X-ray QSO evolution from a very deep ROSAT survey

In the deepest optically identified X-ray survey yet performed, we have identified 32 X-ray-selected QSOs to a flux limit of 2x10^-15 erg cm^-2 s^-1 (0.5-2keV). The survey, performed with the ROSAT Position Sensitive Proportional Counter (PSPC), has 89 per cent spectroscopic completeness. The QSO log(N)-log(S) relation is found to have a break to a flat slope at faint fluxes. The surface density of QSOs at the survey limit is 230+/-40 per square degree, the largest so far of any QSO survey. We use this survey to measure the QSO X-ray luminosity function at low luminosities (L_X<10^44.5 ergs^-1) and high redshifts (1<z<2.5). The highest redshift QSO in the survey has z=3.4. Combined with the QSOs from the Einstein Extended Medium Sensitivity Survey (EMSS) at bright fluxes, we find pure luminosity evolution of the form L_X~(1+z)^3.0(+0.2,-0.3) is an adequate description of the evolution of the X-ray luminosity function at low redshifts. A redshift cut-off in the evolution is required at z=1.4^+0.4_-0.17 (for q_0=0.5). We discuss the form of this evolution, its dependence on the model assumed and the errors on the derived parameters. We show that most previous X-ray surveys, including the EMSS, are consistent with a power-law luminosity evolution index of 3.0. The contribution of QSOs to the 1-2keV cosmic X-ray background is found to be between 31 and 51 per cent.