The population of supermassive black holes ( SMBHs ) is split between those that are quiescent , such as those seen in local galaxies including the Milky Way , and those that are active , resulting in quasars and active galactic nuclei .
Outside our neighborhood , all the information we have on SMBHs is derived from quasars and active galactic nuclei ( AGN ) , giving us a partial view .
We study the evolution of the SMBH population , total and active , by the continuity equation , backwards in time from z = 0 to z = 4 .
Type-1 and type-2 AGN are differentiated in our model on the basis of their respective Eddington ratio distributions , chosen on the basis of observational estimates .
The duty cycle is obtained by matching the luminosity function of quasars , and the average radiative efficiency is the only free parameter in the model .
For higher radiative efficiencies ( \gtrsim 0.07 ) , a large fraction of the SMBH population , most of them quiescent , must already be in place by z = 4 .
For lower radiative efficiencies ( \sim 0.05 ) , the duty cycle increases with the redshift and the SMBH population evolves dramatically from z = 4 onwards .
The mass function of active SMBHs does not depend on the choice of the radiative efficiency or of the local SMBH mass function , but it is mainly determined by the quasar luminosity function once the Eddington ratio distribution is fixed .
Only direct measurement of the total black-hole mass function ( BHMF ) at redshifts z \gtrsim 2 could break these degeneracies , offering important constraints on the average radiative efficiency .
Focusing on type-1 AGN , for which observational estimates of the mass function and Eddington ratio distribution exist at various redshifts , models with lower radiative efficiencies better reproduce the high-mass end of the mass function at high z , but tend to over-predict it at low z , and vice-versa for models with higher radiative efficiencies .