Black Hole and Galaxy Coevolution from Continuity Equation and Abundance Matching

We investigate the coevolution of galaxies and hosted supermassive black holes throughout the history of the Universe by a statistical approach based on the continuity equation and the abundance matching technique. Specifically, we present analytical solutions of the continuity equation without source term to reconstruct the supermassive black hole (BH) mass function from the AGN luminosity functions. Such an approach includes physically-motivated AGN lightcurves tested on independent datasets, which describe the evolution of the Eddington ratio and radiative efficiency from slimto thin-disc conditions. We nicely reproduce the local estimates of the BH mass function, the AGN duty cycle as a function of mass and redshift, along with the Eddington ratio function and the fraction of galaxies with given stellar mass hosting an AGN with given Eddington ratio. We exploit the same approach to reconstruct the observed stellar mass function at different redshift from the UV and far-IR luminosity functions associated to star formation in galaxies. These results imply that the buildup of stars and BHs in galaxies occurs via in-situ processes, with dry mergers playing a marginal role at least for stellar masses . 3 × 10 M⊙ and BH masses . 10M⊙, where the statistical data are more secure and less biased by systematic errors. In addition, we develop an improved abundance matching technique to link the stellar and BH content of galaxies to the gravitationally dominant dark matter component. The resulting relationships constitute a testbed for galaxy evolution models, highlighting the complementary role of stellar and AGN feedback in the star formation process. In addition, they may be operationally implemented in numerical simulations to populate dark matter halos or to gauge subgrid physics. Moreover, they may be exploited to investigate the galaxy/AGN clustering as a function of redshift, mass and/or luminosity. In fact, the clustering properties of BHs and galaxies are found to be in full agreement with current observations, so further validating our results from the continuity equation. Finally, our analysis highlights that (i) the fraction of AGNs observed in slim-disc regime, where anyway most of the BH mass is accreted, increases with redshift; (ii) already at z & 6 substantial dust amount must have formed over timescales . 10 yr in strongly starforming galaxies, making these sources well within the reach of ALMA surveys in (sub-)millimeter bands. Subject headings: black hole physics galaxies: formation galaxies: evolution methods: analytical quasars: supermassive black holes