Theoretical Models of Multi-Waveband QSO Luminosity Functions

The cosmological evolution of the QSO luminosity functions (LFs) at NIR/optical/X-ray bands for 1.3 <~ z <~ 3.5 is discussed based on realistic QSO spectra. The accretion-disk theory predicts that although the QSO luminosities only depend on the mass-accretion rate, dot{M}, the QSO spectra have dependence on the black-hole mass, M_BH, as well. The smaller is M_BH and/or the larger is dot{M}, the harder does the QSO NIR/optical/UV spectrum become. We modeled the disk spectra which can reproduce these features, and calculated the LFs for a redshift of z ~ 3 with the assumption of new-born QSOs shining at the Eddington luminosity. The main results are: (i) the LFs observed at optical and X-ray bands can be simultaneously reproduced. (ii) LFs in the optical and X-ray bands are not sensitive to M_BH, while LFs at the NIR bands are; about a one order of magnitude difference is expected in the volume number densities at L_I,J ~ 10⁴⁶ erg s^-1 between the case that all QSOs would have the same spectral shape as that of M_BH = 10⁹Msolar and the case with M_BH = 10¹¹ Msolar. (iii) The resultant LFs at NIR are dominated by black holes at L_I,J <~ 10⁴⁴ erg s^-1, and by 10¹¹Msolar black holes at L_I,J >~ 10⁴⁶ erg s^-1. Future infrared observations from space (e.g. NGST) will probe the cosmological evolution of black-hole masses. For a redshift of z < 3, on the other hand, the observed optical/X-ray LFs can be fitted if the initial QSO luminosity, L₀, is below the Eddington luminosity, L_Edd. Interestingly, the best-fitted values of l ≡ L₀/L_Edd are different in the B- and X-ray bands; l_B ≈ 2.5 l_x. The reason for this discrepancy is briefly discussed.