Redshift evolution of Black Hole Mass function: main difficulties

• In order to estimate the evolution of the BHMF itself, further assumptions are needed regarding the Eddington ratio and lifetimes and duty-cycles

• An alternative approach is to link the BH mass function to cosmological DM halos mass function, either calculated from semi-analytic models (Haehnelt & Rees 1993; Haiman & Loeb 1998; Kauffman & Haehnelt 2000; Volonteri, Haardt & Madau 2003; Mahamood, Devriendt & Silk 2003), or from cosmological hydro simulations (Di Matteo et al. 2003)

• Need specific recipies to parametrize the uncertain processes of gas cooling and accreting onto the central BH, and of feedback from AGN