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We analyse the redshift dependence of space number density of quasarsassuming that they are the short-lived active stages of the massive galaxiesand arise immediately after the collapse of homogeneous central part ofprotogalaxy clouds. Obtained dependence fits the observational dataChaMP+CDF+ROSAT (Silverman et al. 2005) very well for protogalaxy clouds ofmass $M\approx 8\cdot 10^{11}$ $h^{-1}M_{\odot}$ and ellipticity $e<0.4$. Thelifetime of bright X-ray AGNs or QSOs with $L_X>10^{44.5}$ erg$\cdot s^{-1}$ inthe range of energies $0.3-8$ keV is $\tau_{QSO}\sim 6\cdot10^6$ years when themass of supermassive black hole is $M_{SMBH}\sim 10^{9}$ $M_{\odot}$ and thevalues of other quasar parameters are reasonable. The analysis and allcalculations were carried out in the framework of $\Lambda$CDM-model withparameters determined from 5-years WMAP, SNIa and large scale structure data(Komatsu et al. 2009). It is concluded, that the halo model of galaxy formationin the $\Lambda$CDM cosmological model matches well observational data on AGNsand QSOs number density coming from current optical and X-ray surveys.

Space number density of bright quasars in the halo model of galaxy formation