3.5. Comparison between field and cluster sources
The X-ray luminosity function of sources in globular clusters is not very different from that of the sources outside globular clusters (Maccarone et al. 2003a, Sarazin et al. 2003). The spatial distribution of X-ray sources outside globular clusters in elliptical galaxies is similar to that of the globular cluster sources. In elliptical galaxies, globular clusters often harbor a very large fraction of all X-ray sources (Table 3). This has raised the suggestion that all X-ray sources in elliptical galaxies originate in globular clusters (White et al. 2002). The field sources then could have been ejected from a cluster, or originate in a cluster that was later destroyed by the galactic tidal field. The demand that a cluster lives long enough to form X-ray binaries, and short enough not to be around now, requires fine tuning. Thus, the ejection hypothesis may be more probable.
This would suggest that a large number of globular clusters translates into a large number of X-ray sources, both in the clusters and (due to ejection) outside them. The fraction of X-ray sources in globular clusters would then be similar for different galaxies. In the Milky Way and in M31 there are about 10 luminous low-mass X-ray binaries in the disk for each one in a globular cluster. In elliptical galaxies, there is of order 1 low-mass X-ray binary outside clusters for each one in them (see Table 3). [One should note that the HST FOV is much smaller than that of Chandra. Therefore, in comparing the number of X-ray sources associated with globular clusters with those not located in globular clusters (Table 3), in all those cases where HST data were needed to identify the clusters, one can only consider the X-ray sources which are detected in the regions observed wit HST.] This indicates that the majority of the disk sources in the Milky Way and M31, and by extension in spiral galaxies in general, are formed in the disk; although as noted in the Introduction some individual systems may have escaped from globular clusters.
For elliptical galaxies the case is less clear. White et al. (2002) have noted that the sum of the X-ray luminosities of all X-ray sources in elliptical galaxies scales with the number of globular clusters, and conclude that this indicates that the population outside clusters is formed in the clusters. However, White et al. (2002) also note that the fraction of low-mass X-ray binaries in clusters ranges from about 20 to 70% in ellipticals. In our opinion, this suggests that globular clusters alone are not responsible for all low-mass X-ray binaries. Clearly, the origin of low-mass X-ray binaries in elliptical galaxies deserves more study; in particular the different detection limits in different galaxies must be taken into account. In systems with small numbers, the total luminosity can be affected by just a couple of very luminous sources; we therefore think that the number of sources is a better estimator for the population size than the integrated X-ray luminosity.
If the majority of those luminous LMXBs in elliptical galaxies, not located in globular clusters are primordial, their luminosities could not have been constant throughout their lifetimes (because the product of age and the required mass-transfer rate would exceed the donor mass). There are two ways out of this lifetime problem: (i) they are not primordial but they were formed in globular clusters, and somehow released into the field, or (ii) the majority of them are transients with a low duty cycle (see Piro & Bildsten 2002). If the latter is the case, follow-up observations with Chandra will be able to reveal the variability if a sufficient number of them have outbursts that last only a few years and not much longer. We may add a third solution, which is that (iii) systems formed from primordial binaries will emerge from their early evolution as neutron stars or black holes with detached main-sequence companions. How long it takes for the binary to turn into an X-ray source then depends on the time required for the orbit to shrink due to loss of angular momentum, or for the donor to expand into a giant after completing its main-sequence evolution (see e.g. the review by Verbunt 1993; see also chapter 16 by Tauris and Van den Heuvel). It may be noted that binaries formed in a globular cluster may also go through a long-lived detached phase (Grindlay 1988).