A semi-empirical model to constrain the growth of supermassive black holes

The presence of super massive black holes (SMBHs) at the center of galaxies has been proved by the most recent observations. The mass of these SMBHs is found to correlate with a number of properties of the host galaxies and such relations have been extensively studied from a theoretical and observational point of view. In the present thesis project I investigate the suitability of some established scaling relations at z = 0, in particular Mbh-Mgal,tot and Mbh- sigma relations, in the prediction of the growth of a central black hole. This ultimate information is accessed by the use of cosmological semi-empirical models that generate object-by-object dark matter (DM) merger trees from accurate sub-halo mass and infall redshift probability functions for all sub-halos. In addition to that I study the predicted relative contribution of the gas accretion and BH-BH mergers to the growth of the black holes across cosmic time. I evolve DM halos separated in different bins of mass and relate them to galaxies mass histories through stellar mass-halo mass (SMHM) relations. Each galaxy is then seeded with a SMBH through the afore-mentioned scaling relations which ends up in the realizations of BH accretion curves. Through the comparison between the so obtained accretion curves with the ones created by the employment of continuity equations, is then possible to acquire a general understanding of what type of relation is more efficient in reproducing the evolutionary paths and the relative contribution of BH-BH mergers in this process.