Annu. Rev. Astron. Astrophys. 2006. 44: 323-366
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3. OLD X-RAY BINARY POPULATIONS

At variance with most previous reviews of X-ray observations of galaxies, which tend to concentrate first on nearby well-studied spiral and irregular galaxies, I will begin by discussing the X-ray populations of old stellar systems: E and S0 galaxies. By comparison with spirals, these galaxies present fairly homogeneous stellar populations, and therefore one can assume that their XRB populations are also more uniform, providing a "cleaner" baseline for population studies.

I begin this Section with a historical note (Section 3.1), followed by a summary of the detection of ubiquitous discrete X-ray source populations in spheroids and their spectral and variability properties (Section 3.2), which point to LMXB populations. I then address the characterization of these populations by means of XLFs (Section 3.3), and give an overview of the association of these sources with globular clusters (GCs) and of the properties of GC sources in comparison with field sources (Section 3.4). Finally, I summarize the discussion generated by these results for the dependence of LMXB formation in GCs on the metallicity and dynamical properties of the cluster (Section 3.5), and address the current debate on the formation and evolution of the entire LMXB populations, including both formation in GCs and evolution of field native binary systems (Section 3.6). I conclude this Section with a short discussion of results that may suggest evolution of the X-ray populations of some E and S0 galaxies (Section 3.7).

3.1. Low-Mass X-Ray Binaries in Early-Type Galaxies: There They Are - Past and Present

In the 1989 review (Fabbiano 1989) I argued that LMXBs should be present in E and S0s and might even dominate the X-ray emission of some of these galaxies. This was a controversial issue at the time, because LMXBs could not be detected individually, and their presence was supported only by statistical considerations (e.g., Trinchieri & Fabbiano 1985). Although the spectral signature of LMXBs was eventually detected (Kim, Fabbiano & Trinchieri 1992; Fabbiano, Kim & Trinchieri 1994; Matsushita et al. 1994), uncontroversial detection of samples of these sources in all early-type galaxies has become possible only with the subarcsecond resolution of Chandra (such a population was first reported in NGC4697, where 80 sources were detected by Sarazin, Irwin & Bregman 2000; see Figure 2).

A statistical analysis of a large sample of early-type galaxies observed with Chandra is still to come, but the results so far confirm the early conclusion (see Fabbiano 1989; Kim, Fabbiano & Trinchieri 1992; Eskridge, Fabbiano & Kim 1995a, b) that LMXBs account for a very large fraction of the X-ray emission of some early-type galaxies (those formerly known as "X-ray faint," i.e., devoid of large hot gaseous halos): for example, in NGC4697 (Sarazin, Irwin & Bregman 2000) and NGC1316 (Kim & Fabbiano 2003) the fraction of detected counts attributable to the hot ISM is ~ 23% and ~ 50%, respectively. In both cases, given the harder spectrum of LMXBs, these sources dominate the integrated luminosity in the 0.3-8 keV range. In NGC1316 the integrated LMXB emission, including nondetected LMXBs with luminosities below threshold, could be as high as 4 × 1040 erg s-1. Sivakoff, Sarazin & Irwin (2003) reach similar conclusions for NGC4365 and NGC4382.

Although this review focuses on the X-ray binary populations, I cannot help remarking that the Chandra results demonstrate unequivocally that ignoring the contribution of the hidden emission of LMXBs was a source of error in past analyses. In particular, estimates of galaxy dynamical mass were affected, as discussed in the 1989 review (see also Trinchieri, Fabbiano & Canizares 1986). NGC1316 (Kim & Fabbiano 2003) provides a very clear illustration of this point. In this galaxy the LMXBs are distributed like the optical light and dominate the emission at large radii. Instead, the hot ISM follows a steeper profile (see Figure 3, left), with temperature possibly decreasing at larger radii, suggestive of galactic winds. Use of lower-resolution Einstein data, with the assumption that the entire detected emission originated from a hot ISM in hydrostatic equilibrium, resulted in a large mass estimate for this galaxy (2.0 × 1012 Modot; Forman, Jones & Tucker 1985). This result is not sustained by the present data; because the gaseous halo is less extended than assumed in the Einstein paper, its temperature is lower (because the Einstein spectrum was clearly contaminated by the harder LMXB emission), and the halo may not be in hydrostatic equilibrium.

Figure 3

Figure 3. Left: Radial profile of the low-mass X-ray binary distribution (red dots) in NGC1316 compared with the profiles of the optical light (green) and diffuse hot interstellar medium emission (black data points and best-fit model); Right: X-ray luminosity function (XLF) before (squares are the binned data and the dotted line gives the unbinned XLF) and after completeness correction (filled dots; the solid line gives the best-fit power-law model, binned to resemble the data). These figures are figures 6 and 10 of Kim & Fabbiano (2003).

Estimates of the metal abundance of the hot ISM also must be reconsidered. In NGC1316, spectral analysis of the integrated X-ray emission obtained with ASCA suggested extremely subsolar values (0.1 solar, Iyomoto et al. 1998). This extremely low metallicity is typical of ASCA results for E and S0 galaxies, and cannot be reconciled with the predictions of stellar evolution (e.g., Arimoto et al. 1997). Spectral analysis of the NGC1316 Chandra data (Kim & Fabbiano 2003), after subtraction of the detected LMXBs, and taking into account the unresolved LMXB component, allows larger metallicities of the hot ISM (up to 1.3 Zodot), more in keeping with the expected values.

3.2. Source Spectra and Variability

Populations of several tens to hundreds of sources have been detected in E and S0 galaxies with Chandra (see review by Fabbiano & White 2006), and their number is growing as more galaxies are observed and the depth of the observations increase. With the exception of a few SSSs reported in some galaxies (see Irwin, Athey & Bregman 2003; Humphrey & Buote 2004), the X-ray colors and spectra of these sources are consistent with those expected of LMXBs, and consistent with those of the LMXBs of M31 (Blanton, Sarazin & Irwin 2001; Sarazin, Irwin & Bregman 2001; Finoguenov & Jones 2002; Irwin, Athey & Bregman 2003; Kim & Fabbiano 2003; Sivakoff, Sarazin & Irwin 2003; Humphrey & Buote 2004; Jordan et al. 2004; Kim & Fabbiano 2004; Randall, Sarazin & Irwin 2004; Trudolyubov & Priedhorsky 2004; David et al. 2005).

The most extensive spectral study to date is that of Irwin, Athey & Bregman (2003), who studied 15 nearby early-type galaxies observed with Chandra.They found that the average spectrum of sources fainter than 1039 erg s-1 is remarkably consistent from galaxy to galaxy, irrespective of the distance of the sources from the center of the galaxy. These spectra can be fitted with either power laws with photon index Gamma = 1.56 ± 0.02 (90%) or with bremsstrahlung emission with kT = 7.3 ± 0.3 keV. Sources with luminosities in the (1-2) × 1039 erg s-1 range instead have softer spectra, with power law Gamma ~ 2, consistent with the high-soft emission of black-hole binaries (with masses of up to 15 Modot expected for these luminosities, based on the Eddington limit). Within the errors, these results are consistent with those reported in other studies, although sources in different luminosity ranges are usually not studied separately in these works. Jordan et al. (2004) confirm the luminosity dependence of the average source spectrum in M87; their color-color diagram suggests a spectral softening for sources more luminous than 5 × 1038 erg s-1.

Relatively little is known about the time variability of these sources, because repeated monitoring of the same galaxy is not generally available. Type I X-ray bursts have been detected in some GC sources in M31, identifying these sources as neutron star LMXBs (Pietsch & Haberl 2005). Time variable sources and at least five transients (dimming by a factor of at least 10) have been detected in NGC5128, with two Chandra observations (Kraft et al. 2001). Variable sources are also detected with two observations of NGC1399, taken two years apart (Loewenstein, Angelini & Mushotzky 2005). Sivakoff, Sarazin & Irwin (2003) report time variability in a few sources in NGC4365 and NGC4382 within 40ks Chandra observations; Humphrey & Buote (2004) report two variable sources in NGC1332. Sivakoff, Sarazin & Jordan (2005) report short-timescale X-ray flares from 3 out of 157 sources detected in NGC4697; two of these flares occur in GC sources and are reminiscent of the superbursts found in Galactic neutron star binaries, while the third could originate from a black-hole binary. Maccarone (2005) suggests that these flares may be periodic events resulting from periastron accretion of eccentric binaries in dense globular clusters. The spectral characteristics of the point sources detected in E and S0 galaxies, their luminosities, and their variability, show that these sources are compact accreting X-ray binaries.

3.3. X-Ray Luminosity Functions of Low-Mass X-Ray Binary Populations

The luminosities of individual sources range from the detection threshold (typically a few 1037 erg s-1, depending on the distance of the galaxy and the observing time) up to ~ 2 × 1039 erg s-1. XLFs have been derived in most Chandra studies of early-type galaxies, and modeled to characterize their functional shape (power-law slopes, eventual breaks) and normalization. In the following I first review the work on the shape of the XLF and then discuss the drivers of the normalization (i.e., the total LMXB content of a galaxy).

The high luminosity (LX > a few 1037 erg s-1) shape of the XLF has been parameterized with models consisting of power laws or broken power laws. The overall shape (in a single power-law approximation in the range of ~ 7 × 1037 to a few 1039 erg s-1) is fairly steep, i.e., with a relative dearth of high luminosity sources, when compared with the XLFs of star-forming galaxies (Section 4.2; see also Kilgard et al. 2002, Colbert et al. 2004, Fabbiano & White 2006), but the details of these shapes and the related presence of breaks have been a matter of some controversy.

Two breaks have been reported in the XLFs of E and S0 galaxies: the first is a break at ~ 2-5 × 1038 erg s-1, near the Eddington limit of an accreting neutron star, first reported by Sarazin, Irwin & Bregman (2000) in NGC4697, which may be related to the transition in the XLF between neutron stars and black-hole binaries (Blanton, Sarazin & Irwin 2001 in NGC1553; Finoguenov & Jones 2002 in M84; Kundu, Maccarone & Zepf 2002 in NGC4472; Jordan et al. 2004 in M87; Gilfanov 2004, Kim & Fabbiano 2004, and also Di Stefano et al. 2003 for the XLF of the Sa Sombrero galaxy, NGC4594); the second is a high luminosity break at ~ 1039 erg s-1, first reported by in NGC720 by Jeltema et al. (2003; see also Sivakoff et al. 2003, Jordan et al. 2004). Both breaks are somewhat controversial, because the interpretation of the observed XLFs is crucially dependent on a proper completeness correction (see Section 2.2).

Kim & Fabbiano (2003, 2004) show that incompleteness effects are particularly relevant for the detection of the Eddington break, because the typical exposure times of the data and the distances of the target galaxies in most cases conspire to produce a spurious break at just this value (see Figure 3, right, for an example). Interestingly, no break was required in the case of NGC5128 (Kraft et al. 2001), where the proximity of this galaxy rules out incompleteness near the neutron star Eddington luminosity. An apparent Eddington break that disappears after correction for completeness is also found by Humphrey & Buote (2004) for the XLF of NGC1332. Similarly, Eddington breaks are absent in NGC4365 and NGC4382 (Sivakoff, Sarazin & Irwin 2003), whereas a high luminosity cut-off at 0.9-3.1 × 1039 erg s-1 could be allowed; these researchers also consider the effect of incompleteness in their results.

Other recent papers, however, do not discuss, or do not apply, completeness corrections to the XLFs, so their conclusions on the presence of Eddington breaks need to be confirmed. Randall, Sarazin & Irwin (2004) report a break at ~ 5 × 1038 erg s-1 in NGC4649, with large uncertainties, but do not discuss the derivation of the XLF. Jordan et al. (2004) derive and fit the XLF of M87, and compare it with their own fit of those of NGC4697 and M49 (NGC4472), using the data from Sarazin, Irwin & Bregman (2001) and Kundu, Maccarone & Zepf (2002) respectively. However, completeness corrections are not applied, although the low-luminosity data are not fitted. Jordan et al. (2004) report breaks at 2-3 × 1038 erg s-1 in all cases, or a good fit with a single power law truncated at 1039 erg s-1. Note that these results are not consistent with those of Kim & Fabbiano (2004) where the corrected XLFs of NGC4647 and NGC4472 are well fitted with single unbroken power laws.

Kim & Fabbiano (2004) derive corrected luminosity functions for a sample of 14 E and S0 galaxies, including some with previously reported breaks, and find that all the individual corrected XLFs are well fitted with single power laws with similar differential slopes (-1.8 to -2.2; cumulative slopes are -0.8 to -1.2) in the observed luminosity range. None of these fits require an Eddington break. However, a break may be hidden by the poor statistics in each case. The statistical consistency of the individual power laws justifies coadding the data to obtain a high significance composite XLF of early-type galaxies (Figure 4 left). This composite XLF is not consistent with a single power law, suggesting a break at (5 ± 1.6) × 1038 erg s-1. The best-fit differential slope is -1.8 ± 0.2 in the few 1037 to 5 × 1038 erg s-1 luminosity range for the coadded XLF; at higher luminosity, above the break, the differential slope is steeper (-2.8 ± 0.6). These results are confirmed by the independent work of Gilfanov (2004), who analyzes four early-type galaxies, included in the Kim & Fabbiano (2004) sample (Figure 4 right); however, Gilfanov's differential slope for the high luminosity portion of the XLF is somewhat steeper (-3.9 to -7.3). Both the Kim & Fabbiano and Gilfanov analyses are consistent with a cut-off of the XLF of LMXBs at a few 1039 erg s-1. A more recent paper (Xu et al. 2005) is in agreement with the above conclusions, reporting a consistent Eddington break in the corrected XLF of NGC4552; on the basis of a simulation, this paper concludes that the break may or may not be detected in any individual galaxy XLF, given the relatively small number of sources present in each case.

Figure 4

Figure 4. Left: Cumulative X-ray luminosity function (XLF) of 14 E and S0 galaxies (figure 7 of Kim & Fabbiano 2004), with the single power-law best fit (dashed line), and the broken power-law model (solid line); the M31 and Milky Way low-mass X-ray binary (LMXB) XLFs are sketched in the left lower corner. Right: Cumulative LMXB XLFs from figure 5 of Gilfanov (2004). Note the similarity of the XLFs and the break at ~ 5 × 1038 erg s-1 in the E/SO XLF.

The (5 ± 1.6) × 1038 erg s-1 break is at somewhat higher luminosity than would be expected from the Eddington luminosity of normal neutron star binaries. It may be consistent with the luminosity of the most massive neutron stars (3.2 ± 1 Modot; see Ivanova & Kalogera 2006), He-enriched neutron star binaries (1.9 ± 0.6 Modot; see Ivanova & Kalogera 2006), or low-mass black-hole binaries. This break may be caused by the presence of both neutron star and black-hole binary populations in early-type galaxies; it may also be the consequence of a true high luminosity break in the XLF (e.g., Sivakoff, Sarazin & Irwin 2003). Whatever the cause, the shape of the XLF points to a dearth of very luminous sources in E and S0 galaxies. Note that a high luminosity cut-off is also present in the XLF of Galactic LMXBs (Figure 1).

With the exception of NGC5128 (Cen A), for which the XLF has been measured down to ~ 2 × 1036 erg s-1 (Kraft et al. 2001, Voss & Gilfanov 2006), the available Chandra data does not allow the detection of LMXBs in E and S0 galaxies with luminosities below the mid or high 1037 erg s-1 range. By including Cen A and the LMXB (bulge) population of nearby spirals (Milky Way; see Figure 1, M31, M81) in his study, Gilfanov (2004) suggests that the XLF flattens below 1037 erg s-1. A recent reanalysis of the Cen A data confirms this result (Voss & Gilfanov 2006). Direct deep observations of "normal" early-type galaxies are needed to see if this suggestion is generally valid; a legacy Chandra program will provide the necessary data for NGC3379 and NGC4278 by the end of 2007. These future studies may show complex behavior in the low-luminosity XLFs. For example, in M31 a radially dependent XLF break has been reported in the bulge, which could be related to an increasingly older population at the inner radii (Kong et al. 2002). Also, the GC XLF of M31 has a distinctive break at 2-5 × 1037 erg s-1 (Kong et al. 2003, Trudolyubov & Priedhorsky 2004). The discovery of a similar break in the E and S0 XLFs may argue for a GC-LMXB connection in these galaxies. The "outburst peak luminosity-orbital period" correlation (King & Ritter 1998) predicts a break at this luminosity if a large fraction of the sources are short-period neutron star systems. This is intriguing, because the formation of ultracompact LMXBs is favored in Milky Way GCs (Bildsten & Deloye 2004; see also Section 3.6).

The normalization of the XLF is related to the number of LMXBs in a given galaxy. X-ray-optical/near-IR correlations in bulge-dominated spirals observed with Einstein (Fabbiano, Gioia & Trinchieri 1988; Fabbiano & Shapley 2002) had suggested a connection between the number of LMXBs and the overall stellar content of a galaxy. This connection has now been demonstrated to hold for the LMXB populations of E and S0 galaxies (Gilfanov 2004; Kim & Fabbiano 2004). That stellar mass is the main regulator of the number of LMXBs in a galaxy is not surprising, considering that LMXBs are long-lived systems, but there may be other effects. White, Sarazin & Kulkarni (2002) suggested a link with GC specific frequency (the number of GC per unit light in a galaxy) using low-resolution ASCA data. Kim & Fabbiano (2004; see also Humphrey & Buote 2004 for general agreement with this correlation in the case of NGC1332) find a correlation between K-band luminosity (which is proportional to stellar mass) and integrated LMXB luminosity, but also note that this correlation has more scatter than would be expected in terms of measurement errors. This scatter appears correlated with the GC-specific frequency, confirming a role of GCs in LMXB evolution.

3.4. Association of Low-Mass X-Ray Binaries with Globular Clusters: The Facts

In virtually all E and S0 galaxies with good coverage of GCs, both from the ground and better from Hubble, a fraction of the LMXBs is found in GCs (see earlier reviews by Verbunt & Lewin 2006, Fabbiano & White 2006). Sarazin, Irwin & Bregman (2000) first reported this association in NGC4697 and speculated on a leading role of GCs in LMXB formation, revisiting the original suggestion of Grindlay (1984) for the evolution of bulge sources in the Milky Way. Below, I summarize the observational results on the association of LMXBs with GCs from the large body of papers available in the literature. In Sections 3.5 and 3.6, I will discuss the implications of these results.

3.4.1. Statistics.   It appears that in general ~ 4-5% of the GCs in a given galaxy are likely to be associated with a LMXB (e.g., NGC1399 - Angelini, Loewenstein & Mushotzky 2001; NGC4472 - Kundu, Maccarone & Zepf 2002; NGC1553, NGC4365, NGC4649, NGC4697 - Sarazin et al. 2003; NGC1339 - Humphrey & Buote 2004; M87 - Jordan et al. 2004, Kim et al. 2006). Not surprisingly, as first noticed by Maccarone, Kundu & Zepf (2003), the number of LMXBs associated with GCs varies, depending on the GC-specific frequency of the galaxy, which is also a function of the morphological type. Sarazin et al. (2003) point to this dependence on the galaxy Hubble type, with the fraction of LMXBs associated with GCs increasing from spiral bulges (MW, M31) ~ 10-20%, to S0s ~ 20% (NGC1553, Blanton, Sarazin & Irwin 2001; see also NGC5128, where 30% of the LMXBs are associated with GCs, Minniti et al. 2004), E ~ 50% (NGC4697 - Sarazin, Irwin & Bregman 2000; NGC4365 - Sivakoff, Sarazin & Irwin 2003; NGC4649 - Randall, Sarazin & Irwin 2004; see also NGC4552, with 40% of sources in GCs - Xu et al. 2005), cD ~ 70% (in NGC1399 - Angelini, Loewenstein & Mushotzky 2001; see also M87, where 62% of the sources are associated with GCs - Jordan et al. 2004).

3.4.2. Dependence on low-mass X-ray binary and globular cluster luminosity.   In NGC1399 (Angelini, Loewenstein & Mushotzky 2001) the most luminous LMXBs are associated with GCs. No significant LMXB luminosity dependence of the LMXB-GC association is instead seen in NGC4472 (Kundu, Maccarone & Zepf 2002) or in the four galaxies studied by Sarazin et al. (2003); if anything, a weak trend is present in the opposite sense. The reverse is, however, consistently observed: more luminous GCs are more likely to host a LMXB (Angelini, Loewenstein & Mushotzky 2001; Kundu, Maccarone & Zepf 2002; Sarazin et al. 2003; Minniti et al. 2004; Xu et al. 2005; Kim et al. 2006); this trend is also observed in M31 (Trudolyubov & Priedhorsky 2004). Kundu, Maccarone & Zepf (2002) suggest that this effect is just a consequence of the larger number of stars in optically luminous GCs. Sarazin et al. (2003) estimate that the probability per optical luminosity of LMXBs to be found in a GC is ~ 2.0 × 10-7 LMXBs per Lodot,I for LX geq 3 × 1037 erg s-1.

This probability is consistent with past estimates based on the Milky Way and is a few hundred times larger than the probability of LMXBs occurring in the field per unit integrated stellar light in a galaxy, in agreement with the conclusion that dynamical interactions in GCs favor LMXB formation (Clark 1975).

3.4.3. Dependence on globular cluster color.   The probability that a GC hosts a LMXB is not a function of the GC luminosity alone. GC color is also an important variable, as first reported by Angelini, Loewenstein & Mushotzky (2001) in NGC1399 and Kundu, Maccarone & Zepf (2002, see also Maccarone, Kundu & Zepf 2003) in NGC4472, and confirmed by subsequent studies (e.g., Sarazin et al. 2003, Jordan et al. 2004, Minniti et al. 2004, Xu et al. 2005, Kim et al. 2006). In particular, the GC populations in these galaxies tend to be bi-modal in color (e.g., Zepf & Ashman 1993), and LMXBs preferentially are found in red, younger and/or metal-rich clusters (V-I > 1.1), rather than in blue, older and/or metal-poor ones. The association of LMXBs with high metallicity GCs was observed in the Galaxy and M31 (Bellazzini et al. 1995, Trudolyubov & Priedhorsky 2004). In NGC4472, red GCs are three times more likely to host a LMXB than blue ones (Kundu, Maccarone & Zepf 2002). Similarly, in M87, which has a very rich LMXB population, the fraction of red GCs hosting a LMXB is 5.1% ± 0.7% versus 1.7% ± 0.5% for blue GCs (Jordan et al. 2004), also a factor of three discrepancy. In a sample of six ellipticals yielding 285 LMXB-GC associations (Kim et al. 2006), the mean probability for a LMXB-GC association is 5.2%, the probability of a blue GC to host a LMXB is ~ 2% for all galaxies except NGC1399 (where it is 5.8%), while that of LMXB-red GC association is generally larger, but varies from one galaxy to another (2.7% to 13%).

3.4.4. X-ray colors.   Maccarone, Kundu & Zepf (2003) reported that in NGC4472 LMXBs associated with blue GCs have harder "stacked" X-ray spectra than those in red GCs. However, this result is not confirmed by the analysis of the much larger sample of sources assembled by Kim et al. (2006), where no significant differences are found in the X-ray colors of LMXBs associated with either red or blue GCs. Also, no significant differences are found in the X-ray colors of LMXBs in the field or in GCs (Sarazin et al. 2003; Kim et al. 2006).

3.4.5. Spatial distributions of field and globular cluster low-mass X-ray binaries.   To obtain additional constraints on LMXB formation and evolution, the radial distributions of the LMXBs have been compared with those of the GCs and of the field stellar light. Some of these comparisons have used the entire sample of detected LMXBs, irrespective of GC counterpart; others have also investigated differences between the LMXBs associated with GCs and those in the field.

Investigating the overall LMXB distribution in NGC4472, Kundu, Maccarone & Zepf (2002) suggest that it follows more closely the distribution of the GCs than the stellar light (which differ, with the GC one being more extended) and infer an evolutionary connection of all LMXBs with GCs (see Section 3.6). Other authors instead conclude that overall the LMXB distribution and the stellar light trace each other in E and S0 galaxies (NGC1316, Kim & Fabbiano 2003, shown in Figure 3 left; NGC1332, Humphrey & Buote 2004). As for the XLFs, incompleteness may affect these comparisons and account for some of the discrepant reports: sources may be missed in the crowded inner parts of a galaxy, resulting in an apparently more extended distribution than the real one (see Kim & Fabbiano 2003, Gilfanov 2004).

Comparisons of the radial distributions of field and GC X-ray sources do not reveal any measurable differences (Sarazin et al. 2003; Jordan et al. 2004; Kim et al. 2006). A first comparison of these LMXB distributions with those of the stellar light and GCs was attempted in M87, but was inconclusive, given the statistical uncertainties (Jordan et al. 2004). With their significantly larger LMXB and GC samples, Kim et al. (2006) instead find that the LMXB radial profiles, regardless of association with either red or blue GCs, are closer to the more centrally peaked field stellar surface brightness distribution, than to the overall flatter GC distributions (Figure 5). The implication of this result for the GC sources is that the probability of a GC being associated with a LMXB increases at smaller galactocentric radii.

Figure 5

Figure 5. Radial distributions of low-mass X-ray binaries (LMXBs) in the field (green), in red GCs (red) and in blue GCs (blue), compared with the best-fit GC distributions (red and blue at the bottom of the figure), plotted versus the radius normalized to R25 for a sample of six galaxies. The flattening of the distributions at small radii is likely to be an incompleteness effect. The dotted blue and red lines are the best-fit models of the red and blue GC distributions. The solid lines show the best fits of the LMXB distributions. The black dashed lines represent the stellar light distribution (Kim et al. 2006).

3.4.6. X-ray luminosity functions of field and globular cluster low-mass X-ray binaries.   No significant differences have been found in the XLFs of LMXBs in the field and in GCs (Kundu, Maccarone & Zepf 2002; Jordan et al. 2004). The coadded XLFs of field and GC LMXBs in six ellipticals (Kim et al. 2006) are also consistent within the errors, with a similar percentage of high luminosity sources with LX > 1039 erg s-1.

This similarity of field and GC XLFs does not extend, however, to the X-ray populations of the Sombrero galaxy (Di Stefano et al. 2003) and M31 (from a comparison of the XLFs of bulge and GC sources; Trudoyubov & Priedhorsky 2004). In both cases, the GC XLFs show a more pronounced high luminosity break than the field (bulge) XLFs. In M31 the XLF of GC sources is relatively more prominent at the higher luminosities than that of field LMXBs; in the Sombrero galaxy, GC sources dominate the emission in the 1-4 × 1038 erg s-1 range, but there is a high luminosity tail in the field XLF, which, however, could be due to contamination from a younger binary system belonging to the disk of this galaxy (see Di Stefano et al. 2003).

3.5. Metallicity and Dynamical Effects in Globular Cluster Low-Mass X-Ray Binary Formation

The preferential association of LMXBs with red clusters could be either an age or a metallicity effect. A correlation between the number density of binaries and the metallicity of GCs was first suggested by Grindlay (1987), who ascribed this effect to a flatter IMF in higher metallicity GCs, resulting in a larger number of neutron stars and thus LMXBs. Kundu et al. (2003) argue that metallicity is the main driver, based on the absence of any correlations of LMXB association with different age GC populations in NGC4365. Maccarone, Kundu & Zepf (2004) propose irradiation-induced winds in metal-poor stars to speed up evolution and account for the observed smaller numbers of LMXBs in blue GCs. These winds, however, would cause absorption and thus harder X-ray spectra. Although these authors tentatively reported this spectral effect in NGC4472, studies of a larger sample of sources do not confirm this conclusion (see Section 3.4.4).

Jordan et al. (2004) revisit the IMF-metallicity effect, because the resulting increase in the number of neutron stars agrees with their conclusion that the probability that a GC contains a LMXB is driven by the dynamical properties of the cluster. Based on their study of M87, these researchers propose that the probability pX for a given GC to generate a LMXB has the form pX ~ Gamma rho0-0.42 ± 0.11 (Z / Zodot)0.33 ± 0.1, where Gamma is a parameter related to the tidal capture and binary-neutron star exchange rate and rho0 is the central density of the cluster. This conclusion agrees with three-dimensional hydrodynamical calculations of the dynamical formation of ultracompact binaries in GCs, from red giant and neutron star progenitors (Ivanova et al. 2005). Kim et al. (2006) also invoke dynamical effects to explain the increasing probability of LMXB-GC association at smaller galactocentric radii. They suggest that the GCs nearer to the galaxy centers are likely to have more compact cores and higher central densities to survive tidal disruption, compared with the GCs at the outskirts, characteristics that would also increase the chance of dynamical LMXB formation.

3.6. Constraints on the Formation and Evolution of Low-Mass X-Ray Binaries: Field Binaries or Globular Cluster Sources?

The formation processes of LMXBs have been debated since these sources were discovered in the Milky Way (see Giacconi 1974). LMXBs may result from the evolution of a primordial binary system, if the binary is not disrupted when the more massive star undergoes collapse and a supernova event, or may be formed by capture of a companion by a compact remnant in GCs (see Grindlay 1984, reviews by Verbunt 1993, Verbunt & van den Heuvel 1995). The same scenarios are now being debated for the LMXB populations of E and S0 galaxies. If GCs are the principal (or sole) birthplaces, formation kicks or evaporation of the parent cluster have been suggested as an explanation for the existence of field LMXBs in these galaxies (see e.g., Kundu, Maccarone & Zepf 2002).

The correlation of the total LMXB luminosity in a galaxy with the GC specific frequency (White, Sarazin & Kulkarni 2002; Kim & Fabbiano 2004; see Section 3.3) suggests that GCs are important in the formation of LMXBs. White, Sarazin & Kulkarni (2002) proposed formation in GCs as the universal LMXB formation mechanism in early-type galaxies. Other authors have supported this hypothesis, because of the similarity of field and GC LMXB properties (see Section 3.4; e.g., Maccarone, Kundu & Zepf 2003). However, this conclusion is by no means certain or shared by all. Beside uncertainties in the correlations (Kim & Fabbiano 2004), the relationship between the fraction of LMXBs found in GCs and the GC specific frequency (see Section 3.4.1) is consistent with the simple relationship expected if field LMXBs originate in the field while GC LMXBs originate in GCs (Juett 2005; Irwin 2005). This picture would predict different spatial distributions of field and GC LMXBs, an effect not seen so far, although, as Juett (2005) notes, the prevalence of LMXBs in red (more centrally concentrated) GCs and the effect of supernova kicks in the distribution of binaries may make the two distributions less distinguishable.

Piro & Bildsten (2002) and Bildsten & Deloye (2004) compare the observational results with theoretical predictions for the evolution of field and GC binaries. Piro & Bildsten remark that the large X-ray luminosities of the LMXBs detected in early-type galaxies (> 1037 and up to 1039 erg s-1) imply large accretion rates (> 10-9 Modot yr-1). In an old stellar population these sources are likely to be fairly detached binaries that accumulate large accretion disks over time, and undergo transient X-ray events when accretion is triggered by disk instabilities. These transients would have recurrence times greater than 100 years and outbursts of 1-100 years duration. In this picture field binaries should be transient, a prediction that is supported by the detection of transients in the NGC5128 LMXB population (Kraft et al. 2001) and by the discovery of a population of quiescent X-ray binaries in the Sculptor dwarf spheroidal galaxy (Maccarone et al. 2005). Piro & Bildsten also point out that GC sources tend to have shorter orbital periods and would be persistent sources, reducing the fraction of transients in the LMXB population. Interestingly, Trudolyubov & Priedhosky (2004) report only one recurrent transient in their study of GC sources in M31, although 80% of these sources show some variability; however, they also find six persistent sources in the 1038 erg s-1 luminosity range.

Bildsten & Deloye (2004) instead look at ultracompact binaries formed in GCs to explain the bulk of the LMXBs detected in E and S0 galaxies. A motivation for this work is the large probability of finding LMXBs in GCs (per unit optical light, see Section 3.4.2), which makes formation in GCs more efficient than in the field. Ultra-compact binaries would be composed of an evolved low-mass donor star (a white dwarf), filling its Roche lobe, in a 5-10 minute orbit around a neutron star or a black hole. The entire observable life of such a system is ~ 107 years, much shorter than the age of the galaxies and the GCs, therefore their total number would be indicative of their birth rate. From this consideration Bildsten & Deloye derive a XLF with a functional slope in excellent agreement with the measurements of Kim & Fabbiano (2004) and Gilfanov (2004). Bildsten & Deloye also predict a break at LX ~ 1037 erg s-1 in the XLF, which would correspond to the luminosity below which such a system would be a transient. As discussed in Section 3.3, there is some evidence of a low-luminosity break in the composite XLF of Gilfanov (2004), which, however, includes data from spiral bulges as well.

Confirmation of this break in a number of E and S0 populations by itself would not be proof of the Bildsten & Deloye scenario, because the break may occur from the evolution of field binaries. For example, a flattening of the XLF at the lower luminosities is found in the population synthesis of Pfahl, Rappaport & Podsiadlowski (2003, their figure 3), if irradiation of the donor star from the X-ray emission of the compact companion is considered in the model. More recently, Postnov & Kuranov (2005) have proposed that the mean shape of the XLF of Gilfanov (2004) can be explained by accretion on neutron star from Roche lobe overflow driven by gravitational wave emission, below ~ 2 × 1037 erg s-1, and by magnetic stellar winds at higher luminosities. Optical identification of X-ray sources with GCs and an estimate of the transient fraction at different luminosities would help to discriminate among possible scenarios; planned deep time-monitoring Chandra observations may provide the observational constraints.

The nature of the most luminous sources in E and S0 galaxies (those with LX above the 5 × 1038 erg s-1 break, Kim & Fabbiano 2004) is the subject of a recent paper by Ivanova & Kalogera (2006). These researchers point out that only a small fraction of these luminous sources are associated with GCs (at least in M87, see Jordan et al. 2004) and that they are too luminous to be explained easily with accreting neutron star systems that may form in GCs (Kalogera, King & Rasio 2004). With the assumption that these sources are accreting black-hole binaries, these authors explore their nature from the point of view of the evolution of field native binaries. In this picture most donor stars would be of low enough mass (< 1-1.5 Modot given the age of the stellar populations in question) that the binary would be a transient (see Piro & Bildsten 2002) and therefore populate the XLF only when in outburst emitting at the Eddington luminosity; this would happen from main-sequence, red-giant, and white-dwarf donors. In this case the XLF is a footprint of the black-hole mass spectrum in these stellar populations, which is an important ingredient for linking the massive star progenitors with the resulting black hole. Ivanova & Kalogera derive a differential slope of ~ -2.5 for the black-hole mass spectrum, and an upper black-hole mass cut-off at ~ 20 Modot, to be consistent with the observed cumulative XLF of Kim & Fabbiano (2004) and Gilfanov (2004). Depending on the magnetic breaking prescription adopted, either red-giant donors or main-sequence donors would dominate the source population. A word of caution is in order here, because the similar shape of GC and field LMXB XLFs (Kim et al. 2006, see Section 3.4.6) suggests that high-luminosity black-hole sources may also be found in GCs, at odds with theoretical discussions (e.g., Kalogera, King & Rasio 2004).

3.7. Young Early-Type Galaxies and Rejuvenation

There have been some puzzling and somewhat controversial results suggesting that the stellar populations of some early-type galaxies may not be uniformly old, as implied by their optical characteristics, but may hide a small fraction of younger stars, which give rise to luminous and easily detectable X-ray binaries. Rejuvenation (e.g., by a merger event or close encounter with a dwarf galaxy) has been suggested to explain the presence of very luminous and asymmetrically distributed X-ray source populations in some galaxies [NGC720 - Jeltema et al. 2003; NGC4261 (shown in Figure 6) and NGC4697 - Zezas et al. 2003]. Sivakoff, Sarazin & Carlin (2004) report an exceptionally luminous population of 21 sources with LX > 2 × 1039 erg s-1 (in the ULX regime, see Section 6) in the X-ray bright elliptical NGC1600, which is twice the number of sources that would be expected from background AGNs and suggests an XLF slightly flatter than in most ellipticals. In all these cases, however, both cosmic variance affecting the background AGN density and distance uncertainties may play a role. Moreover, Giordano et al. (2005) report the identification of the NGC4261 sources with GCs, undermining the suggestion that they may be linked to a rejuvenation event.

Figure 6

Figure 6. The left panel shows a Chandra image of NGC4261; note the distribution of the luminous point sources, which clearly do not follow the optical light shown in the right panel; Both images are from http://chandra.harvard.edu/photo/category/galaxies.html; credit NASA/CXC; Zezas et al. (2003).

The behavior opposite the one just discussed is reported in an X-ray and optical study of the nearby lenticular galaxy NGC5102 (Kraft et al. 2005). In this galaxy, where the stellar population is young (<3 × 109 years old), and where there is evidence of two recent bursts of star formation, a definite lack of X-ray sources is observed. NGC5102 has also a very low specific frequency of GC ( ~ 0.4). Kraft et al. speculate that the lack of LMXBs may be related either to insufficient time for the evolution of a field binary and/or to the lack of GCs.

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