Supermassive Black Hole Mass Functions at Intermediate Redshifts from Spheroid and AGN Luminosity Functions

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 MBH − Lsph correlation at a redshift by considering a passive evolution of Lsph in the local relationship. The resultant BHMFs (spheroid-BHMFs) from LFs of red sequence galaxies indicates a slight decrease of number density with increasing redshift at MBH > 10 M⊙. Since a redshift evolution in slope and zeropoint of theMBH−Lsph 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 SMBH number density by ∼ 0.3 dex. 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 MBH > 10 M⊙, but exhibit a significant decrease with redshift in the lower mass range. Interestingly, these AGNBHMFs are quite different in the range of MBH 6 10 M⊙ 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 MBH > 10 M⊙, 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.