... population[*]
Appendices A and B are only available in electronic form at http://www.aanda.org 
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... 2XMM[*]
http://xmmssc-www.star.le.ac.uk/Catalogue/2XMM/ 
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... May 2007[*]
XMM-Newton observations started on January 2000. 
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... 4.5-10 keV[*]
In the 4.5-10 keV band pn photons with energies between 7.8-8.2 keV were excluded in order to avoid the instrumental background produced by Cu K-lines (Lumb et al. 2002). 
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... transmission[*]
Eexpmap calculates the mirror vignetting function at one single energy, the centroid of the energy band. Because the mirror vignetting is a strong function of energy, in the cases where the energy band is broad, this approach produces a less accurate determination of the effective exposure across the FOV. This is more important at high energies, where the dependence of the vignetting on the energy is much stronger. In order to reduce this effect, for the energy bands 0.5-2 keV, 4.5-10 keV and 2-10 keV we first computed exposure maps in narrower energy bands: 0.5-1 keV and 1-2 keV for band 0.5-2 keV; 2-4.5 keV, 4.5-6 keV, 6-8 keV and 8-10 keV for band 2-10 keV, and 4.5-6 keV, 6-8 keV and 8-10 keV for band 4.5-10 keV. Then we used the weighted mean of these maps to get the exposure maps in the broader energy bands. In order to weight the maps we used the number of counts that we should have detected in each narrow band for a source with a power-law spectrum of photon index $\Gamma $ = 1.9 at energies below 2 keV and $\Gamma $ = 1.6 at energies above 2 keV (the same spectral model we used to convert the count rates of the sources to fluxes, see Sect. 2.4). The resulting exposure maps do not strongly depend on the assumed spectral slope. For example, $\Delta \Gamma $ = $\pm $0.3 changes the exposure map by $\la$0.003% in the 0.5-2 keV band and $\la$1.3% in the 2-10 keV and 4.5-10 keV bands respectively. 
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... colour[*]
The X-ray colour or hardness ratio is defined as the normalised ratio of the count rates in two energy bands, HR = (H-S)/(H+S), where H and S are the count rates in the harder and softer of the two energy bands respectively. 
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... large[*]
The mean error of the X-ray colours was found to be $\sim$0.1-0.15 for sources detected in the 0.5-2 keV, 0.5-1 keV, 1-2 keV and 4.5-10 keV energy bands and $\sim$0.2 for sources detected in the 2-4.5 keV and 2-10 keV energy bands. 
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... distributions[*]
In order to account for the uncertainty in both the measured flux and X-ray colour, we added the probability density distribution of the X-ray colour-flux of each individual source. This distribution was defined as a 2d Gaussian centred at the measured value of the X-ray colour and flux and with dispersion equal to the corresponding 1$\sigma $ errors of the parameters. 
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... band[*]
The flux was chosen to be high enough to guarantee that the expected flux in the energy bands at higher energies is well above the flux limit in the bands. 
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...1996)[*]
From the bolometric luminosity-temperature relation, a cluster with a temperature $\sim$3 keV has a luminosity $\sim$ $10^{43}~{\rm erg~s^{-1}}$. If the cluster is at a redshift of 0.2 the expected observed flux will be $\sim$3 $\times $ $10^{-14}~{\rm erg~cm^{-2}~s^{-1}}$, i.e. in the range of fluxes sampled by our survey. From the cluster luminosity function objects with very high temperature ($\sim$10 keV) are relatively rare, while for a flux limited survey the volume sampled for less luminous clusters (hence with low temperatures) is small. This implies that flux limited surveys are expected to be dominated by clusters with typical luminosities $\sim$ $10^{43}{-}10^{44}~{\rm erg~s^{-1}}$ (i.e. with temperatures $\sim$3-4 keV). More luminous clusters ($\sim$ $10^{45}~{\rm erg~s^{-1}}$) will be relatively rare, and, at the flux level sampled by our survey, they will be at high redshift ($z \sim 1$) and hence they will exhibit X-ray spectra very similar to the more common, less luminous objects (Henry et al. 1991). 
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... 5 pixel[*]
The images were created with a 4 arcsec pixel side. 
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... band[*]
The effective area of the XMM-Newton detectors decreases rapidly above $\sim$5 keV and it is very low above $\sim$10 keV, hence we expect that the results in the 2-12 keV band will not differ significantly from those in the 2-10 keV band. 
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Copyright ESO 2008