X-RAY QSO EVOLUTION FROM A VERY DEEP ROSAT SURVEY

In the deepest optically identified X-ray survey yet performed, we hav e identified 32 X-ray-selected QSOs to a flux limit of 2 x 10(-15) erg cm(-2) s(-1) (0.5-2 keV), The survey, performed with the ROSAT Positi on Sensitive Proportional Counter (PSPC), has 89 per cent spectroscopi c completeness. The QSO log(N)-log(S) relation is found to have a brea k 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 an y QSO survey, We use this survey to measure the QSO X-ray luminosity f unction at low luminosities (L(X)<10(44.5) erg s(-1)) and high redshif ts (1<z<2.5). The highest redshift QSO in the survey has z = 3.4. Comb ined with the QSOs from the Einstein Extended Medium Sensitivity Surve y (EMSS) at bright fluxes, we find pure luminosity evolution of the fo rm L(X) proportional to(1 + z)(3.0(+0.2,-0.3)) is an adequate descript ion 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(-0.17+0.4 ) (for q(0) = 0.5). We discuss the form of this evolution, its depende nce on the model assumed and the errors on the derived parameters. We show that most previous X-ray surveys, including the EMSS, are consist ent with a power-law luminosity evolution index of 3.0. The contributi on of QSOs to the 1-2 keV cosmic X-ray background is found to be betwe en 31 and 51 per cent.