Cosmological Growth History of Supermassive Black Holes and Demographics   in the High-z Universe : Do Lyman-Break Galaxies Have Supermassive Black   Holes?
  We study the demographics of supermassive black holes (SMBHs) in the local and high-z universe with hard X-ray luminosity functions (HXLFs) of AGNs. First, we compare the mass accretion history at z>0 with optical luminosity functions (OLFs) and that with HXLFs. We consider the constraints on parameters of mass accretion (energy conversion efficiency and Eddington ratio) and conclude that the constraints based on HXLFs are more adequate rather than that based 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 any redshifts. For an application, we examine if Lyman-Break galaxies (LBGs) at z=3 already 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 of SMBHs at z=0 should exceed the observational estimate because such SMBHs should further grow by accretion. We show that the special conditions should be met in order that a large part of LBGs have SMBHs (for example, large energy conversion efficiency and frequent mergers and/or direct formations at z>3). The possibility that nearly all LBGs have SMBHs with large mass ratio, such as M_BH/M_stellar > 0.005, is reliably ruled out.(abridged) 
T.Hosokawa (Kyoto Univ.)