6.1. Connecting spheroid formation with QSOs

The scenario described above opens the possibility to understand the physics of the HS, its dependence on the environment, the nature of peculiar elliptical galaxies with extended low surface density gaseous disks, as well as the connection with high redshift objects like QSOs and submillimeter sources.

QSOs provide now an important probe up to z 6. Unfortunately, their lifetime and their connection with the host galaxy are still rather uncertain. An approach to the bulge-AGN evolution, in the context of the hierarchical scenario, has been proposed by e.g., Cattaneo et al. (1998), Cattaneo (1999, 2002), Kauffmann & Haehnelt (2000), and Wyithe & Loeb (2002). In these semi-analytical models, several assumptions and prescriptions are used to calculate the gas fractions in the merging disks (related to gas infall and SF) and the lifetime of QSOs. The models are able to reproduce roughly the ratio M_SMBH / M_bulge and the evolution of the QSO luminosity function. The major difficulty arises at the low redshift side: the observed QSO population decreases dramatically since z ~ 2 to z = 0, while the merging rate decreases only a little. Cavaliere & Vittorini (2000) have studied this problem. An important fact to take into account is that the gas fraction decreases in galaxies with time. Furthermore, since SF in the inner disk regions is faster than at the periphery, the low angular momentum gas - which feeds the SMBH - is exhausted at a rate higher than the average. Using complete galaxy evolutionary models (e.g., Firmani & Avila-Reese 2000), this effect could be included into the QSO models to explain the luminosity evolution of QSOs at low z's. Another interesting aspect has to do with the multipliciy of processes able to activate SMBH. While it is reasonable to imagine that at early times QSOs have been activated mainly by major mergers, later on other processes besides mergers may become competitive in the inner region of a galaxy to stimulate a gas inflow and a SMBH feeding. The environment seems to be a key ingredient. Observations show that QSOs were more clustered at high redshifts than at low ones.