Using the fundamental plane to unveil the history of accretion: redshift evolution

From the local BHMF and BHARF, it is then possible to evolve a continuity equation (Small & Blandford 1992) backwards in time, provided a redshift evolution of both XLF and RLF of AGN (and neglecting mergers)
For a given couple of evolving XLF and RLF, and a given local BH Mass function, it is possible to calculate the history of accretion onto SMBH with just three free parameters:
- the efficiency of accretion (here I assume e=0.1)
- the value of xcr, where the accretion mode change takes place (observationally constrained to be 10-3 < xcr < 10-2 )
- the correspondong value of the critical accretion rate (or, equivalently, an X-ray bolometric correction)

From the local BHMF and BHARF, it is then possible to evolve a continuity equation (Small & Blandford 1992) backwards in time, provided a redshift evolution of both XLF and RLF of AGN (and neglecting mergers)