A DEEP ROSAT SURVEY .4. THE EVOLUTION OF X-RAY-SELECTED QSOS

We report on a new estimate of the QSO X-ray luminosity function and its evolution with redshift based on a sample of 107 QSOs detected at faint X-ray fluxes, S(0.5 - 2 keV) > 4 x 10(-15) erg s(-1)cm(-2), with the ROSAT X-ray satellite. For q(0) = 0.5, the X-ray evolution of QSOs in this sample is consistent with strong luminosity evolution, L(X)*(z)proportional to (1 + z)(3.25+/-0.1), at low redshifts (z < 1.60) and a constant comoving space density at higher redshifts. The derived rate of evolution at low redshifts is thus significantly higher than that obtained previously for the Einstein Extended Medium Sensitivity Survey (EMSS). Indeed, most luminosity evolution models provide a very poor fit (rejected at the 99 per cent confidence level) when applied to the combined EMSS and ROSAT samples, although a polynomial evolution model, L(X)*(z) proportional to 10((1.14z-0.23z2)), provides an adequate fit for q(0) = 0. For q(0) = 0.5, a simple power-law luminosity evolution model with a redshift cut-off (L(X)*(z) proportional to (1 + z)(2.51+/-0.1), z(max) = 1.25) is an acceptable fit to the EMSS and ROSAT samples only if a sizeable dispersion in the QSO X-ray spectral index (sigma(alpha(X)) similar to 0.5) is included. More complex evolutionary forms, such as a variable luminosity function slope or density evolution combined with luminosity evolution, also fail to provide an adequate fit to the combined data-set. Possible systematic differences between the Einstein and ROSAT energy bands (e.g. spectral index variations) may account for some of the observed discrepancy between the QSO samples. Based on the observed range in the parameter values for the best-fitting evolutionary models, we obtain formal values of 34-53 per cent for the QSO contribution to the 1-2 keV X-ray background.