Introduction.

The formation and growth of structure in the Universe depends upon certain fundamental cosmological parameters which govern the environment in which the structures form. Clusters of galaxies, as the largest virialised objects in the Universe, offer a unique insight into the formation of structure and hence into the parameters governing their evolution.

The X-ray properties of clusters offer a useful way of probing this evolution. The X-ray emission is due mainly to bremsstrahlung radiation from the hot intra-cluster gas (which is the dominant component of baryonic matter in clusters) and therefore the X-ray luminosity ( $L_{\textrm{\scriptsize {X}}}$) is expected to be positively correlated to the system mass. A measurement of the evolution of $L_{\textrm{\scriptsize {X}}}$ is therefore a natural choice for the study of the evolution of clusters of galaxies.

Several surveys have been made in the past which measure the evolution of the X-ray luminosity function (XLF) with differing results. Notably the Einstein Extended Medium Sensitivity Survey (EMSS) of Henry et al. (1992) and Gioia et al. (1990) finds moderate negative evolution of the number density of high redshift clusters ($z>0.3$) of high $L_{\textrm{\scriptsize {X}}} > 5 \times 10^{44}$ ergs s$^{-1}$, i.e. there are more high luminosity clusters in the present than there were in the past, but no evolution of moderate luminosity clusters. This agrees well with simple hierarchical formation theories in which the most massive clusters will have formed most recently. More recent surveys, (Rosati et al. 2000, Burke et al. 1997, Vikhlinin et al. 1998b, Jones et al. 1998, Nichol et al. 1999, Borgani et al. 2001) find no evidence for evolution in the XLF at low to moderate luminosities at $z<0.9$. At high luminosities there remains some ambiguity, probably due to the low numbers of high luminosity clusters in the surveys. There are three surveys, in addition to the EMSS, reporting statistically significant evolution at high luminosities. Vikhlinin et al. (1998b), Rosati et al. (2000) and Gioia et al. (2001) all find moderate (typically a factor $\sim 3$ in the space density) negative evolution of high luminosity clusters at $z>0.3$ (or $z>0.5$ in the case of Rosati et al. 2000). Nichol et al. (1999) also find significant evolution but in a non-independent sample based partly on the Vikhlinin et al. (1998b) survey. Contrarily, in the survey of Jones et al. (2000b) and Ebeling et al. (2001) no evidence for significant evolution is found at $z<0.9$.

Because any evolution of the XLF would be most apparent at high luminosities (since more massive clusters evolve more quickly than less massive clusters in a bottom-up formation scenario), and because evolution in this most critical part of the XLF is still an area of controversy, it is thus desirable to extend observations of the evolution of the XLF to high luminosity clusters at high redshift. The EMSS remains one of the only samples which contains a reasonable number of high luminosity, massive clusters at high redshift and therefore it is the sample most suited to constraining cluster evolution at high $L_{\textrm{\scriptsize {X}}}$.

It has been suggested (Jones et al. 1998) that the evolution of the XLF found for high redshift clusters in the EMSS maybe partly an artefact due to an incorrect conversion from detected flux to total flux. Furthermore it is suggested that a systematic increase in the fluxes of the EMSS $z>0.3$ clusters by a factor of $\approx 1.25$ would account for the observed difference in the EMSS and ROSAT log$N$ -- log$S$ relations. An explanation for such a difference is offered by Henry (2000) where it is pointed out that the inclusion of the effect of the Einstein point spread function (psf) was omitted when correcting from detected flux to total flux in the original EMSS and that the inclusion of such an effect would increase the total fluxes of $z>0.3$ clusters by a mean factor of 1.373. However, it is also pointed out by Henry (2000) that the inclusion of other effects, viz. integrating the cluster emission out only as far as the virial radius (as opposed to infinity as in Henry et al. 1992) and using a slightly different value for the mean King profile surface brightness slope, $\beta$, would almost cancel out the correction due to including the psf and thus the original EMSS formulation was fortuitously correct.

The corrections made in converting from detected flux to total flux in the EMSS were large. The original EMSS sample of X-ray clusters were detected using a $2.4' \times 2.4'$ cell, and the flux falling outside this cell was corrected for assuming a King profile with $\beta = \frac{2}{3}$ and a core radius of $r_{\textrm{\scriptsize {c}}}=250$ kpc. The average conversion factor from total flux to detected flux is 1.8 for clusters at $z>0.3$ in the EMSS survey, and this factor is very sensitive to the assumed core radius. This correction was never claimed to be applicable to individual clusters by Henry et al. (1992) but rather was used as a mean correction for the sample. There is some evidence that the core radius assumed in deriving the correction is a good average (Vikhlinin et al. 1998b, table 3.1 of this paper) although figure 3.5 shows that for individual clusters the measured core radius can have a significant effect on the derived luminosity.

Therefore it is possible that the negative evolution seen in the EMSS may not be representative of cluster evolution, and a reanalysis of the luminosities of EMSS clusters is necessary to determine more accurately the evolution of the XLF.

Nichol et al. (1997) have reanalyzed the EMSS sample using ROSAT Position Sensitive Proportional Counter (PSPC) data and find that there is evolution of the XLF, albeit at a lower rate than originally found. We feel, however, that a further reanalysis is justified for the reasons given in section 3.6.1.

A reanalysis of the EMSS is also important because the sample has been used to derive X-ray temperature functions (XTFs), which are used to derive accurate values for $\Omega_{0}$. Although the temperatures are independent of the fluxes and core radii, which are remeasured in this paper, the volume surveyed is not. Therefore in order to compute the XTF accurately it is necessary to have reliable measurements of the cluster fluxes.

In this paper we use a simple aperture photometry method to reanalyze the fluxes of the EMSS sample for clusters with $z>0.3$ using ROSAT PSPC data. We use a large (3 Mpc radius) aperture so that the total fluxes are almost independent of the model surface surface brightness profile. The total fluxes are calculated firstly with the same King profile used in Henry et al. (1992) for a direct comparison with the original Einstein data. The core radii of the clusters are then measured from surface brightness fitting and the total fluxes are recalculated using the appropriately corrected King profiles. The XLF is then computed using the new data and compared to the original XLF of Henry et al. (1992). It is assumed that $H_{0}=50$ km s$^{-1}$ Mpc$^{-1}$ and $q_{0} = 0.5$ throughout.