Black Hole and Galaxy Coevolution From Continuity Equation and Abundance Matching

Abstract

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 slim-to 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 11 M ⊙ and BH masses 10 9 M ⊙ , 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 8 yr in strongly starforming galaxies, making these sources well within the reach of ALMA surveys in (sub-)millimeter bands.

Stellar Mass Function of Active and Quiescent Galaxies via the Continuity Equation

“…Aversa et al (2015) have been the first to show that it can be also applied to the stellar component in galaxies, to link the evolution across cosmic times of the SFR function to the stellar mass functions. The continuity equation in integral formulation is written…”

“…the first factor is the cosmic time derivative of the (unknown) stellar mass function minus a source term due to dry mergers (i.e., adding the whole mass content in stars of merging objects without contributing significantly to in-situ star formation), and the second factor is the overall time spent by a galaxy in a bin of SFR obtained from the star formation history. The interested reader can find in Aversa et al (2015) an extended discussion of how and under which hypothesis the standard differential form of the continuity equation is recovered. In general, the continuity equation above is integrodifferential and has to be solved numerically.…”

“…In the abundance matching formalism, this relationship is obtained via the equation (see Aversa et al 2015 for details) holding when a lognormal distribution of M H at given M ⋆ with dispersion σ log MH is assumed.…”

“…6) to compute the average SFR Ṁ ⋆ (M ⋆ , z) associated to a given stellar mass M ⋆ . This reads holding when a lognormal distribution ofṀ ⋆ at given M ⋆ with dispersion σ logṀ⋆ ≈ 0.15 dex is adopted (see Aversa et al 2015). The comparison of the resulting main sequence with the observational data will actually constitute an additional constraint on the assumed star formation histories for individual galaxies (see Eqs.…”

Selection bias in dynamically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation

“…For instance, a robust estimate of the black hole mass function can provide valuable constraints on the mechanisms governing black hole growth over cosmic time, such as mergers or disc instabilities (e.g., Kauffmann & Haehnelt 2000;Vittorini et al 2005;Bower et al 2006;Fontanot et al 2006;Lapi et al 2006;Menci et al 2006;Malbon et al 2007;Shankar et al 2009b;Bournaud et al 2011;Fanidakis et al 2011; ? ; Dubois et al 2013;Hirschmann et al 2014;Sesana et al 2014;Aversa et al 2015;Fontanot et al 2015;Sijacki et al 2015), as well as on the average radiative efficiencies/black hole spin and/or fraction of obscured sources (e.g., Soltan 1982;Elvis et al 2002;Shankar et al 2013b;Aversa et al 2015;Tucci & Volonteri 2016). However, because direct dynamical measurements of black hole masses are difficult to obtain, considerable effort has been invested in identifying easily observed proxies for M bh .…”