Soft X-ray AGN luminosity function from ROSAT surveys -: I.: Cosmological evolution and contribution to the soft X-ray background

We investigate the evolution of the 0.5-2 keV soft Xray luminosity function (SXLF) of active galactic nuclei (AGN) using results from ROSAT surveys of various depth. The large dynamic range of the combined sample, from shallow large-area ROSAT All-Sky Survey (RASS)-based samples to the deepest pointed observation on the Lockman Hole, enabled us to trace the behavior of the SXLF The combined sample includes about 690 ACNs. As previously found, the SXLF evolves rapidly as a function of redshift up to z similar to 1.5 and is consistent with remaining constant beyond this redshift. We have tried to find a simple analytical description of the SXLF in the overall redshift and luminosity range, using Maximum-Likelihood fits and Kolgomorov-Smirnov tests. We found that a form of the Luminosity-Dependent Density Evolution (LDDE), rather than the classical Pure Luminosity Evolution (PLE) or the Pure Density Evolution (PDE) models, gives an excellent fit to the data. Extrapolating one form of the LDDE model (LDDE1) explains approximate to 60% of the estimated soft extragalactic Cosmic X-ray Background (CXRB). We have also found another representation (LDDE2), which produces approximate to 90% of the CXRB and still gives an excellent fit to the sample AGNs. These two versions of the LDDE models can be considered two extremes of the possible extrapolations of the SXLF below the Aux limit of the survey. We have also investigated the evolution of the number density of luminous QSOs with Log L-x > 44.5 [h(50)erg s(-1)], where the evolution can be traced up to the high luminosity. We have compared the results with similar quantities in optically- and radio-selected luminous QSOs. Unlike these QSOs, evolution of the ROSAT-selected QSOs does not show evidence for the decrease of the number density in z greater than or similar to 3. The statistical significance of the difference is, however, marginal.