provisional source.

We computed aperture photometry for each source using the ACIS Extract package, versions 3.96, 3.101, and 3.128 (Broos et al. 2002; Townsley et al. 2003; Getman et al. 2005), along with some custom code. The algorithm proceeded in several steps.

First, for each source and each observation, we obtained a model PSF with the CIAO tool mkpsf. For most sources, we used a PSF for a fiducial energy of 4.5 keV. However, if a source was only detected with wavdetect in the soft band, we used a PSF for an energy of 1.5 keV. To determine a region from which we would extract source counts, we then constructed a polygon enclosing 90% of the PSF. If the polygons for two sources overlapped in the observations in which the sources were closest to the aim point, we generated a smaller polygon. The final extraction regions were enclosed between 70% and 90% of the PSF. Sources for which the PSF fraction was < 90% were considered to be confused. Moreover, because the PSF grows rapidly beyond 7' from the aim point, we also considered sources to be confused if they were located beyond 7' from the aim point and their PSFs overlapped. Photometry was not computed for observations in which confused sources fell > 7' off-axis. Fortunately, these second type of confused sources were always located on-axis in another observation, or else they would not have been identified. Finally, for similar reasons, we only computed photometry for sources that lay within 7' of Sgr A* if the relevant observations had Sgr A* as the aim point.

Second, we extracted source event lists, source spectra, effective area functions, and response matrices for each source in each observation. The detector responses and effective areas were obtained using the CIAO tools mkacisrmf and mkarf, respectively. For each source, the spectra from all of the relevant observations were summed. The responses and effective areas were averaged, weighted by the exposures in each observation.

Third, we extracted background events from circular regions surrounding each point source in each observation, omitting events that fell within circles that circumscribed ≈ 90% of the PSFs around any point sources. The background regions were chosen to contain ≈ 100 total counts for the wide survey, and ≈ 1000 total counts for the deeper Sgr A* field. Fewer than 1% of the counts in the background region originate from known point sources. For each source, the background spectra from all of the relevant observations were scaled by the integrals of the exposure maps (in units of cm² s) over the source and the background regions, and then summed to create composite background spectra.

Fourth, we eliminated spurious sources. We compared the number of source and background counts to estimate the probability that no source was present, based on Poisson statistics (Weisskopf et al. 2007). If a source had a > 10% chance of being spurious, we eliminated it from our catalog. We eliminated 1962 sources in this way. We also eliminated sources in which the majority of events were cosmic ray afterglows. Specifically, we removed 46 sources because the events associated with the candidate source fell in a single pixel during 5–10 consecutive frames. Our final catalog contains 9017 X-ray sources, and is listed in Table 2. The majority of sources, 7152, were found with wavdetect. Of the sources detected with wavdetect, 4823 were detected in the full band, 948 in the soft band, and 1381 in the hard band. Another 1865 sources were only detected with wvdecomp. In the Sgr A* field alone, we found 3441 sources with wavdetect, of which 2715 were detected in the full composite image, 275 in 2002, 48 in 2004, 90 in 2005, and 313 in individual observations. An additional 364 were found in the Sgr A* field with wvdecomp.

Fifth, we compared the source and the background spectra using the Kolmogorov–Smirnov (KS) statistic, in order to flag potentially spurious objects that could be variations in the background. Caution should be used when studying sources that resemble the background. For instance, in the central parsec around Sgr A*, there is an overabundance of faint (≲10⁻⁶ photons cm⁻² s⁻¹), soft point sources that have spectra consistent with that of the background warm plasma (note that almost all of the excess bright sources that we discuss in Section 3.1 do have spectra that are distinct from the background). Therefore, we suspect that most of these are ∼ 0.1 pc scale variations in the density of that plasma. Unfortunately, we cannot be certain. Indeed, the spectrum of the bright X-ray source associated with IRS 13 (CXOUGC J174539.7 − 290029) resembles the background according to the KS test. If the diffuse background is merely unresolved point sources (Wang et al. 2002a; Revnivtsev et al. 2006; Revnivtsev & Sazonov 2007), then most faint point sources should have spectra that resemble the background.

Sixth, we computed the net counts in the 0.5–2.0 keV, 2.0–8.0 keV, 2.0–3.3 keV, 3.3–4.7 keV, and 4.7–8.0 keV bands. We estimated the photon flux from each source, by dividing the net counts by the average of the effective area function in each band. Table 3 lists the 0.5–2.0 keV and 2–8 keV fluxes, the latter of which is the sum of the fluxes in the three subbands. Figure 3 displays histograms of the net counts and fluxes in the 0.5–2.0 keV and 2–8 keV bands. Histograms of upper limits are also plotted, for sources that were detected in one band but not the other.

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Table 3. Galactic Center X-Ray Source Photometry

									F0.5 − 2	F2 − 8
									(10−7 cm−2 s−1)
No. 1	Name CXOUGC J 2	log(PKS) 3	Ct,0.5-2 4	Cb,0.5-2 5	Cnet,0.5-2 6	Ct,2-8 7	Cb,2-8 8	Cnet,2-8 9	10	11	$\bar{E}$ 12	HR0 13	HR1 14	HR2 15
1	174457.1 − 285740	−4.50	86	26.3	59.7+16.4−14.0	185	186.4	<23.7	6.8	⋅⋅⋅	1.0	<−0.555	⋅⋅⋅	⋅⋅⋅
2	174457.4 − 285622	−0.09	52	53.0	<14.2	357	298.8	58.2+33.6−28.3	⋅⋅⋅	8.2	4.6	⋅⋅⋅	>0.031	−0.169+0.612−0.615
3	174459.1 − 290604	−2.57	118	88.1	29.9+18.8−16.7	498	349.1	148.9+32.3−40.4	1.9	13.3	3.5	0.116+0.415−0.411	0.299+0.294−0.263	−0.254+0.254−0.396
4	174459.9 − 290324	−1.09	96	91.1	<15.0	369	334.6	34.4+29.6−28.9	⋅⋅⋅	2.4	3.1	>− 0.066	<0.194	⋅⋅⋅
5	174459.9 − 290538	−0.97	107	115.0	<22.7	550	434.9	115.1+40.2−40.2	⋅⋅⋅	10.3	4.8	⋅⋅⋅	>0.243	−0.012+0.357−0.374
6	174500.2 − 290057	−1.99	41	25.1	15.9+11.4−9.5	138	133.5	<19.2	1.5	⋅⋅⋅	0.5	−0.065+0.506−0.779	<0.006	⋅⋅⋅
7	174500.6 − 290443	−1.90	50	44.5	<10.8	316	200.3	115.7+31.5−27.0	⋅⋅⋅	11.1	4.6	⋅⋅⋅	>0.400	0.053+0.247−0.246
8	174501.3 − 285501	−40.35	175	69.8	105.2+22.4−21.0	13585	3163.7	10421.3+165.9−165.9	9.7	1625.1	4.7	0.861+0.027−0.028	0.462+0.021−0.021	0.146+0.017−0.017
9	174501.4 − 290408	−4.12	92	100.1	<21.7	523	371.2	151.8+38.3−38.3	⋅⋅⋅	11.9	5.4	⋅⋅⋅	>0.029	0.578+0.242−0.230
10	174501.7 − 290313	−0.76	89	104.1	<25.7	561	433.0	128.0+40.4−40.4	⋅⋅⋅	8.7	5.1	>0.390	0.163+0.596−0.547	0.351+0.362−0.335
11	174501.8 − 290206	−2.37	39	34.2	<10.1	248	144.9	103.1+27.7−24.1	⋅⋅⋅	8.0	4.6	⋅⋅⋅	>0.440	−0.058+0.244−0.253
12	174501.9 − 285719	−0.88	41	19.9	21.1+11.2−9.7	163	143.6	19.4+18.6−18.1	2.1	3.2	3.2	<−0.296	>− 0.014	<0.288
13	174502.2 − 285749	−5.62	60	38.7	21.3+13.3−12.0	378	281.3	96.7+36.2−27.7	1.6	6.6	2.6	0.517+0.257−0.238	−0.221+0.259−0.259	<−0.564
14	174502.4 − 290205	−2.76	70	31.1	38.9+12.5−14.5	159	109.7	49.3+19.1−21.9	1.8	3.2	2.8	−0.570+0.288−0.417	0.417+0.568−0.391	−0.339+0.409−0.640
15	174502.4 − 290453	−7.28	172	91.6	80.4+24.0−19.0	349	340.4	<27.8	3.3	⋅⋅⋅	0.9	−0.577+0.233−0.333	<−0.064	⋅⋅⋅
16	174502.5 − 290415	−0.04	69	56.4	12.6+10.5−12.5	218	194.8	<15.4	0.6	⋅⋅⋅	3.1	0.071+0.948−0.918	<−0.149	⋅⋅⋅
17	174502.7 − 290127	−1.10	80	101.9	<30.8	372	312.8	59.2+34.1−28.8	⋅⋅⋅	3.4	6.3	⋅⋅⋅	>− 0.097	0.161+0.550−0.683
18	174502.8 − 290429	−0.49	139	86.3	52.7+18.3−20.0	308	279.6	<18.9	2.2	⋅⋅⋅	2.9	<−0.609	⋅⋅⋅	>0.065
19	174502.9 − 285920	−1.28	43	33.7	<7.5	234	164.0	70.0+27.0−23.2	⋅⋅⋅	9.0	4.9	⋅⋅⋅	>0.581	0.084+0.323−0.294
20	174503.7 − 285805	−0.63	17	15.3	<6.9	143	75.0	68.0+19.4−19.6	⋅⋅⋅	11.2	4.7	>0.181	0.210+0.596−0.445	0.320+0.312−0.294
21	174503.8 − 290004	−1.94	56	51.9	<12.8	341	232.2	108.8+30.3−30.2	⋅⋅⋅	6.8	4.3	>0.108	0.418+0.436−0.293	−0.165+0.292−0.322
22	174504.1 − 285902	−0.22	27	19.9	<6.9	90	71.8	18.2+15.4−14.1	⋅⋅⋅	1.2	2.7	>− 0.282	0.228+0.767−0.716	<−0.148
23	174504.2 − 285653	−2.59	46	56.2	<18.2	419	353.4	65.6+34.7−32.1	⋅⋅⋅	10.3	6.5	⋅⋅⋅	⋅⋅⋅	>0.435
24	174504.2 − 290410	−2.66	121	66.9	54.1+16.6−19.1	250	249.8	<27.0	2.1	⋅⋅⋅	0.9	<−0.518	⋅⋅⋅	⋅⋅⋅
25	174504.2 − 290610	−1.31	129	124.1	<19.0	543	496.0	47.0+41.3−41.3	⋅⋅⋅	3.1	4.6	⋅⋅⋅	>0.406	−0.140+0.485−0.851

Note. A portion of the full table is shown here, for guidance as to its form and content. The columns are described in the text.

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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Finally, using custom code that was not part of ACIS Extract, we computed 90% uncertainties on the net counts in each band, through a Bayesian analysis of the Poisson statistics, with the simplifying assumption that the uncertainty on the background is negligible (Kraft et al. 1991). We used the net counts to compute the hardness ratios (h − s)/(h + s), where h and s are the numbers of counts in the higher and lower energy bands, respectively. The resulting hardness ratios are bounded by −1 and +1. We defined a soft color using counts in the 2.0–3.3 keV and 0.5–2.0 keV bands (HR0), a medium color using counts in the 3.3–4.7 keV bands and 2.0–3.3 keV bands (HR1), and a hard color using counts in the 4.7–8.0 keV and 3.3–4.7 keV bands (HR2). We calculated uncertainties on the ratios using the 90% uncertainties on the net counts and Equation (1.31) in Lyons (1991; p. 26). The hardness ratios are listed in Table 3, and histograms showing their distributions are displayed in Figure 4.

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The soft color, HR0, was used to distinguish foreground sources from objects that were likely to lie near or beyond the Galactic center. We select foreground X-ray sources as those with soft colors in the range −1.0 ⩽ HR0 < −0.175, which corresponds to absorption columns equivalent to N_H ≲ 4 × 10²² cm⁻². Most of these should lie within 4 kpc of Earth (e.g., Marshall et al. 2006). We selected X-ray sources that were located near or beyond the Galactic center as those either that had soft colors HR0 ⩾ −0.175, or that were not detected in either of the 0.5–2.0 or 2.0–3.3 keV bands. This X-ray selection corresponds to absorption columns equivalent to N_H ≳ 4 × 10²² cm⁻². We find 2257 foreground X-ray sources, and 6760 sources near or beyond the Galactic center. Foreground and absorbed sources are plotted separately in Figure 4. Most absorbed sources do not have measured soft colors.

We searched for variability using the arrival times of the events. We searched for three kinds of variations: long-term variations that occurred between observations, short-term variability within individual observations, and periodic variability within individual observations.

2.3.1. Long-Term Variability

We searched for variations that occurred between observations by comparing the event-arrival times from all of the observations to a constant flux model using the KS statistic. Any source with a < 0.1% chance of being described by a constant flux model was considered to vary on long timescales. There were 856 sources that exhibited long-term variability, 137 of which also exhibited short-term variability. Therefore, about 10% of the sources vary on the day-to-month timescales between observations.

We characterized these long-term variations by computing the mean photon flux during each observation of a variable source. Table 4 lists the source name, observations in which the largest and the smallest fluxes were observed, the values of the largest and the smallest fluxes, and the ratios of those values. Figure 5 compares the amplitude of the variations to the maximum flux. In order to exclude measurements with poor signal-to-noise, the largest flux was defined as the measurement with the largest lower limit, and the smallest flux was defined as the measurement with the smallest upper limit. In most (740) cases, the smallest flux was consistent with zero, and the lower limits to the flux ratios were provided. In 224 cases, the uncertainties in the largest and the smallest fluxes overlapped, and the formal lower limit to the ratio was less than 1. The statistics on faint sources with low-amplitude variability tended to be poor, so Table 4 would be best used to identify highly variable sources for further study.

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Table 4. Sources with Long-Term Variability

Number	Name (CXOUGC J)	Location	Min. ObsID	Fmin (10−7 cm−2 s−1)	Max. ObsId	Fmax (10−7 cm−2 s−1)	Fmax/Fmin
2	174457.4 − 285622	gc	5953	<10	4684	31 ± 8	>2.2
7	174500.6 − 290443	gc	7556	<27	3392	14 ± 4	>0.4
8	174501.3 − 285501	gc	4684	8 ± 6	1561a	12437 ± 166	1530+5824−676
12	174501.9 − 285719	f	2284	<10	5953	16 ± 8	>0.8
16	174502.5 − 290415	gc	2943	<5	7556	64 ± 41	>4.2
23	174504.2 − 285653	gc	4683	<6	5953	16 ± 9	>1.1
31	174504.8 − 285410	f	5951	<16	6363	38 ± 14	>1.5
35	174505.2 − 285713	f	2953	<25	4683	16 ± 7	>0.4
45	174506.1 − 285710	gc	5954	<6	2953	26 ± 21	>0.9
53	174507.0 − 290452	gc	6113	<31	2953	29 ± 20	>0.3
54	174507.1 − 285720	gc	5950	<6	2951	21 ± 15	>1.0
58	174507.5 − 285614	f	3665	<12	6640	47 ± 44	>0.3
71	174508.4 − 290033	f	3663	<5	5360	375 ± 67	>61.1
80	174509.2 − 285457	gc	2951	<9	5954	20 ± 13	>0.8
89	174509.5 − 285502	gc	3392	<3	6363	19 ± 10	>3.1
96	174510.1 − 285624	f	3549	<6	1561a	16 ± 12	>0.7
98	174510.2 − 285505	gc	3663	<5	6642	51 ± 40	>2.3
100	174510.3 − 290642	gc	7557	<24	2954	55 ± 23	>1.3
101	174510.4 − 285433	gc	4683	<5	5953	19 ± 8	>2.5
102	174510.4 − 285544	gc	5950	<5	3665	11 ± 4	>1.6
103	174510.4 − 285545	gc	5950	<5	3665	12 ± 4	>1.6
106	174510.6 − 285437	gc	3549	<7	3663	14 ± 8	>0.9
109	174510.8 − 285606	gc	6641	<22	3665	12 ± 4	>0.4
112	174510.9 − 285508	gc	5954	<9	4683	18 ± 7	>1.3
129	174511.6 − 285915	gc	5953	<3	3392	8 ± 2	>1.6
143	174512.1 − 290005	gc	2952	<7	3393	15 ± 3	>1.6
155	174512.4 − 285318	gc	7555	<27	3393	11 ± 4	>0.3
164	174512.8 − 285441	gc	6644	<22	2953	33 ± 20	>0.6
191	174514.1 − 285426	gc	5953	<7	5954	55 ± 20	>4.7
226	174515.1 − 290006	gc	4684	<3	3392	10 ± 2	>2.8

Notes. The columns of the table are: the record number from Table 2, the source name, a flag stating whether a source is in the foreground or near the Galactic center, the ObsID in which the minimum flux was observed, the minimum flux, the ObsID in which the maximum flux was observed, the maximum flux, and the ratio of the maximum to minimum fluxes.

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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2.3.2. Short-Term Variability

We searched for variability within each observation by comparing the light curves to constant count rate models using the KS statistic. If the arrival times of events had a < 0.1% chance of being described by a uniform distribution, we considered a source to have short-term variability. We identified 294 sources, or 3% of our sample, as having clear short-term variations.

We roughly characterized the nature of the variability by dividing each time series into intervals that were consistent with having constant count rates, using the Bayesian Blocks algorithm of Scargle (1998). In brief, the algorithm compared the probability that an interval could be described by two different count rates to the null hypothesis that the photons arrived with a single rate. If the ratio of the two probabilities exceeded a user-specified prior odds ratio, then the interval was divided at the time that produced two intervals with the largest calculated likelihood. This process was iterated until no subintervals were divided any further. We chose to apply the algorithm in order to describe each variable light curve with the fewest intervals with distinct rates (blocks). We applied three progressively looser odds ratios, successively demanding that the probability for the two-rate model exceed the null hypothesis by factors of 1000, 100, and 10 if the larger odds ratio failed to identify a change point. In this way, large flares were described with a few "blocks" using a large odds ratio, whereas small-amplitude variations were still characterized using a smaller odds ratio. This approach was deemed necessary in part because the Bayesian interpretation of the odds ratios does not have a good frequentist analog that could be compared to the probabilities returned by the KS test, and in part because the KS test and the Bayesian blocks tests are most sensitive to slightly different forms of variability. Ultimately, only 60% of the variable sources identified with the KS test were characterized with more than one block in the Bayesian block algorithm.

Despite the mismatch between the two tests, the characteristics of the variable sources identified by both the KS and the Bayesian blocks tests are illustrative. In Table 5, we list some properties of the variable sources: their names, the ObsIDs in which variability occurred, the odds ratio at which the Bayesian blocks algorithm identified a source as variable, the number of blocks used to describe the events, the durations of the brightest portions of the light curves, the minimum and the maximum fluxes, and the ratios of the maximum to minimum fluxes. Figure 6 compares the duration and amplitude of the variability. For 40% of the variable sources, the minimum flux was consistent with zero, so the ratio represents a lower limit to the variability amplitude. We find that all variations had timescales of > 10 minutes. The amplitudes ranged from barely detectable 30% variations in the flux (CXOUGC J174534.8 − 290851), to one flare in which the flux increased by a factor of 250 (CXOUGC J174700.7 − 283205). Foreground sources are overrepresented among variable sources—they compose only 25% of our entire catalog, but 50% of the short-term variables—which is consistent with the expectation that they are nearby K and M dwarf flare stars (e.g., Laycock et al. 2005).

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Table 5. Sources with Short-Term Variability

							Fmin	Fmax
							(10−7 photons cm−2 s−1)
Number	Name (CXOUGC J)	Location	ObsID	Prior Odds	Nblocks	Tpeak (s)			Fmax/Fmin
1	174457.1 − 285740	f	1561b	100	2	3152	<17	193+72−55	>3.3
3	174459.1 − 290604	gc	3663	10	2	19600	<11	48+17−15	>1.4
71	174508.4 − 290033	f	5360	1000	2	2736	<63	673+119−103	>1.6
186	174513.7 − 285638	gc	4684	10	2	21312	<7	36+12−9	>1.4
257	174516.6 − 285412	f	4684	1000	2	16512	5+7−4	90+23−19	20.0 ± 24.4
304	174517.8 − 290653	gc	3392	1000	2	110160	4+5−4	40+6−5	9.6 ± 10.5
364	174519.5 − 285955	gc	4683	10	2	6896	3+3−2	57+26−19	18.2 ± 18.0
398	174520.3 − 290143	gc	2943	1000	2	3472	5+5−3	134+58−42	29.6 ± 29.0
424	174520.6 − 290152	f	3392	1000	5	33360	34+6−5	526+35−33	15.3 ± 2.7
424			3393	1000	4	22144	15+3−3	858+55−52	56.1 ± 11.0
424			5951	1000	2	23760	9+8−5	104+17−15	11.3 ± 8.2
470	174521.7 − 290151	gc	5950	100	2	10400	2+4−2	52+19−15	22.9 ± 30.4
472	174521.8 − 285912	f	3392	1000	3	18560	3+3−2	103+17−15	30.0 ± 21.6
663	174525.1 − 285703	f	3665	1000	2	1664	12+4−3	566+176−137	49.0 ± 20.6
811	174527.1 − 290730	gc	3549	10	2	3296	<6	87+57−38	>5.9
1100	174530.3 − 290341	gc	3392	1000	3	21440	5+8−5	91+15−13	17.3 ± 20.5
1100			5950	1000	2	17120	55+9−8	136+20−17	2.5 ± 0.5
1183	174531.1 − 290219	gc	3393	10	2	70704	8+3−2	25+4−4	2.9 ± 1.0
1525	174534.2 − 290011	f	3392	100	2	49392	<1	14+4−3	>2.7
1569	174534.5 − 290236	gc	3392	1000	2	73504	<1	10+3−2	>2.4
1608	174534.8 − 290851	f	1561a	100	2	21168	<11	78+17−14	>1.3
1676	174535.5 − 290124	gc	3549	1000	2	15920	1234+77−73	1877+71−68	1.5 ± 0.1
1676			5950	100	2	16544	156+14−13	267+27−24	1.7 ± 0.2
1676			6644	1000	2	2304	179+78−57	809+155−131	4.5 ± 1.9
1686	174535.6 − 290133	gc	3665	1000	3	61632	14+6−4	178+15−14	12.9 ± 5.0
1686			6641	1000	2	4336	650+238−183	5389+222−213	8.3 ± 2.7
1691	174535.7 − 285357	f	5951	100	2	29264	10+11−8	79+13−12	7.9 ± 7.5
1706	174535.8 − 290159	gc	3393	1000	2	90464	<3	14+3−3	>0.8
1748	174536.1 − 290806	gc	3393	1000	2	75104	3+4−3	31+6−5	8.9 ± 9.3
1765	174536.3 − 285545	f	3392	100	4	7568	3+2−1	252+81−63	94.5 ± 60.5

Notes. The columns of the table are: the record number from Table 2, the source name, a flag stating whether a source is in the foreground or near the Galactic center, the ObsID in which the variability was identified, the odds ratio used as a prior in the Bayesian blocks routine when characterizing the variability, the number of blocks used to describe the data, the duration of the block with the maximum flux, the minimum flux, the maximum flux, and the ratio of the maximum to minimum fluxes. The table only includes variable sources that were successfully characterized by the Bayesian blocks routine.

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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2.3.3. Periodic Variability

We searched for periodic variability in the brightest sources by adjusting the arrival times of their photons to the solar system barycenter and computing Fourier periodograms using the Rayleigh statistic (Bucceri et al. 1983). The individual X-ray events were recorded with a time resolution of 3.2 s, so the Nyquist frequency was ≈ 0.15 Hz, which represents the limit above which our sensitivity could not be well characterized. However, we computed the periodogram using a maximum frequency of ≈ 0.2 Hz, to take advantage of the limited sensitivity to higher frequency signals, and to ensure that any observed signal was not an alias.

We considered sources that, in individual observations, produced a large enough number of counts (N_γ) that a fully modulated signal could be detected with 99% confidence. The power P_meas required to ensure that a source had a chance <1 − C of being produced by white noise can be computed if one knows the number of trials in a search, (N_trial), and is given by inverting $C \approx N_{\rm trial} e^{-P_{\rm meas}}$. Here, P_meas is normalized to have a mean value of 1, and the approximation is valid for P_meas≫1 (Ransom et al. 2002). A count threshold can be determined by noting that, if background photons are negligible, the fractional root-mean-squared amplitude of a sinusoidal signal (A) is given by A ≈ (2P_meas/N_γ)^1/2. A fully modulated signal has A = 0.71. After iterating to determine the number of trials corresponding to each count limit, we found that a source with N_γ = 86 could be identified with C = 0.99 if it produced a fully modulated signal.

In total, we searched for pulsations in 717 event lists from 256 different sources, which required 2 × 10⁷ trials. A single signal that had C >  0.99 given this number of trials must have had P_meas >  21.4. However, multiple observations were searched for many sources, so we recorded signals with lower powers and checked whether they also appeared at the same frequency in other observations.

We identified two sources with periodic variability at > 99% confidence, CXOUGC J174532.7 − 290550 and CXOUGC J174543.4 − 285841. We had previously identified both of these by combining 500 ks of exposure over the course of two weeks (Muno et al. 2003c). The other sources in Muno et al. (2003c) were too faint for their periodic variability to be identified in individual observations. We also identified a third source as a good candidate for having periodic variability, CXOUGC J174622.7 − 285218. Signals from this source were identified with periods of ≈ 1745 s in observation 4500 with P_meas = 10.9 from 763 photons, and in observation 7048 with P_meas = 13.4 from 310 photons (Figure 7). The joint probability that these signals were produced at the same frequency by noise (Ransom et al. 2002), given N_trial = 2 × 10⁷, was only 1.4%. Periodic signals were neither detected from this source in observation 945 because the source fell on a chip edge, nor in observations 2273 and 2276 because their exposures were too short.

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We refined our initial estimates of the period for CXOUGC J174622.7 − 285218 for each observation by computing pulse profiles from nonoverlapping 10⁴ s intervals, and modeling the differences between the assumed and the measured phases using a first-order polynomial. The reference epochs of the pulse maxima for the two observations were 53165.3781(6) and 54145.1644(7) (MJD, Barycentric Dynamical Time). The best-fit periods were 1745 ± 3 s and 1734 ± 16 s for observations 4500 and 7048, respectively. The pulse profiles for each observation are displayed in Figure 8. The fractional rms amplitudes of the pulsations were 21% and 32%, respectively. Given the long period for this source, it is most likely a magnetically accreting white dwarf (Muno et al. 2003c).

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We calculated the sensitivity of our observations using synthetic star tests, following the basic methods described in Bauer et al. (2004) and Muno et al. (2006a; see Wang 2004 for another approach). We generated maps of our sensitivity both for each of the stacked observations (i.e., centered on ObsIDs 3392, 4500, 5892, 7034–7048, and 944), and for a fiducial field with an exposure time of 12 ks for those regions only covered by the shallow exposures of Wang et al. (2002a). In brief, for each pointing, we generated a background map by (1) removing events from within a circle circumscribing ≈ 90% of the energy of the PSF around each detected source, and then (2) filling the "holes" in the image with numbers of counts drawn from Poisson distributions with means equal to those of surrounding annuli. We then simulated 100 star fields per pointing. We placed ≈ 5000 point sources at random positions in each background image, with fluxes distributed as N(>S) ∝ S^−α with a slope α = 1.5, and minimum fluxes that would produce three counts in a 100 ks exposure. We converted these fluxes to expected values for the numbers of counts using an exposure map. The exposure map was normalized to produce the mean flux-to-counts conversion for X-ray sources located at or beyond the Galactic center (HR0> − 0.175; Muno et al. 2006a).²⁶ Then, to account for the Eddington bias, we drew observed numbers of counts from Poisson distributions with mean values equal to the expected counts. Next, we obtained model images of the PSF from the routine mkpsf, averaged them when appropriate, and used the composite PSF as the probability distribution to simulate the two-dimensional image of the counts. These were added to the synthetic exposure. Finally, we searched the synthetic image for point sources using wavdetect for the 12 ks exposures, and wvdecomp for the stacked observations. By comparing the input and the output lists, we estimated the minimum flux at which a source would be detected in 50% and 90% of the trials over a grid of points covering our survey. We interpolated between these points to make a map of the sensitivity for each image.

None of our observations are formally confusion-limited at our completeness limits (Hogg 2001; see also Muno et al. 2003). If the background diffuse X-ray emission are unresolved stellar sources, then confusion caused by undetected sources is accounted for naturally by our background maps.

In order to produce a global sensitivity map, we combined the sensitivity maps from the above simulations by recording the best sensitivity at each point in the image. The map of 90% confidence limits is displayed in Figure 9. The effective area of the survey as a function of limiting photon flux and luminosity is displayed in Figure 10. We are sensitive to ≈4 × 10³² erg s⁻¹ (0.5–8.0 keV, assuming D = 8 kpc) at 90% confidence over 1 deg², and to ≈1 × 10³² erg s⁻¹ over 0.1 deg². This is a factor of ≈ 2 improvement over Muno et al. (2006a).

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However, we still find that the majority of X-ray sources are detected at fluxes below our completeness limits. Of the 6760 sources that are likely to lie at or beyond the Galactic center (HR0> − 0.175), only 15% are brighter than the 90% completeness limit at the point at which they were detected, and only 40% are brighter than the 50% completeness limit. This is caused by two effects. First, 20% of the sources are detected only in the hard band, whereas our completeness limits are for the full band. Second, the number-flux distribution is steep (Section 3.3), such that many of the faint sources are only detected because of positive Poisson fluctuations in their count rates.

These maps are used in selecting complete samples of sources for measuring the spatial (Section 3.2) and flux (Section 3.3) distributions. Sources below our completeness limits are still securely detected, although other sources with similar intrinsic fluxes have been missed.

Experience with matching X-ray and optical sources as part of the Chandra Deep Fields and Orion Ultradeep projects suggests that the positions of the X-ray sources can be refined with respect to those provided by the wavelet algorithms (Alexander et al. 2003; Getman et al. 2005). Therefore, we used the implementations of their techniques in ACIS Extract to refine the positions of our sources. For each source, we made a composite image by combining the event lists from each relevant observation, and then made a matching composite PSF image that we weighted by the values of the exposure maps at the source positions. From this image, we computed two additional estimates for the source position: the mean positions of the events within each source region, and a centroid determined by cross-correlating the PSF and the source images. Following Getman et al. (2005), if a source lay within 5' of the aim point, we used the mean position of the events within the source extraction region. If the source lay beyond 5', we used the position determined by cross-correlating the source image and the PSF image. However, if the offset of the refined position from the wavelet position was larger than the smallest source extraction radius that we used, we assumed that a nearby source had caused confusion, and retained the wavelet position.

Unfortunately, we could not empirically calibrate the uncertainties on our source positions, because even the foreground infrared sources had such a high density that ≈ 50% of those that fell within 3'' of an X-ray source were chance alignments. Therefore, we computed 95% positional uncertainties using Equation (5) in Hong et al. (2005a),²⁷ which is based on the positions of sources reported by wavdetect in simulated observations,

$$\begin{eqnarray} r_{\rm err} & = & 0\farcs 25 + \frac{0\farcs 1}{\log _{10}(c + 1)} \left[1 + \frac{1}{\log _{10}(c + 1)}\right] \nonumber \\ & + & 0\farcs 03 \left[ \frac{\theta }{\log _{10}(c + 2)}\right]^2 + 0\farcs 0006 \left[\frac{\theta }{\log _{10}(c + 3)}\right]^4. \end{eqnarray} \tag{ 1 }$$

Here, θ is the offset in arcminutes of the source from the nominal aim point, and c is the net number of counts. For sources detected in composite images, we defined c to be the net counts summed over all observations, and θ to be the exposure-weighted averages of the sources' offsets from the aim points of their respective observations. For sources detected in individual observations, we defined c and θ to be the values for the observations in which the sources were identified.

If r_err is larger than the smallest radius of the region used to extract photometry for the source (the "source radius"), the uncertainty was set equal to the radius of the extraction region. These sources are marginally detected, and the high background in the Galactic center produces a large tail in the distribution of possible positions. We retained them because they passed all of our other selection criteria.

Hong et al. (2005a) established Equation (1) by running wavdetect on simulated, single observations that were generated using a ray-tracing code. Unfortunately, our observations are more complicated. On the one hand, most of the positions are determined from composite images generated from observations with very different aim points. The inclusion of data with large θ could add uncertainty to our measurements. On the other hand, our positions have been refined compared to the wavdetect values, so the uncertainty on some sources could be smaller. Therefore, we view Equation (1) as a compromise. Nonetheless, a comparison of the offsets between 500 foreground X-ray sources and the blue 2MASS sources that are their counterparts (as described in detail in J. Mauerhan et al., in preparation) reveals that the positions in the new catalog are ≈ 60% better than in Muno et al. (2003a, 2006a).

We also note that because of the way we averaged the PSF, the positions and uncertainties for the sources that vary in flux between observations (10% of our sample) could be misestimated. For example, a variable source that was only bright in an off-axis observation would have a larger uncertainty than might be expected if it were also bright during an on-axis observation. We have not evaluated whether systematic offsets in the positions are expected.

Table 2 contains the locations of the point sources, parameters related to the observations of each source, and information on the data quality. Its columns are as follows.

• 1.  
  Record locators that can be used to cross-correlate with other tables.
• 2.  
  The source names, which are derived from the coordinates of the source based on the IAU format, in which least-significant figures are truncated (as opposed to rounded). The names should not be used as the locations of the sources.
• 3.  
  The right ascensions and declinations of the sources, in degrees (J2000).
• 4.  
  Same as column 3.
• 5.  
  The 95% uncertainties in the positions (the error circles). There are 5810 sources with uncertainties ⩽ 1'' (half of which are within 7' of Sgr A*), and 1950 with uncertainties ⩽ 05 (85% of which are within 7' of Sgr A*).
• 6.  
  Flag indicating how the positions were derived. A "d" indicates that the position is from the mean position of events, a "c" indicates that it was derived by cross-correlating the image and the PSF, and a "w" indicates that it was derived from a wavelet algorithm. Sources marked with a "w" are likely to be confused with a nearby source, or in a region of high background.
• 7.  
  The images in which the sources were identified. The tags "full," "2002," "2004," and "2005" indicate that a source was found in composite images of the Sgr A* field. All other values are the observations in which a source was detected. Two sources added manually are tagged with "hand."
• 8.  
  Additional information about how the sources were detected. The tag "full" refers to any source detected with wavdetect in the 0.5–8.0 keV band; "soft" sources were detected in the 0.5–2.0 keV but not the full band; "hard" sources were detected in the 4–8 keV band but neither of the other two bands. The tag "tile" indicates that the source was detected in a composite 0.5–8.0 keV image with wvdecomp.
• 9.  
  The offsets (θ) from the aim point, in arcmin. If a source position was estimated from a composite image, θ is the mean offset weighted by the exposure. If a position was taken from a single observation, θ is the offset for that observation.
• 10.  
  The number of observations used to compute the photometry for each source.
• 11.  
  The exposure times in seconds.
• 12.  
  The fractions of the PSF enclosed by the source extraction regions.
• 13.  
  The fiducial energies of the PSFs used to construct the source extraction regions.
• 14.  
  The smallest radius for the extraction region that was used for a source, in arcseconds. This is determined from the observation in which the source was closest to the aim point. It is also an absolute upper bound to the positional uncertainty for a source.
• 15.  
  The 50% completeness limit at the position of the source. Sources brighter than these completeness limits can be used to compute spatial and flux distributions, although the sensitivity map (Figure 9) is needed to compute the corresponding survey area.
• 16.  
  Flags denoting quality, and other information: "a" for sources used to register the astrometry of fields; "s" for sources variable on short timescales, as indicated by probabilities of < 0.1% that the event-arrival times for at least one observation were consistent with a uniform distribution according to the KS test; "l" for sources that were variable on long timescales, as indicated by a probability of < 0.1% that the fluxes for all observations were consistent with a uniform distribution according to the KS test; "e" for sources that may be part of an extended, diffuse feature (Muno et al. 2004a); "c" for sources confused with another nearby source; "g" for sources that fell near the edge of a detector in one or more observations; "b" for sources for which the source and the background spectra have a > 10% chance of being drawn from the same distribution according to a KS test; "x" for sources for which the 0.5–2.0 keV band photometry is inaccurate because the satellite was programmed to omit photons below 1 keV from the telemetry; and "p" for sources that suffered from photon pile-up.

Table 3 contains the X-ray photometry for each source. It contains the following columns.

• 1.  
  The record locators.
• 2.  
  The source names.
• 3.  
  The log of the probabilities that the source and the background spectra are derived from the same distribution, according to a KS test. Large negative values indicate that the source and the background spectra are distinct, and therefore that the source is most likely real.
• 4.  
  The total numbers of counts in the 0.5–2.0 keV band.
• 5.  
  The estimated numbers of background counts in the 0.5–2.0 keV band.
• 6.  
  The net numbers of counts in the 0.5–2.0 keV band, and the 90% lower and upper uncertainties. In the case of nondetections, an upper limit is provided.
• 7.  
  The total numbers of counts in the 2–8 keV band.
• 8.  
  The estimated numbers of background counts in the 2–8 keV band.
• 9.  
  The net numbers of counts in the 2–8 keV band, and the 90% lower and upper uncertainties. In the case of nondetections, an upper limit is provided.
• 10.  
  The fluxes in the 0.5–2.0 keV band, in units of photons cm⁻² s⁻¹.
• 11.  
  The fluxes in the 2–8 keV band, in units of photons cm⁻² s⁻¹.
• 12.  
  The mean energy of photons in the source region, statistically corrected for the background.
• 13.  
  The soft colors and 90% upper and lower uncertainties.
• 14.  
  The medium colors and 90% upper and lower uncertainties.
• 15.  
  The hard colors and 90% upper and lower uncertainties.

These tables were designed to be inclusive, so sources of questionable quality are included. For instance, 134 sources have net numbers of counts in the 0.5–8.0 keV band that are consistent with 0 at the 90% confidence level. These sources are only detected in a single band and are presumably either very hard or very soft, detected in single observations because they were transients, or detected in stacked observations with wvdecomp at marginal significance. We have chosen to include them because they passed the test based on Poisson statistics from Weisskopf et al. (2007).

In Figure 11, we plot the hard color versus the flux from each source. Foreground sources are indicated with open red circles, and sources at or beyond the Galactic center with filled blue circles. There are 6381 Galactic center sources and 1091 foreground sources with measured hard colors. We have calculated the hardness ratios and photon fluxes that we would expect to get from these energy bands for a variety of spectra and 0.5–8.0 keV luminosities using PIMMS and XSPEC. In Figure 11, we plot the colors and fluxes expected for power-law spectra with the dotted lines, and for a optically thin thermal plasma with the solid lines. We have assumed a distance of 8 kpc and 6 × 10²² cm⁻² of absorption from interstellar gas and dust.

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The median hard color for the Galactic center sources is 0.17. For interstellar absorption, this corresponds to a Γ ≈ 0.5 power law. Using a simulated spectrum, we have determined that the photon fluxes can be converted to energy fluxes according to 1 photons cm⁻² s⁻¹ = 8.7 × 10⁻⁹ erg cm⁻² s⁻¹ (0.5–8.0 keV). The deabsorbed 0.5–8.0 keV flux is approximately 1.7 times larger, so that for a distance D = 8 kpc, 10³⁴ erg s⁻¹ equals 9 × 10⁻⁵ photons cm⁻² s⁻¹. The large median value of the hard color is inconsistent with that expected from a thermal plasma (of any temperature) attenuated by interstellar gas and dust. However, our earlier study of the spectra of brighter sources suggest that intrinsic absorption is present, and that the underlying spectrum is consistent with a kT = 7–9 keV thermal plasma (Muno et al. 2004b). For sources that are intrinsically absorbed, the luminosities will be significantly higher than implied by Figure 11.

We present the spatial distribution of X-ray sources located near or beyond the Galactic center (HR0> − 0.175) in Figure 12. We examined only sources brighter than 2 × 10⁻⁶ photons cm⁻² s⁻¹, and only included a source if the 50% confidence flux limit at its position was less than or equal to 2 × 10⁻⁶ photons cm⁻² s⁻¹. This flux limit was chosen as a compromise between the area over which the distribution is derived, which decreases for lower flux limits (Figure 9), and the number of sources used in the distribution, which tends to increase for lower flux limits (Figure 3). In the top panel of Figure 12, we display the locations of each of the 479 sources that met the flux criteria. The area over which the flux limit is <2 × 10⁻⁶ photons cm⁻² s⁻¹ is displayed in white, and the greyed areas indicate regions of poorer sensitivity. A concentration of X-ray sources is evident near the position of Sgr A*. In the bottom panels of Figure 12, we display histograms of the numbers of sources per unit area, as functions of Galactic longitude and latitude. Only regions of good sensitivity are used.

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We then compared the spatial distributions to that of the stellar mass that has been inferred from infrared observations. Our mass model consists of the young nuclear bulge and cusp and the old Galactic bulge from Launhardt et al. (2002), and the model for the Galactic disk from Kent et al. (1991; see Muno et al. 2006a for further details). To make a direct comparison with our unevenly sampled spatial distributions, we integrated the model for the stellar mass from 6 to 14 kpc along the line of sight at points on a 1' grid covering our survey region, and interpolated the resulting values onto the image. We then summed the values of the integrated mass over areas of good sensitivity, to match the longitude and latitude bins of the observed histogram. Finally, we minimized chi-squared over one parameter to scale the binned mass model to the observed distributions of X-ray sources. We find a best-fit scaling factor of 5 × 10⁻⁷ X-ray sources per solar mass for sources brighter than 2 × 10⁻⁶ photons cm⁻² s⁻¹ for both the latitude and the longitude distributions. For the longitude distribution, χ²/ν = 22.4/19, and for the latitude distribution, χ²/ν = 20.6/17. The best-fit models are displayed with solid lines in the bottom panels of Figure 12.

The models are acceptable descriptions of the data. However, in the plot as a function of longitude, at the inner few arcminutes around Sgr A*, and just to the east toward the Arches and the Quintuplet regions, there is an ≈ 2.8σ excess in the number of observed X-ray sources. We find that this excess is also present with similar significance if we chose tighter or looser flux limits between 1 and 5 × 10⁻⁶ photons cm⁻² s⁻¹. The model also predicts more sources than observed at L = 05–06 at the 1σ level, but this is probably because the Sgr B molecular complex attenuates X-rays from sources behind it.

We computed the number-flux distribution based on the maximum-likelihood algorithm described in Murdoch et al. (1973), which we modified to use Poisson statistics in the manner described in Appendix B of Muno et al. (2006a). We examined three regions that had well defined flux limits and effective exposure times: the inner 8' around Sgr A*, the 8' around the Arches cluster (excluding the overlap with the Sgr A* field), and the portions of the survey covered by the 40 ks pointings taken between 2006 and 2007. We assumed that the number-flux distribution was a single power law over the ranges of fluxes that we measured, N(>S) = N₀(S/S₀)^−α. We display the resulting cumulative number-flux distributions in Figure 13, and list the best-fit parameters in Table 6. Our distributions extend a factor of ≈ 2 deeper than in Muno et al. (2006a).

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The fit to the distribution from the Sgr A* region is formally poor, because the distribution steepens at low fluxes (Muno et al. 2003a). However, we do find that the Arches region has a flatter flux distribution (α = 1.0 ± 0.3) than either the inner 8' around Sgr A (1.55 ± 0.09) or the wide survey field (1.3 ± 0.1). The difference is only significant at the 1.4σ level. Nonetheless, given that there are also excess sources coincident with the Arches region in the spatial distribution, we suggest that there is a genuine overabundance of bright X-ray sources in this region of recent star formation.

A similar asymmetry has been identified in the flux of diffuse emission from helium-like iron (Koyama et al. 2007). We suggest that both the excess point sources and the excess iron emission are related to the concentration of young stars in this region, the most dramatic manifestations of which are the Arches and the Quintuplet clusters (e.g., Figer et al. 1999). The iron emission is probably diffuse, hot plasma that forms in shocks where the stellar winds from the clusters impact the interstellar medium (ISM; 2002, 2004, 2006). The excess point sources are probably young, OB and Wolf–Rayet stars in binaries (e.g., Mauerhan et al. 2007).