Flux Measurement.

For each cluster with a PSPC observation the data were reduced in the following way. The raw data were downloaded from the LEDAS ROSPUB archive. The data were first cleaned for bad times and a corrected exposure time was obtained. A spectral cube was sorted, of $384 \times 384$ spatial bins and 10 energy bins, and a background cube was associated with it. Cubes were used as this makes correcting for photon vignetting more accurate than if images were used when a mean photon energy would have to be assumed. The background was measured in an annulus from $0.15^{\circ}$ - $0.25^{\circ}$ to avoid the original target of the pointing and the shadows of the window support structure. The cluster was masked out of this background annulus if it were coincident with it. Point sources within the background annulus were removed. The point sources were found using the ASTERIX PSS routine (Allan & Vallance 1995) which employs a maximum likelihood search based on the Cash (1979) statistic. The point source searching procedure was iterated until no more significant point sources were found. A final check of the background was made by eye. Any obvious contaminations were removed and the procedure was re-run. The expected particle background was calculated using the method of Snowden et al. (1992). The measured value of the background was then extrapolated over the field as a function of energy, taking into account the unvignetted particle background, and subtracted from the source. The background-subtracted cube was then corrected for energy-dependent vignetting. The exposure was corrected for dead time.

From the background-subtracted cube the number of counts within an aperture of 3Mpc in radius was extracted (this corresponds to $9.09'$ at $z = 0.3$ and $6.57'$ at $z=0.6$). Point sources within the aperture found by inspection of raw and smoothed images, were masked out (except in the cluster cores, where the high surface brightness cluster emission may have masked faint point sources). An aperture of 3 Mpc was chosen as the correction to total flux is small and it is much larger than the PSPC psf even at an off-axis angle of $30'$. The average error on the count rate was $\sim 6\%$ based on counting statistics.

The counts within the aperture were corrected assuming a King profile of $\beta = \frac{2}{3}$ and initially a core radius of $r_{\textrm{\scriptsize {c}}}=250$kpc, to obtain the total number of counts. The correction factor for such a profile is 1.09. This correction is based on integrating the emission out to infinity. Whilst it may be more physically accurate to integrate out only as far as the virial radius (Henry 2000), our aim is to compare our $ROSAT$ luminosities with the previous measurements of Gioia & Luppino (1994) and Nichol et al. (1997), and to the local XLF of Ebeling et al. (1997), who all integrated to infinity. Henry (2000) notes that because of other effects in the EMSS, although the published EMSS luminosities were integrated to infinite radius, on average they agree with luminosities integrated only to the virial radius, and thus may be correct. We wish to investigate in detail these, and other, effects, in the EMSS luminosities. In order to do this, and to better understand differences with previous work, we will initially follow the method of previous investigations and integrate to infinite radius, but then discuss the effects of integrating only to the virial radius.

To convert from count rates to fluxes a Raymond & Smith (1977) spectral model was assumed. A model spectrum was constructed for each cluster and wherever possible the model parameters were taken from the literature. For the cluster MS0418.3-3844 no measured temperature exists and therefore $T_{\textrm{\scriptsize {X}}}$ was assumed to be 6 keV and for all clusters except MS0451.5-0305 the metallicity is assumed to be $0.3 \times$ solar. The hydrogen column densities were taken from Dickey & Lockman (1990). Absorbed and unabsorbed fluxes and luminosities were measured in the appropriate energy bands. The model takes into account K-corrections when calculating luminosities.

Exceptions to the method described above were made in the cases of MS0353.6-3642 and MS0418.3-3844. Both these clusters fell very close to the shadow of the window support structure in the PSPC image, and consequently extracting a count rate over a 3 Mpc radius would not yield accurate results. For these clusters radial profiles were taken to estimate the radius at which the surface brightness fell to the background level and the counts within that radius were measured. These radii were $0.04^{\circ}$ and $0.05^{\circ}$, corresponding to 823 kpc and 1080 kpc, for MS0353.6-3642 and MS0418.3-3844 respectively. The counts were corrected for the same King profile as previously and converted to fluxes and luminosities in an identical manner as before.