Quasars in a merger model: comparison with the observed luminosity   function
  Connection between the quasar luminosity function and galaxy mass function is investigated in the framework of a phenomenological approach which relates AGN formation to galaxy mergers. Quasars are assumed to be short-lived, the luminosity of a quasar is controlled by the masses and angular momenta of the merged galaxies which have formed the quasar, and the amount of gas in them (the masses and momenta determine the quantity of mass which loses its angular momentum and can fall to the center). The proposed model can explain the shape and evolution of the quasar luminosity function, and allows us to estimate the parameters: the fraction of matter which falls into the center $\eta$ (which seems to be related to the quantity of gas in the galaxies) and $\kappa$ (an average density contrast in the regions where quasars form). The obtained values of $\kappa$ vary from $\sim 4--7$ at $z=0.5$ to $\sim 1--2$ at $z=2$, $\eta$ vary from a few per cent at $z=0.5$ to a few tens per cent or even values close to 1 at $z=2$. In contrast to the cases considered earlier by the authors, the Eddington limit which, probably, can be exceeded in quasars plays an essential role. 
D.S.Krivitsky and V.M.Kontorovich