The X-ray Luminosity Function.

The X-ray luminosity is much easier to measure than the X-ray temperature. Therefore there have been rather more measurements of the X-ray luminosity function (XLF) than of the XTF.

The XLF, $\Phi(L_{{\rm X}})$ is defined such that ${\rm d}N$ is the number of clusters per unit comoving volume with luminosities between $L_{{\rm X}}$ and $L_{{\rm X}}+{\rm d}L_{{\rm X}}$ and is given by,

$${\rm d}N=\Phi(L_{{\rm X}}){\rm d}L_{{\rm X}}.$$ (17)

A suitable parametric form for XLF is that of Schechter (1976), originally proposed for the optical luminosity function of galaxies,

$$\Phi(L_{{\rm X}}){\rm d}L_{{\rm X}}=\Phi^{*}\left ( \frac{L_... ...m X}}}{L^{*}}}{\rm d}\left (\frac{L_{{\rm X}}}{L^{*}} \right )$$ (18)

where $L^{*}$ is a constant and $\alpha$ is the slope of the faint end.

The local XLF is well determined. For example, the ROSAT Brightest Cluster Survey (BCS) of (Ebeling et al. 1998, Ebeling et al. 1997) and the ROSAT-ESO Flux Limited X-ray cluster survey (Böhringer et al. 2001, Böhringer et al. 2001) provide a benchmark against which evolution can be measured, these samples being particularly useful at the high $L_{{\rm X}}$ end. Fainter clusters and groups are better studied with deeper surveys, e.g. the ROSAT Distant Cluster Survey (Rosati et al. 1998). There is excellent agreement between all these surveys in the low redshift regime, see Rosati (2002), figure 6. of which is reproduced as figure 3.1 in this work.

Figure 3.1: Determinations of the local X-ray luminosity function taken from Rosati (2002).

The agreement at higher redshifts is more contentious. There appears to be common ground up to moderate X-ray luminosities ( $L_{{\rm X}} \sim 3 \times 10^{44}$ erg s$^{-1}$) with the EMSS, RDCS, SHARC (Serendipitous High Redshift Archival ROSAT Cluster survey, Burke et al. 1997, Nichol et al. 1999), the 160 deg$^{2}$ ROSAT survey (Vikhlinin et al. 1998b, Mullis et al. 2003) and WARPS (Wide Angle ROSAT Pointed Survey, Jones et al. 1998, Jones et al. 2000a) surveys all consistent with no evolution out to $z \approx 0.7$. In the more sensitive high $L_{{\rm X}}$ regime there is less agreement. Negative evolution was reported by Gioia et al. (1990) and Henry et al. (1992) for the EMSS survey, this is supported by the 160 sq. degree ROSAT survey (Vikhlinin et al. 1998b), the RDCS (Rosati et al. 2000) and the ROSAT North Ecliptic Pole survey (Gioia et al. 2001). These results are in contrast to those found for the WARPS survey (Jones et al. 2000a). The exact degree of evolution (if any) is unclear largely due to the small numbers of high redshift, high luminosity clusters in the surveys.

The next section examines more closely the evolution of the XLF from a reanalysis of the EMSS sample of clusters of galaxies with $z = 0.3$-0.6.