Cosmological evolution models for QSO/active galactic nucleus luminosity functions: Effects of spectrum-luminosity correlation and massive black holeremnants

We investigate a large number of cosmological evolution models for QSOs and active galactic nuclei (AGNs). We introduce a spectrum-luminosity correlat ion as a new input parameter and adopt the estimated mass function (MF) of massive black holes in the centers of nearby galactic nuclei as a constrain t to distinguish among different QSO/AGN models. We explore three basic typ es of phenomenological scenarios : (1) models with multiple short-lived (si milar to a few10(6)-10(8) yr) populations, (2) models with a single long-li ved (similar to 10(9) yr) QSO population, and (3) models with recurrent QSO /AGN activities that are driven by long-term variabilities of the disk inst ability type. In each model, we derive the expected theoretical luminosity function (LF) and the MF of black holes that grow through mass accretion. W e assess the plausibility of each model based on whether each model's LF an d MF are compatible with the observed data. We find that the best fits to t he observed LFs are obtained in the model with multiple short-lived populat ions and without any significant spectral evolution. This finding suggests that the QSO populations may be composed of many short-lived generations (s imilar to a few10(8) yr) and that there is no significant spectral evolutio n within each generation. On the other hand, we also show that there is no satisfactory model that can simultaneously account for the observed LF and the estimated MF. We speculate that some of the present-day black holes fou nd in galactic nuclei may have formed without undergoing the QSO/AGN phase.