FIELD AND GLOBULAR CLUSTER LOW-MASS X-RAY BINARIES IN NGC 4278

The GC sources S96, S163, S185, and S194 of B09 were selected for individual analysis, based on the luminosity criterion discussed in Section 2. When using a "canonical" power-law model (Γ = 1.7; N_H = N_H(Gal.), see B09), S96 was detected with co-added average luminosity of ∼3.8 × 10³⁸ erg s⁻¹ and the other three sources with similar co-added luminosities of ∼2.5 × 10³⁸ erg s⁻¹ (Figure 3). S96 and S194 are associated with blue GCs, S163 and S185 with red GCs.

The results of the spectral analysis are summarized in Table 3, which lists source number; observations used (following Table 1); net source counts and count rate, both with 1σ statistical error; model; Cash statistics; reduced χ², number of degrees of freedom and probability (when using Cash statistic, we present a value of "goodness" in place of probability. This value represents the percentage of Monte Carlo simulations produced from the best-fit data model, which return a lower value of Cash than has been obtained with the source data); best-fit N_H, Γ, and kT, all with 1σ error for one interesting parameter (F indicates that N_H was frozen at the Galactic value); (0.3–8.0 keV) absorption-corrected best-fit luminosity, calculated from exposure-weighted luminosities for variable sources. B09 show that S96 is fairly steady in both luminosity and HR throughout the six observations, S185 experiences significant changes in flux across the different observations with no HR variation, while S163 and S194 change in both luminosity and HR multiple times (see Figure 3). We show the results for the fits of different portions of the data (see below) and of the "grouped" spectra of each source in Table 3. Figure 6 shows 1σ and 2σ confidence contours for two interesting parameters for both PO (N_H and Γ) and DBB (N_H and kT) models, for the different spectral/luminosity states of S163 and S194. The confidence contours for the co-added spectra of the four sources are compared in Figure 7. In all cases, there is no strong statistical preference for a PO or DBB model, but the allowed parameter spaces for a given model may differ significantly in some cases. The above applies to all the results presented in this paper.

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Table 3. Single GC Fit Results

Source	Obs.	Counts	Count Rate	Model	Statistic			PCash	$P_{\chi ^2}$	NH	Γ	kT	LX
			(10−3 $\rm s^{-1}$)		C-stat	χ2/ν	ν	(%)	(%)	($10^{20}\; \rm cm^{-2}$)		(keV)	(1038 erg$\;\rm s^{-1}$)
96	All	826.4 ± 28.7	1.3 ± 0.3	PO	...	1.4	25	...	0.08	8.8 ± 7.3	1.5 ± 0.2	...	5.05
				DBB	...	1.5	26	...	0.05	F	...	1.4 ± 0.3	4.11
163	Group 1	124.2 ± 11.1	1.5 ± 0.4	PO	370	...	...	89	...	27.0 ± 13.8	2.5 ± 0.5	...	5.48
	(1 + 3)			DBB	368	...	...	93	...	8.8 ± 6.0	...	0.7 ± 0.2	2.61
	Group 2	453.7 ± 21.3	1.2 ± 0.1	PO	1042	...	...	57	...	11.0 ± 4.3	1.4 ± 0.1	...	4.09
	(2 + 4 + 5 + 6)			DBB	1036	...	...	65	...	F	...	1.6 ± 0.2	3.16
	Group 3	267.0 ± 16.3	1.3 ± 0.1	PO	572	...	...	60	...	9.3 ± 5.2	1.4 ± 0.2	...	4.17
	(2 + 4)			DBB	569	...	...	70	...	F	...	1.6 ± 0.2	3.29
	Group 4	186.7 ± 13.7	1.2 ± 0.1	PO	470	...	...	52	...	14.4 ± 7.5	1.5 ± 0.3	...	4.06
	(5 + 6)			DBB	467	...	...	71	...	3.9 ± 3.7	...	1.6 ± 0.4	3.14
	All Obs.	577.9 ± 21	1.3 ± 0.2	PO	1419	...	...	55	...	12.9 ± 3.8	1.6 ± 0.1	...	4.14
				DBB	1411	...	...	68	...	2.6 ± 2.6	...	1.4 ± 0.2	3.04
185	All Obs.	550.4 ± 24.0	1.2 ± 0.1	PO	1423	...	...	44	...	12.5 ± 4.3	1.7 ± 0.2	...	3.50
				DBB	1357	...	...	74	...	2.7 ± 2.7	...	1.2 ± 0.1	2.53
194	Group 1	150.3 ± 11	1.8 ± 0.2	PO	431	...	...	78	...	23.3 ± 10.0	1.8 ± 0.4	...	6.00
	(1 + 3)			DBB	427	...	...	89	...	9.7 ± 5.9	...	1.1 ± 0.1	3.94
	Group 2	121.9 ± 11	1.1 ± 0.1	PO	250	...	...	45	...	3.9 ± 3.9	1.9 ± 0.3	...	2.81
	(2)			DBB	251	...	...	98	...	F	...	0.7 ± 0.1	1.87
	Group 3	307.4 ± 16	1.1 ± 0.1	PO	702	...	...	49	...	5.7 ± 4.1	1.6 ± 0.2	...	3.25
	(4 + 5 + 6)			DBB	694	...	...	90	...	F	...	1.1 ± 0.1	2.29
	All Obs.	579.6 ± 24	1.3 ± 0.4	PO	...	0.65	14	...	0.82	F	1.3 ± 0.1	...	3.60
				DBB	...	0.74	15	...	0.75	F	...	1.5 ± 0.2	3.09

Notes. Based on the B10 simulations (see the text) a significant/strong DBB component is expected in Group 1 spectra of S163 and S194, and in S185.

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For S163 we grouped the data as follows: Group 1 contains the softest and highest count rate observations (L_X ∼ 4 × 10³⁸ erg s⁻¹ in Figure 3, where the luminosity is from B09, calculated for the same assumed spectrum with N_H = N_H(Gal.) and Γ = 1.7 in all cases, therefore it represents just a scaling of the detected count rate) and Group 2 contains all the other observations that have similar, harder spectra compared to Group 1. We also subdivided the Group 2 observations based on luminosity: Group 3 contains the two intermediate count rate observations, with B09 L_X ∼ 3 × 10³⁸ erg s⁻¹, and Group 4 contains the two lowest count rate observations, with B09 L_X ∼ 1 × 10³⁸ erg s⁻¹. Although the parameter spaces overlap, the best-fit values suggest that S163 alternates between a high/soft state, with Γ ∼ 2.5 ± 0.5 (or kT∼0.7 ± 0.2keV) and a low/hard state with Γ ∼ 1.4 (or kT ∼1.6 keV), before finally settling down in the low/hard state. With the exception of the PO fit of the high/soft Group 1 spectrum, which requires intrinsic absorption with N_H ∼ 2 × 10²¹ cm⁻², N_H is consistent with N_H(Gal.). The larger N_H in the power-law fit of the high-luminosity data suggests spectral curvature, favoring the DBB model (see Figure 8, left, based on the simulations of B10).

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A similar procedure was followed for S194: Group 1 contains the two highest count rate observations; Group 2 contains a single observation which has markedly low HR and intermediate count rate; Group 3 contains the observations with the lowest count rate, and with HR consistent with that of Group 1. S194 appears to go through two distinct state transitions, beginning with a high/hard state with a B09 luminosity of ∼3 × 10³⁸ erg s⁻¹ and Γ ∼ 1.8 ± 0.4 (or kT ∼1.1 ± 0.1 keV), changing to a high/soft state with a slightly lower B09 luminosity of ∼2 × 10³⁸ erg s⁻¹ and slightly softer spectrum (kT ∼0.7 ± 0.1 keV), and then settling in a luminosity-independent hard state. In the power-law fit, the highest luminosity Group 1 has N_H>N_H(Gal.) while N_H is consistent with N_H(Gal.) in the DBB fit, which may be indicative of a thermal disk dominant emission (see B10). The other spectra are all consistent with N_H(Gal.) in the PO fits, which may be indicative of a significant power-law component (see Figure 8, right, based on B10).

The grouped spectra of all the observations for each of the four sources, except S185, are consistent with N_H(Gal.) for both models. These spectra are fitted with "average" Γ ∼ 1.3–1.7 in the PO model; the best-fit PO for S185 instead has N_H larger than line of sight. The latter result may be indicative of a significant disk component (see Figure 8, left). The DBB fits return generally consistent values of kT ∼ 1.2–1.5 keV. Using the best fit models for the co-added spectra, we derive luminosities slightly higher than the values in B09, but the differences are understandable given the differences of the best-fit parameters with those assumed in B09 (power-law spectrum with N_H = N_H(Gal.) and Γ = 1.7). In all cases, the luminosity variability patterns of B09 are still present.

The results of the spectral analysis of three B09 field sources, S146, S158, and S184, each with average B09 luminosity of ∼5.0 × 10³⁸ erg s⁻¹ over the six observations (Figure 4), are summarized in Table 4, which follows the same format as Table 3. The contours for the two interesting parameters for both PO and DBB models for the three sources can be seen in Figure 9.

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Table 4. Single Field Fit Results

Source	Obs.	Counts	Count Rate	Model	Statistic			PCash	$P_{\chi ^2}$	NH	Γ	kT	LX
			(10−3 $\rm s^{-1}$)		C-stat	χ2/ν	ν	(%)	(%)	($10^{20}\; \rm cm^{-2}$)		(keV)	(1038 erg $\rm s^{-1}$)
146	Group 1	861.7 ± 29.4	2.05 ± 0.5	PO	...	0.61	29	...	0.95	12.6 ± 6.1	1.4 ± 0.2	...	8.19
	(1 + 3 + 4 + 5 + 6)			DBB	...	0.58	30	...	0.97	F	...	1.6 ± 0.2	6.15
	Group 2	154.3 ± 12.4	1.4 ± 0.1	PO	247	...	...	33	...	19.9 ± 7.5	2.1 ± 0.3	...	4.77
	(2)			DBB	246	...	...	71	...	3.9 ± 3.9	...	1.0 ± 0.2	2.90
	All Obs.	1016.2 ± 31.9	2.22 ± 0.6	PO	...	0.67	35	...	0.93	15.3 ± 5.7	1.6 ± 0.2	...	6.97
				DBB	...	0.60	36	...	0.97	F	...	1.5 ± 0.1	5.23
158	Group 1	463.7 ± 21.5	2.47 ± 0.3	PO	801	...	...	58	...	20.7 ± 5.1	1.9 ± 0.2	...	8.56
	(1 + 3 + 4)			DBB	790	...	...	68	...	5.3 ± 3.7	...	1.2 ± 0.1	5.66
	Group 2	244.8 ± 15.6	2.27 ± 0.2	PO	299	...	...	58	...	22.7 ± 6.2	2.2 ± 0.2	...	7.99
	(2)			DBB	293	...	...	82	...	5.9 ± 3.8	...	0.9 ± 0.1	4.55
	Group 3	443.2 ± 21.1	2.72 ± 0.3	PO	...	0.95	15	...	0.50	8.9 ± 4.0	1.7 ± 0.1	...	7.72
	(5 + 6)			DBB	...	1.05	16	...	0.39	F	...	1.2 ± 0.1	6.98
	All Obs.	1151.7 ± 33.9	2.51 ± 0.7	PO	...	1.23	41	...	0.14	21.4 ± 4.0	1.9 ± 0.2	...	7.00
				DBB	...	1.25	41	...	0.13	1.9 ± 1.9	...	1.2 ± 0.1	4.91
184	Group 1	241.0 ± 15.5	2.60 ± 0.5	PO	532	...	...	53	...	13.1 ± 5.6	1.6 ± 0.2	...	8.72
	(1 + 6)			DBB	533	...	...	72	...	2.2 ± 2.2	...	1.6 ± 0.2	6.72
	Group 2	557.8 ± 23.6	2.2 ± 0.4	PO	...	1.11	19	...	0.33	4.5 ± 4.5	1.3 ± 0.2	...	6.72
	(2 + 3 + 4)			DBB	...	1.10	20	...	0.34	F	...	1.7 ± 0.3	5.72
	Group 3	290.0 ± 17.0	2.70 ± 0.2	PO	366	...	...	83	...	25.5 ± 7.0	1.8 ± 0.2	...	10.36
	(5)			DBB	374	...	...	94	...	8.0 ± 4.2	...	1.4 ± 0.2	7.16
	All Obs.	1090.4 ± 33.0	2.4 ± 0.6	PO	...	1.25	38	...	0.14	5.0 ± 2.7	1.4 ± 0.1	...	6.96
				DBB	...	1.35	39	...	0.07	F	...	1.5 ± 0.2	5.47

Notes. Based on the B10 simulations (see the text) a significant/strong DBB component is expected in S146, S158 and Group 1 and Group 3 spectra of S184.

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For S146, Figure 4 shows that the HR does not vary; the B09 luminosity (count rate) is also constant, except for Obs. 2, where it is a factor of six lower. We divided the data in two groups: Group 1, which excludes Obs. 2; and Group 2 (Obs. 2). The PO fits for both groups give N_H ∼ 10 × N_H(Gal.); Γ is 1.4 ± 0.2 for Group 1 and larger (Γ = 2.1 ± 0.3) for Group 2 (see Figure 9). The DBB fit gives N_H consistent with N_H(Gal.); reflecting the steeper spectrum, the lower-luminosity Group 2 has a lower value of kT (1.0 ± 0.2 keV against 1.6 ± 0.2 keV for Group 1). The N_H>N_H(Gal.) in the PO fits suggests that the DBB model may be a better representation of the emission spectrum, or that a sizeable disk component may be present in the emission (see simulations of B10; Figure 8, left).

For S158, Figure 4 shows that there are variations in both luminosity and HR between different observations. Accordingly, we fitted jointly spectra as follows: Group 1 contains the observations which show the hardest spectra, and have a similar B09 luminosity of ∼5 × 10³⁸ erg s⁻¹; Group 2 contains the observation with the softest spectrum, which also has a B09 luminosity in the range of Group 1; Group 3 contains the observations which have the lowest B09 luminosity (∼3 × 10³⁸ erg s⁻¹) and intermediate HR. The results echo those for S146, with the PO model requiring intrinsic absorption, while the DBB model gives results consistent with the line of sight N_H (but best-fit N_H>N_H(Gal.), except for Group 3). The confidence contours show that the values of Γ (or kT in the DBB model) are consistent within 2σ, although the Group 2 parameter range suggests a softer spectrum. As for S146, the N_H>N_H(Gal.) in the PO fits suggests that the DBB model may be a better representation of the emission spectrum (see simulations of B10; Figure 8, left).

For S184, both luminosity and HR variations are small. Group 1 contains observations 1 and 6, which displayed the highest B09 luminosity of ∼5 × 10³⁸ erg s⁻¹ and consistent HR; Group 2 contains observations which had a slightly lower B09 luminosity of ∼4.5 × 10³⁸ erg s⁻¹, and also have a similar HR (Obs. 2, 3, 4); Group 3 contains Obs. 5, which has consistent L_X with Group 1, but different X-ray colors. The PO model fits give larger N_H>N_H(Gal.) for the higher luminosity Group 1 and Group 3, together with a steeper power-law index, when compared to the Group 2 results (Table 4, Figure 9). This again may suggest a larger disk fraction in the spectrum of Groups 1 and 3 (see B10). The DBB fits are in both groups consistent with N_H(Gal.) and also have similar kT ∼ 1.5–1.6 keV.

The grouped total spectra (Figure 10) of the three sources in the PO fits have best-fit N_H exceeding N_H(Gal.), although the contours are marginally consistent with this value, except for S158, which shows definite intrinsic absorption. The DBB parameter spaces are instead consistent with N_H(Gal.) in all cases. S158 (in both models) appears marginally softer. We derive best-fit luminosities slightly exceeding those in B09. The luminosity variability patterns of B09 are reproduced, with the exception of S158. In the case of S158, the variability behavior derived from B09 differs to that inferred here. This discrepancy arises from the different extraction regions used in the source counts photometry. In B09, S158 has been classified as an overlapping source and therefore a pie-sector correction was made to account for this (see Section 2.1 of B09 for details). Here a smaller extraction region was used to exclude any counts from the overlapping source. For both methods this resulted in a reduction in source count of ∼5% for observations 1, 2, 3, and 4. However, for observations 5 and 6 there was a reduction of ∼50% in B09, compared to only 7% and 9% in this work. From inspection of the raw counts this is a consequence of the asymmetric distribution of source counts in observations 5 and 6.

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Table 5 gives our results for PO, DBB, and combined PO+DBB model fits for the high-, mid-, and low-luminosity GC source groups. Figure 11(top) shows the two-parameter 1σ and 2σ confidence contours for the PO and DBB models. For the PO model, the mid- and high-luminosity spectra have consistent parameter spaces, with best-fit Γ = 1.5 and best-fit N_H exceeding the Galactic N_H, although the parameter space of the mid-luminosity sample is consistent with this value. The low-luminosity group parameter space suggests an intrinsically absorbed softer spectrum with Γ ∼ 2.0 ± 0.15, which is inconsistent with the higher luminosity groups at the >2σ confidence level. The elevated best-fit N_H required by the PO fits may point to a dominant average thermal emission (see Figure 8, left; B10). The DBB best-fit N_H is below the Galactic N_H for all the spectra, however the Galactic value is within the allowed parameter space in all cases; at N_H = N_H(Gal.), the mid- and high-luminosity spectra are fitted with kT in the range ∼1.3–1.6 keV, while the low-luminosity spectrum is consistent with a lower kT of ∼1.1 ±  0.09 keV, indicating a softer spectrum, as in the case of the PO fits.

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Since the high- and mid-luminosity confidence spaces are consistent, we also combined these data for a single fit, in order to improve the statistics of the results. The resulting N_H significantly exceeds N_H(Gal.), and Γ remains near 1.5. The combined parameter space is inconsistent with that of the low-luminosity group, at >3σ confidence (not shown). For the DBB fit to the combined high+mid spectra, freezing N_H = N_H(Gal.) gives a best-fit temperature of 1.5 keV. Overall the fits are good, with most reduced χ²_ν values around 1.0, the exception being the high, and high + mid luminosity samples which have χ²_ν ∼ 1.4. Using PO + DBB models does not improve the quality of the fit (not shown). One possible reason for the poorer fits of the high-luminosity spectrum is the small number of sources included, with variable spectra, which may not be approximated adequately by the simple fit models. There are only four high-luminosity GC sources, two of which show long-term variability and two that show short-term variability (B09).

Table 6 summarizes the results for PO and DBB and combined PO + DBB model fits for the high-, mid-, and low-luminosity field LMXB samples. The large difference between the sum of the "high," "mid," and "low" counts and the counts in the "all" group is a consequence of the omission of some field sources in the three luminosity groups, which have been included in the "all" group. As discussed in Section 2, these sources were excluded from the sub-groups due to large overlaps with other field sources with different luminosity cuts.

The two-parameter confidence contours for the PO and DBB fits are shown in Figure 11 (bottom). The 3σ two-parameter power-law contours of the high-luminosity field spectrum (not shown) are inconsistent with either the medium- or low-luminosity spectra, requiring intrinsic absorption in excess of N_H(Gal.); as discussed in Section 3, this result may suggest a dominant disk emission in these luminous sources (see B10; Figure 8, left). The medium- and low-luminosity parameter spaces overlap at 2σ confidence values and are consistent with N_H = N_H(Gal.), suggesting an average power-law-dominated spectrum (see B10). Fixing N_H for these two sub-samples at the Galactic value, the allowed intervals of photon indices are inconsistent at >2σ. All the spectra are consistent with Γ ∼1.6–1.7, however the medium-luminosity spectrum may be consistent with a steeper power law (Γ ∼ 1.8 ± 0.08) when N_H is frozen at Galactic value.

In all cases, the DBB fits tend to have minimum χ² at N_H < N_H(Gal.); moreover, the confidence contours for medium- and low-luminosity sample exclude N_H(Gal.), suggesting the presence of a low-energy excess in the data, which may be connected with the presence of a significant power-law component (see Figure 8, right, B10). Freezing N_H = N_H(Gal.), we obtain best-fit kT∼1.4, 0.9 and 1.2 keV for high, medium, and low-luminosity spectra respectively, with χ²_ν values of 1.2, 1.6 and 1.1, respectively (see Table 6). So while the DBB fits are acceptable in this instance for both high- and low-luminosity spectra, the PO model provides a significantly better fit for the medium-luminosity spectrum. As shown in the Table 6, the values of kT found are inconsistent with one another at the 2σ level, if we freeze N_H = N_H(Gal.). However, as discussed above, our comparison with the B10 simulations suggests that DBB only emission is not likely, especially in the lower luminosity samples.

The results of the joint fit of co-added spectra in selected luminosity ranges show differences when comparing GC and Field samples. The high-luminosity contours (solid in Figure 11) do not overlap in the power-law fit, but the range of Γ is the same, while the field sources are fitted with significantly higher N_H.; the contour are instead consistent in the DBB fit. The mid-luminosity contours (dotted in Figure 11), have a similar range of N_H in the PO fit, but the range of Γ is steeper for the field sources (1.7–2 versus 1.3–1.7 for the GC spectra). This difference is reflected in the DBB contours, where the field temperatures are lower; however the latter spectra are also badly fit with the DBB model, as discussed above, and require in this model unphysical low N_H, suggestive of a power-law spectrum (B10; Figure 8, right).

The low-luminosity parameter spaces (dashed in Figure 11) only partially overlap in the PO fits, with the GC spectrum being fitted with steeper power laws and requiring N_H higher than Galactic, while the field spectrum is consistent with Galactic N_H. The DBB parameter spaces have consistent kT ∼ 1.1 keV, but require best-fit N_H < N_H(Gal.) for the field LMXB spectrum, consistent with a power-law component in the emission (B10, Figure 8, right); although the best-fit N_H is also below the Galactic value for the GC spectrum, N_H(Gal.) is within the confidence contours.

Table 7 summarizes the results of the spectral fits for the sources associated with either red or blue GCs. Figure 12 shows the two-parameter confidence contours for the PO and DBB model fits for these spectra. For the PO model, the 1σ parameter spaces barely touch, suggesting slightly lower N_H in the red GC spectra; however, the 2σ parameter spaces are consistent. For both red and blue samples, the PO fit is consistent with N_H>N_H(Gal.). In the DBB fits, the red GC parameter space is within that of the blue sample and again suggests lower N_H. Although, both red and blue GC spectra have unphysical low best-fit N_H in the DBB fits, only for the blue sample is the allowed parameter space consistent with N_H(Gal.). This result is consistent with the red sample having a predominantly power-law spectrum (see B10), the power-law χ² is also more acceptable for the red spectrum than the DBB χ².

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Because of their luminosities in the ${\sim} (3\hbox{--}8) \times 10^{38} \;\rm erg\; s^{-1}$ range (B09; Tables 2 and 3), the seven sources that belong to this category are either neutron star (NS) binaries emitting above the Eddington limit or BH binaries (BHBs). The intensity/spectral variability results provide further insights on the nature of some of these systems. Galactic BH LMXBs typically show X-ray spectra that can be fitted with either a power-law or a multi-color disk model, or a combination of these two models. These sources typically alternate between spectral states, which can be either accretion disk dominated (the thermal or high/soft state) or power-law dominated (the low-luminosity hard state and the high-luminosity steep power law or very high state; see reviews: McClintock & Remillard 2006; Remillard & McClintock 2006; Done et al. 2007). These power-law states have been modeled in terms of varying accretion rates, resulting in either Comptonized emission and/or jets. Similar spectral behavior has been observed in Galactic NS and BH LMXBs, the determining difference being the presence of a hard boundary-layer component in NS sources, which may arise from the NS surface–disk interface. (e.g., Done et al. 2007; Fender et al. 2004).

Our data do not have enough statistics to allow meaningful results for a composite power-law plus disk model, but can be fitted with both individual power-law (PO) and disk (DBB) models (Section 3). When fitted with disk models, the average spectrum of each source is consistent with best-fit $kT_{\rm{in}}$ in the range ∼0.7–1.7 keV; the power-law fits give a range of best-fit Γ ∼ 1.2–2.0. Overall, except for the low end of the power-law indices, these values are in the range of those found in BHBs (see McClintock & Remillard 2006). The flatter power-laws could be indicative of the increased 1–10 keV emission due to the boundary layer in NS binaries (see Figure 26 of Done et al. 2007), although the luminosities of these sources exceed the NS Eddington luminosity.

Of the four GC LMXBs in this group of sources, two (S163 and S194) appear to undergo luminosity/spectral transitions (see Figure 3). S163 may alternate between a higher count-rate disk-dominated state and a lower count-rate hard state. Although the changes in count rate are of a factor of ∼4 at the most, there are Galactic BHBs, showing this type of spectral/count-rate transitions (e.g., H1743−322, XTE J1859+226, and GX339−4; see Remillard & McClintock 2006). As discussed in Section 3.1, the high-luminosity state is characterized by a disk temperature of $kT_{\rm{in}} = 0.7 \pm 0.2$ keV when the data are fitted with a single DBB model; this temperature is in the range of temperatures measured in BHBs in thermal state (see McClintock & Remillard 2006). The single power-law fit returns a relatively steep index (Γ ∼ 1.5–2.5) and requires significant intrinsic absorption; the simulations of B10 demonstrate that a spectrum consisting of both power-law and significant disk emission would give rise to spuriously high best-fit N_H, when fitted with a single power-law model. All of the above suggests that we have observed S163 in a thermally dominated state. The lower count-rate observations instead are fitted with power-law models with Γ ∼ 1.4, and absorption consistent with Galactic N_H. These power-laws may suggest a "hard" perhaps jet dominated state, although the indices are in the low range of those measured in Galactic BHBs in hard state (Remillard & McClintock 2006; McClintock & Remillard 2006). We may rule out a simple thermal disk dominated emission in this source because the single DBB fits return higher disk temperature (kT ∼ 1.6–2.0 keV) than that measured at higher count rate, resulting in a $L_{\rm disk} -T_{\rm{in}}$ relation much shallower than the $L_{\rm X} \sim T^4_{\rm{in}}$ relation expected in disk-dominated systems (e.g., Makishima et al. 2000); however, this result may derive from the presence of Comptonized radiation, as in the case of GRO J1655-40 (Kubota et al. 2001).

In S194, except for the highest count-rate state where N_H>N_H(Gal.) in the power-law fit suggesting a thermal-dominated state, no strong N_H signature is detected. If these spectra are thermal, they may suggest fluctuations of the disk temperature, in response to fluctuations in the accretion rate (see, e.g., Smith et al. 2002; Fabbiano et al. 2003). The results are consistent with the $L_{\rm X} \mbox{--} T_{\rm{in}}^4$ relation.

Changes in luminosity do not necessarily result in a change in the spectral state: the GC source S185 changes in count rate by a factor of ∼2, however the spectral parameters are steady, a behavior observed in some Galactic BH candidates (McClintock & Remillard 2006). However, this source also has the smallest number of counts of any of the individual analyzed sources, and so it is possible that changes in spectral state went undetected.

The luminous field sources S146, S158 and S184 may all largely be in a thermal disk-dominated state, since in most cases the power-law fits result in large intrinsic N_H values (see Section 3.2). Given the substantially super-Eddigton luminosities of these sources (${>}5 \times 10^{38} \;\rm erg\; s^{-1}$) for a NS counterpart, it is likely that they are BHBs. In S146 we may have observed the result of a drop in accretion rate during the second Chandra observation, resulting in a drop in both luminosity and disk temperature. For S158, our results suggest that this source is first observed in a high/soft state, becomes softer with decreasing luminosity possibly because of cooling of the disk, and then may transition to a low/hard state with an increasing larger power-law component. This last transition is suggested by the power-law contours moving toward the galactic N_H line, and similarly the DBB contours allowing values of N_H < N_H(Gal.) (Figure 11), suggesting excess low energy emission above the DBB model that could be due to a prominent power-law component (see Figure 8; B10). For S184, the differences between the spectra occur only in the power-law fits, while the confidence contours of the DBB fits overlap and allow Galactic line of sight N_H, although the best-fit N_H of the lower luminosity spectra falls well below the Galactic value. Therefore, while we do not find a strong signature for a state transition, the spectral results may suggest that the source is transitioning between an initial high/soft state and a low/hard state.

Figure 15 displays the results of the spectral fits in $L_{\rm X} \mbox{--}T_{\rm{in}}$ (or L_X–Γ) plots, using the additional constraints from the B10 simulations (see Section 3). Whenever it could not be established that a given spectrum was either disk or power-law dominated, the results were plotted in both diagrams. The analogous results of B10 for the luminous LMXBs of NGC 3379 are also plotted. The thermal spectra are generally consistent with increases of disk temperature with increasing luminosity, and within the uncertainties with the $L_{\rm X} \mbox{--} T_{\rm{in}}^4$ relation. These results suggest that these luminous LMXBs, both in the field and in GCs, are consistent with accreting BHBs with BH masses in the ∼5–15 solar mass range. Interestingly, this is the range of masses found in Galactic BHBs (see Ozel et al. 2010), further reinforcing the connection between these extragalactic LMXB populations and their Galactic counterparts.

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Some of these sources are in GCs. The possibility of BHBs forming and residing in GCs is a debated issue, since none has been found in the Milky Way, and theoretical expectations regarding their properties, transient behavior, and detectability argue that 10 solar mass BHBs should be hard to discover compared with NS binaries (Kalogera et al. 2004; see Ivanova et al. 2010 for a recent discussion of BH binary formation in GCs). However, very luminous GC sources have been found with Chandra in several early-type galaxies, suggesting that GC BHBs exist (see Verbunt & Lewin 2006; Kim et al. 2006). In one case at least, in NGC 4472, both the high luminosity (${\sim} 4 \times 10^{39} \;\rm erg\; s^{-1}$) and a factor of seven intensity variability provide a convincing candidate of a GC BHB (Maccarone et al. 2007). In the elliptical galaxy NGC 1399, the optical spectrum of a GC hosting a luminous X-ray source may suggest the presence of a 1000 M_☉ BH (Irwin et al. 2010). Our work on the luminous LMXBs in NGC 3379 has also suggested GC "stellar mass" BHB candidates, and possibly a more massive BH (B10).

The analysis of the joined spectra of the three luminosity samples for the field LMXBs (Section 4) suggests that the average spectrum of the four high-luminosity sources is more likely to be thermal, while the average spectra of medium (6 × 10³⁷–1.5 × 10³⁸ erg s⁻¹) and low-luminosity (L_X < 6 × 10³⁷ erg s⁻¹) sources may include strong power-law components. The high-luminosity joined spectrum is strongly inconsistent with the line-of-sight Galactic N_H, requiring considerable intrinsic absorption in the PO fit; the DBB fit, however, is consistent with N_H(Gal.). Looking at the spectral simulations of B10, this result suggests the presence of a significant (or dominant) thermal DBB component in the emission (Figure 8, left). Conversely, the mid- and low-luminosity results require N_H significantly below N_H(Gal.) in the DBB fit, suggesting the presence of a power-law spectrum (Figure 8, left and right; see B10). Smaller N_H values in lower-luminosity LMXBs are also reported in the spectral study of the NGC 4697 LMXB population (Sivakoff et al. 2008); these authors however do not comment on possible fit biases and suggest "real" accumulation of absorbing material in these sources. While we cannot exclude this hypothesis, we believe that a firm conclusion on intrinsic luminosity-dependent N_H cannot be supported at this moment, given the combined weight of our results and those of B10.

The parameter space of the high-luminosity average GC spectrum in the power-law fit does not overlap with that of the high-luminosity field sources: although the range of Γ is consistent, the GC spectrum, while requiring large intrinsic absorption columns, does not appear as absorbed as that of the field sources. In both cases, these large N_H values are consistent with the presence of thermal disk emission; interestingly, the field sources have luminosities larger than those of the GC sources in these two samples, so if they are in a thermal state, they may have smaller residual power laws in their spectra, which would result in spurious larger N_H (see Brassington et al. 2010). The DBB fits give consistent results in the two cases.

The mid-luminosity field and GC power-law parameter spaces are both consistent with N_H(Gal.), therefore dominant intrinsic power-law components are consistent with these results. However, the GC spectrum is harder (flatter power law) than that of the field sources. The GC spectrum is also consistent with a DBB model and Galactic N_H; the field spectrum, instead, is not well fitted by the DBB model, which would also require unphysical low N_H, suggesting that this "average" spectrum includes a significant power-law component (B10).

However, since the high- and mid-luminosity samples typically include only a small number of sources, vagaries of small-object samples compounded with spectral variability may affect our results. Instead, one would expect that these variability effects may be averaged out in the low-luminosity spectra, which in both cases include a large number of sources. We find a suggestive difference in the results of the joint spectral analysis of the large samples of 17 GC and 41 field LMXBs with L_X < 6 × 10³⁷ erg s⁻¹. While, as discussed above, the low-luminosity field spectrum is consistent with a power-law-dominated emission and Galactic N_H, the GC spectrum requires high values of N_H. As shown in Figure 11, the parameter spaces of these sources barely overlap in the power-law fits. The DBB contours of the GC spectrum allow N_H(Gal.), which is excluded in the similar fit for the low-luminosity field sources. We discuss possible implications of this result below.

Considering the results of the joined fit of the entire field and GC LMXB samples, we obtain best-fit Γ ∼ 1.6–1.7. This range is consistent with previous reports of joint fits of LMXB populations detected with Chandra observations in elliptical galaxies (e.g., Irwin et al. 2003; Sivakoff et al. 2008).

While it is a well-established observational fact that higher metallicity red GCs are more likely to host LMXBs, the effect of metallicity on LMXB formation and evolution is a debated issue (Bellazzini et al. 1995; Maccarone et al. 2004; Ivanova 2006; see reviews: Fabbiano 2006; Verbunt & Lewin 2006; Kim et al. 2006). A discriminant among proposed scenarios may be offered by the X-ray spectra of LMXBs in red and blue GCs.

A tendency for LMXBs in metal-rich GCs to have softer spectra was suggested in M31 (Irwin & Bregman 1999) and NGC 4472 (Maccarone et al. 2003), but was not verified by the analysis of the X-ray colors of a larger sample of sources culled from six elliptical galaxies observed with Chandra (Kim et al. 2006). Harder spectra in metal-poor GC LMXBs would be expected in the irradiated wind model of Maccarone et al. (2004) because of the enhanced absorption associated with these winds, which would also speed up the evolution of the donor star and be responsible for a shorter lifetime of the LMXB (and thus the smaller number of LMXBs associated with blue, metal poor GCs). The different scenario advocated by Ivanova (2006) instead suggests that the relative lack of LMXBs in blue GCs may be related to the lack of outer convective zone in metal-poor main-sequence stars. Without outer convective zones, magnetic braking and thus the formation of an LMXB would not occur. The Ivanova model does not predict a particular spectral signature in the X-ray band. The relative lack of LMXBs in blue GCs could also be due to a smaller stellar encounter rate, resulting from the smaller stellar radii of low-metallicity stars (see Berger et al. 2006), although the reduction in radius is probably too small to affect strongly the encounter rate; we would not expect a spectral signature in this scenario either.

Our results show (Figure 12) that the allowed parameter spaces of the red and blue GC samples spectral fitting (for both power-law and disk models) could be consistent with the presence of larger N_H in the blue sample, as predicted by Maccarone et al. (2004). However, this effect is only suggestive in our GC sample. A similar result was found by Sivakoff et al. (2008) in NGC 4697.

The differences between the low-luminosity spectral results in field and GC sources discussed in Section 6.2, if taken at face value, may point to a possible intriguing difference between GC and field sources. If the average metallicity of the GC sources is smaller than that of the field sources, in the Maccarone et al. (2004) scenario we may also expect to see larger intrinsic absorption in the GC sample, compared to the field. We note, however, that only 5 of these 17 GC sources are in blue low-metallicity GCs. Alternatively, these differences may point to physical differences in the nature of accreting binaries formed in the field and in GC, resulting—for the same luminosity range of L_X < 6 × 10³⁷ erg s⁻¹—in accretion-disk-dominated systems in GC and power-law-dominated systems in the field, as discussed in Section 6.2. In addition, it is also possible that because of source crowding in GCs, the emission of these fainter GC X-ray sources may be the result of the collective emission of a different population of LMXBs, fainter than that of the field sources, which are likely to be individual LMXBs. This puzzling result will need to be checked with future studies of LMXB populations in other early-type galaxies.

As discussed in Section 5, we find that in NGC 4278 LMXBs tend to be found preferentially in more luminous and red GCs, as observed in other galaxies. These effects, first reported by Angelini et al. (2001), Kundu et al. (2002), and Sarazin et al. (2003) have been confirmed in several studies (see review, Fabbiano 2006), and most recently in the survey of 11 Virgo galaxies by Sivakoff et al. (2007).

A surprising result of our analysis of correlations between L_X, optical magnitude V, and galactocentric distance R_G is the presence of a significant L_X–R_G correlation in the GC-LMXB sample of NGC 4278. This L_X–R_G effect is absent in the field LMXB sample, suggesting that it is an intrinsic property of GC sources in this galaxy. One possible scenario is that these more central GCs have a richer LMXB population than GCs at larger R_G. The possibility of multiple sources is allowed by the observed variability pattern, given the statistics of our data. Typically we find that GC sources vary by a factor of a few, so even if a source dominates the emission we cannot exclude the presence of fainter but still luminous LMXBs in a single GC, which cannot be detected individually—even with Chandra—given the distance of NGC 4278 (see light curves in Figure 3 and in B09); moreover, if the population of LMXBs is richer (effectively, if the XLF is modified by increasing the normalization; see, e.g., Kim et al. 2009 for a study of LMXB XLF), the larger L_X could be due to a single source, resulting from the increased probability to sample the low-probability, high-luminosity tail of the LMXB XLF in these GCs. A second, more difficult to understand, possibility is that there is a change in the slope of the XLF, producing prevalently more luminous sources in GCs at smaller R_G.

Our correlation analysis of Section 5 excludes that the L_X–R_G relation may be a byproduct of a GC luminosity/mass effect (i.e., more luminous/massive GC being found at smaller R_G), which would result in a larger fraction of LMXBs formed in richer stellar populations. If it is not due to an underlying luminosity effect, the L_X–R_G correlation could be related to the structure of the GC itself changing with galactocentric radius. If the NGC 4278 GCs tend to be more compact at smaller R_G, stellar encounters would be favored, and thus LMXB production. Interestingly, relatively more compact GCs have been found at smaller R_G in galaxies such as the Milky Way, M31, NGC 5128, and the LMC (van den Bergh et al. 1991; Hodge 1962; Crampton et al. 1985; Hesser et al. 1984; see Brodie & Strader 2006). In these galaxies, cluster diameter does not correlate with cluster luminosity, consistent with a lack of luminosity effect, as we have discussed above.

The GC LMXB formation rate depends on the rates of tidal capture and binary exchange which are functions of the size of the GC and the central stellar density (Γ ∼ ρ^1.5₀r²_c; Verbunt & Lewin 2006; Verbunt 2003, where ρ₀ is the central stellar density and r_c is the core radius; Bregman et al. 2006 advocate for the use of the half-mass (or light) radius r_h rather than r_c which can be hard to determine). In the Galaxy, LMXBs tend to occur preferentially in more dense and compact GCs (Bregman et al. 2006), and a correlation of LMXB occurrence with GC mass and half-mass radius is also found in the Virgo Cluster galaxies (Sivakoff et al. 2007). Moreover, the observed number of close binaries emitting X-rays in Galactic GCs has been found to be correlated with Γ, and the number of LMXBs is also expected to be correlated with Γ (Pooley et al. 2003). For a given GC luminosity (there is no observed V dependence), we would have Γ ∼ r^−2.5_c and we could then approximate the functional dependence of these dynamical effects as Γ ∼ R^−1.2_G, using the square-root dependence between GC diameter and R_G of van den Bergh et al. (1991). A function of this type could be consistent with the L_X–R_G relation observed in NGC 4278, considering the range of approximations made in deriving the Γ–R_G relation and the wide observed scatter of Figure 13. If this scenario holds, the L_X–R_G relation may be due to a larger number of LMXBs in GCs at smaller R_G (increase in the XLF normalization), rather that to intrinsically luminous single LMXBs being prevalently formed in GCs closer to the central regions of the galaxy (flattening of the XLF slope).