Deriving the Quasar Luminosity Function from Accretion Disk Instabilities
We have derived the quasar luminosity function assuming that the quasar activity is driven by a thermal-viscous unstable accretion disk around a supermassive black hole. The instabilities produce large amplitude, long-term variability of a single source. We take a light curve of a single source and calculate the luminosity function, from the function of time it spends at each luminosity. Convolving this with an assumed mass distribution we fit well the observed optical luminosity function of quasars at four redshifts. As a result we 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 by a factor ~10 at the low redshift. The number of high mass sources declines rapidly, and so low mass sources become dominant at lower redshift. The main conclusions are following: 1) The quasar long-term variability due to the disk thermal-viscous instabilities provides a natural explanation for the observed quasar luminosity function. 2) The peak of the mass function evolves towards lower black hole masses at lower redshifts by a factor ~10. 3) High mass sources die subsequently when redshift gets smaller. 4) The number of high mass sources declines rapidly, and so low mass sources become dominant at lower redshift. 5) The periodic outbursts of activity appear as long as the matter is supplied to the accretion disk. 6) Since the time-averaged accretion rate is low, the remnant sources (or sources in the low activity phase) do not grow to very massive black holes. 7) A continuous fuel supply at a relatively low accretion rate (~0.01 - 0.1 \dot M_{Edd}$) for each single source is required over the lifetime of the entire quasar population.