Deriving the Quasar Luminosity Function from Accretion-Disk Instabilities

We have derived the quasar luminosity function assuming that the quasaractivity is driven by a thermal-viscous unstable accretion disk around asupermassive black hole. The instabilities produce large amplitude, long-termvariability of a single source. We take a light curve of a single source andcalculate the luminosity function, from the function of time it spends at eachluminosity. Convolving this with an assumed mass distribution we fit well theobserved optical luminosity function of quasars at four redshifts. As a resultwe obtain the evolution of the mass distribution between redshifts 2.5 and 0.5.The maximum of the active black hole mass function moves towards lower mass bya factor ~10 at the low redshift. The number of high mass sources declinesrapidly, and so low mass sources become dominant at lower redshift. The mainconclusions are following: 1) The quasar long-term variability due to the diskthermal-viscous instabilities provides a natural explanation for the observedquasar luminosity function. 2) The peak of the mass function evolves towardslower black hole masses at lower redshifts by a factor ~10. 3) High masssources die subsequently when redshift gets smaller. 4) The number of high masssources declines rapidly, and so low mass sources become dominant at lowerredshift. 5) The periodic outbursts of activity appear as long as the matter issupplied to the accretion disk. 6) Since the time-averaged accretion rate islow, the remnant sources (or sources in the low activity phase) do not grow tovery massive black holes. 7) A continuous fuel supply at a relatively lowaccretion rate (~0.01 - 0.1 \dot M_{Edd}$) for each single source is requiredover the lifetime of the entire quasar population.