The redshift distribution of the X-ray background

Context: The X-ray background (XRB) is produced by a large number of faint sources distributed over a wide range of redshifts. The XRB carries information on the spatial distribution and evolution of these sources.
Aims: The goals are 1. to determine the redshift distribution of the soft X-ray background photons produced by all types of extragalactic sources, in order to relate fluctuations of the background to the large scale structures; 2. to determine the redshift distribution of the soft XRB produced by AGN in order to calculate the evolution of the AGN X-ray luminosity density.
Methods: A set of major X-ray surveys was used to determine the redshift distributions of the X-ray sources selected at various flux levels. Simple analytic fits to the data allow us to determine the smooth relationship between the redshift distribution and the source flux. The redshift distribution of the integral XRB flux was obtained by averaging the fits over the source counts.
Results: It is shown that the distribution of extragalactic XRB photons in the 0.5{-}2 keV band is adequately represented by the function: d n_XRB / dlog z = 5.24 z^1.52 exp(-z/0.63). The huge voids postulated to explain the cold spots in the CMB maps create dips in the total XRB flux. However, the expected magnitude of the effect is comparable to the fluctuation amplitude of the XRB generated by the individual sources contributing to the background. The cosmic evolution of the AGN X-ray luminosity density up to a redshift of 5 is calculated in an elegant and straightforward way. Systematic uncertainties of the present method are assessed and shown to be small. At a redshift greater than one the present results could be compared directly with some recent estimates obtained in a standard way and the agreement between both methods is very good.