The contribution of quasars to the cosmic X-ray background

Adopting the Schmidt-Green (1983) function and the Heisler- Ostriker (1988) function as the optical evolution function and the Avni- Tananbaum (1986) (AT) function as the X-ray luminosity conditional probability function, we have calculated the contribution U of quasars (QSOs) to the cosmic X-ray background (CXB) and have determined its sensitivities to the values of q_0_, α_0_, α_x_ and all parameters of the AT function, and have found that the values q_0_, α_0_,α_x_ and the parameters A_0_, A_z_ and A of the AT function affect the U value significantly. Therefore the U value is a sensitive test of the optical and the X-ray evolutionary functions. We have further tested the evolutionary function of QSOs by comparing the calculated X-ray counts with observations and considering the feasibility of the α_ox_-α^lim^_ox_ (α_ox_ reflects the calculated ratio of the optical and X-ray luminosities while α^lim^_ox_ is calculated from the observed limiting X-ray flux) distribution of undetected sources. Although the α^*^_ox_- α^lim^_ox_ distribution gives only a one way limit, it is relatively sensitive to the AT function parameters. Using this distribution and using the X-ray counts we have revised the parameters of the X-ray evolution function. Finally, we have obtained the contribution of QSOs and active galactic nuclei (AGNs) with M < - 20.5^m^ to be about 10% and 30-60% to the CXB at 2 keV respectively.