Towards a Comprehensive Fueling-Controlled Theory on the Growth of Massive Black Holes and Host Spheroids

We study the relation between nuclear massive black holes and their host spheroid gravitational potential. Using AMR numerical simulations, we analyze how gas is transported in the nuclear (central kpc) regions of galaxies. We study the gas fueling onto the inner accretion disk (sub-pc scale) and the star formation in a massive nuclear disk like those generally found in proto-spheroids (ULIRGs, SCUBA Galaxies). These sub-pc resolution simulation of gas fueling that is mainly depleted by star formation naturally satisfy the `M_BH - $M_virial' relation, with a scatter considerably less than the observed one. We found a generalized version of Kennicutt-Schmidt Law for starbursts is satisfied, in which the total gas depletion rate (dot{M}_gas = dot{M}_BH + dot{M}_SF) is the one that scales as M_gas/t_orbital. We also found that the `M_BH - sigma' relation is a byproduct of the `M_BH - M_virial' relation in the fueling controlled scenario.