Evolutionary tracks of the black holes in the isothermal simulations. Since only the massive simulations lead to appreciable black hole masses, the mass-poor simulations remain in the lower left corner. The other simulations move on a path parallel to the Eddington limit (black line), then they bend and feature a constant accretion rate. The dashed black line indicates the sub-Eddington limit for redshifts of 0.6 < z < 0.8 from Steinhardt & Elvis (2010). It does not pose a strong limit for these simulations.