Joint Formation of QSOs and Spheroids: QSOs as clocks of star formation in Spheroids

Direct and indirect observational evidence leads to the conclusion that high redshift QSOs did shine in the core of early type proto-galaxies during their main episode of star formation. Exploting this fact, we derive the rate of formation of this kind of stellar systems at high redshift by using the QSO Luminosity Function. The elemental proportions in elliptical galaxies, the descendents of the QSO hosts, suggest that the star formation was more rapid in more massive objects. We show that this is expected to occur in Dark Matter haloes, when the processes of cooling and heating is considered. This is also confirmed by comparing the observed sub-mm counts to those derived by coupling the formation rate and the star formation rate of the spheroidal galaxies with a detailed model for their SED evolution. In this scenario SCUBA galaxies and Lyman Break Galaxies are early type proto-galaxies forming the bulk of their stars before the onset of QSO activity.