A deep ROSAT survey – I. 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 ×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 (0. 5). By combining this sample with the EMSS survey, we confirm that the z = 0 XLF exhibits a ‘break’ at low luminosities |L ₗ^* (0) =10^43. 9 0. 1|erg s–1. For a q0 = 0 universe, we obtain a steep power-law slope for the XLF, | (L ₗ) L ₗ^-3. 4 0. 1| at luminosities above this ‘break’ and a flatter slope, | (L ₗ) L ₗ^-1. 7 0. 2|⁠, at lower luminosities. Although power-law model, LX ∝ (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, LX∝ exp (kτ), 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 ₗ) L_ opt^0. 88 0. 8|⁠.