4.3. X-ray Luminosity Functions
The XLFs of the early-type galaxies observed with Chandra are generally steeper than those of star-forming galaxies (see Section 2.4), i.e. with a relative lack of luminous HMXBs. These XLFs are generally well fitted with power-laws or broken power laws with (cumulative) slopes ranging from -1.0 to -1.8, and breaks have been reported both at 2-3 × 1038 ergs s-1, the Eddington luminosity of an accreting neutron star (Sarazin, Irwin & Bregman 2000; Blanton, Sarazin & Irwin 2001; Finoguenov & Jones 2002; Kundu, Maccarone & Zepf 2002), and at higher luminosities (1039 ergs s-1) (Jeltema et al. 2003, in NGC 720). While the former break may be related to a transition between neutron star and black hole binaries (Sarazin, Irwin & Bregman 2000), the latter, high luminosity break, could be produced by a decaying (aging) starburst component from binaries formed in past merging and star bursting episodes (Wu 2001). This possibility was suggested in the case of NGC 720 (Jeltema et al. 2003). The XLFs of NGC 5128 (Kraft et al. 2001), obtained at different times and reflecting source variability, are well fitted with single power-laws in the luminosity range of 1037 - 1039 ergs s-1. In NGC 1291 (Irwin, Sarazin & Bregman 2002), no super-Eddington sources are detected.
The effects of detection incompleteness have been considered by Finoguenov & Jones (2002), and have been recently explored extensively by Kim & Fabbiano (2003) in their derivation of the XLF of NGC 1316. Low-luminosity sources may be missed because of higher background/diffuse emission levels in the inner parts of galaxies, and also because of the widening of the Chandra beam at larger radii. Correcting for these effects with an extensive set of simulations, Kim & Fabbiano (2003) found that an apparent 2-3 × 1038 ergs s-1 break in the XLF of NGC 1316 disappeared when incompleteness was taken into account, and the XLF of this galaxy could be represented by an unbroken power-law down to luminosities of ~ 3 × 1037 ergs s-1 (Fig. 13). This result shows that caution must be exercised in the derivation of XLFs, and that perhaps some of the previous reports should be reconsidered. If the XLFs extend unbroken to lower luminosities, the amount of X-ray emission from undetected LMXBs in early-type galaxies can be sizeable, as it is the case in NGC 1316. This result is important not only for our understanding of the XRB populations, but also for the derivations of the parameters of the hot interstellar medium in these system (see Kim & Fabbiano 2003). Ignoring the contribution to the emission of hidden XRBs results in biases and erroneous results and may give the wrong picture of the overall galaxy dynamics and evolution. Moreover, the dominance at large radii of XRB emission over the hot ISM (see Fig. 12) in some (X-ray faint) ellipticals, does also affect adversely mass measurements of these galaxies from low-resolution X-ray data (Kim & Fabbiano 2003).