A DEEP ROSAT SURVEY .1. THE QSO X-RAY LUMINOSITY FUNCTION

We have used a new sample of 42 QSOs, identified at faint flux limits [S(0.5-2 keV) > 6 x 10(-15) erg s-1 cm-2] by the ROSAT satellite, to extend the coverage of the QSO X-ray luminosity function (XLF) at low luminosities (< 10(45) erg s-1) and high redshifts (z > 0.5). By combining this sample with the EMSS survey, we confirm that the z = 0 XLF exhibits a 'break' at low luminosities, L(X)*(0) = 10(43.9 +/- 0.1) erg s-1. For a q0 = 0 universe, we obtain a steep power-law slope for the XLF, PHI(L(X)) is-proportional-to L(X)-3.4 +/- 0.1, at luminosities above this 'break' and a flatter slope, PHI(L(X)) is-proportional-to L(X)-1.7 +/- 0.2, at lower luminosities. Although a power-law model, L(X) is-proportional-to (1 + z)k, gives an acceptable fit for the evolution of the XLF in a q0 = 0 universe, the derived rate of evolution is higher (k = 2.8 +/- 0.1) than previously obtained from the EMSS survey due to the unexpectedly high numbers of 1 < z < 2 QSOs detected in the ROSAT survey. At higher redshifts, the power-law evolution model in a q0 = 0.5 universe gives a significantly better fit if a cut-off in the evolution is introduced at z = 2. We also find that exponential models for the X-ray luminosity evolution, L(X) is-proportional-to exp(ktau), are strongly ruled out. The predicted contribution to the X-ray background at 2 keV for the q0 = 0, power-law model is nominally 71 per cent, although the remaining uncertainty in the faint-end slope and high-redshift evolution of the XLF permits the actual QSO contribution to lie anywhere in the 30-90 per cent range obtained by Shanks et al. from ROSAT source-count constraints. Comparison of the optical and X-ray luminosity functions yields an X-ray to optical luminosity relation of the form L(X) is-proportional-to L(opt)0.88 +/- 0.08.