Illustration of the two different, mutually exclusive assumptions (Sect. 6.2.3). In both figures we assume . We also plot the influence of with a vector of the most likely values (see Appendix C). Left: Eddington ratio λ (Eq. (4)) versus redshift. We draw the Eddington limit at λ = 1.0 (dashed line). We assume . Black diamonds are the calculated Eddington ratios assuming the M_BH–M_Gal relation while the open squares linked by a thin line represent the same black hole assuming the offset from the local relation from (Nesvadba et al. 2011, see text for details). Right: M_BH from the two different hypotheses, assuming the local M_BH–M_Gal (bottom axis) and assuming λ = 0.1 (left axis). The dashed line represent the one-to-one relation. The blue points (arrows and star) are the black hole masses measured from Hα lines (Nesvadba et al. 2011) and compared to the black hole masses from the stellar masses from (De Breuck et al. 2010). These points therefore do not assume λ = 0.1.