Supermassive black hole mass functions at intermediate redshifts from spheroid and AGN luminosity functions

Abstract

Redshift evolution of supermassive black hole mass functions (BHMFs) is investigated up to z~ 1. BHMFs at intermediate redshifts are calculated in two ways. One way is from early-type galaxy luminosity functions (LFs); we assume an M_BH-L_sph correlation at a redshift by considering a passive evolution of L_sph in the local relationship. The resultant BHMFs (spheroid-BHMFs) from LFs of red-sequence galaxies indicate a slight decrease of number density with increasing redshift at M_BH>= 10^7.5-8M_solar. Since a redshift evolution in slope and zeropoint of the M_BH-L_sph relation is unlikely to be capable of making such an evolution in BHMF, the evolution of the spheroid-BHMFs is perhaps due mainly to the decreasing normalization in the galaxy LFs. We also derive BHMFs from LFs of morphologically selected early-type galaxies. The resultant BHMFs are similar to those from the red-sequence galaxies, but show a small discrepancy at z~ 1 corresponding to an increase of supermassive black hole (SMBH) number density by ~0.3dex. We also investigate how spheroid-BHMFs are affected by uncertainties existing in the derivation in detail.

The other way of deriving a BHMF is based on the continuity equation for number density of SMBHs and LFs of active galactic nucleus (AGN). The resultant BHMFs (AGN-BHMFs) show no clear evolution out to z= 1 at M_BH>= 10⁸M_solar, but exhibit a significant decrease with redshift in the lower mass range. Interestingly, these AGN-BHMFs are quite different in the range of M_BH<= 10⁸M_solar from those derived by Merloni (2004), where the fundamental plane of black hole activity is exploited.

Comparison of the spheroid-BHMFs with the AGN-BHMFs suggests that at M_BH>= 10⁸M_solar, the spheroid-BHMFs are broadly consistent with the AGN-BHMFs out to z~ 1. Although the decrease of SMBH number density with redshift suggested by the spheroid-BHMFs is slightly faster than that suggested by the AGN-BHMFs, we presume this to be due at least partly to a selection effect on the LFs of red-sequence galaxies; the colour selection could miss spheroids with blue colours. The agreement between the spheroid-BHMFs and the AGN-BHMFs appears to support that most of the SMBHs are already hosted by massive spheroids at z~ 1 and they evolve without significant mass growth since then.