Radiative feedback from quasars and the growth of massive black holes in stellar spheroids

We discuss the importance of feedback via photoionization and Compton heating on the co-evolution of massive black holes (MBHs) at the centre of spheroidal galaxies, and their stellar and gaseous components. We first assess the energetics of the radiative feedback from a typical quasar on the ambient interstellar medium (ISM). We then demonstrate that the observed   M _BH–σ  relation could be established following the conversion of most of the gas of an elliptical progenitor into stars, specifically when the gas-to-stars mass ratio in the central regions has dropped to a low level  ～0.01  or less, so that gas cooling is no longer able to keep up with the radiative heating by the growing central massive black hole (MBH). A considerable amount of the remaining gas will be expelled and both MBH accretion and star formation will proceed at significantly reduced rates thereafter, in agreement with observations of present-day ellipticals. We find further support for this scenario by evolving over an equivalent Hubble time a simple, physically based toy model that additionally takes into account the mass and energy return for the spheroid evolving stellar population, a physical ingredient often neglected in similar approaches.