What does the local black hole mass distribution tell us about the evolution of the quasar luminosity function?

We present a robust method to derive the duty cycle of QSO activity based on the empirical QSO luminosity function and on the present-day linear relation between the masses of supermassive black holes and those of their spheroidal host stellar systems. It is found that the duty cycle is substantially less than unity, with characteristic values in the range 3− 6× 10. Finally, we tested the expectation that the QSO luminosity evolution and the star formation history should be roughly parallel, as a consequence of the above–mentioned relation between BH and galaxy masses.