Cosmological Growth History of Supermassive Black Holes and Demographics in the High‐zUniverse: Do Lyman Break Galaxies Have Supermassive Black Holes?

We study the demographics of supermassive black holes (SMBHs) in the localand high-z universe with hard X-ray luminosity functions (HXLFs) of AGNs.First, we compare the mass accretion history at z>0 with optical luminosityfunctions (OLFs) and that with HXLFs. We consider the constraints on parametersof mass accretion (energy conversion efficiency and Eddington ratio) andconclude that the constraints based on HXLFs are more adequate rather than thatbased on OLFs. The sub-Eddington case is allowed only when we use HXLFs. Next,we estimate the upper limit of the cumulative mass density of SMBHs at anyredshifts. For an application, we examine if Lyman-Break galaxies (LBGs) at z=3already have SMBHs in their centers which is suggested by recent observations.If most of LBGs already has massive SMBHs at z=3, the resultant mass density ofSMBHs at z=0 should exceed the observational estimate because such SMBHs shouldfurther grow by accretion. We show that the special conditions should be met inorder that a large part of LBGs have SMBHs (for example, large energyconversion efficiency and frequent mergers and/or direct formations at z>3).The possibility that nearly all LBGs have SMBHs with large mass ratio, such asM_BH/M_stellar > 0.005, is reliably ruled out.(abridged)Comment: 30 pages including 5 figures, accepted for publication in Ap