The kinetic luminosity function and the jet production efficiency of growing black holes

We derive the kinetic luminosity function for flat spectrum radio jets, using the empirical and theoretical scaling relation between jet power and radio core luminosity. The normalization for this relation is derived from a sample of flat spectrum cores in galaxy clusters with jet-driven X-ray cavities. The total integrated jet power at z=0 is W_{tot} ~ 3x10^40 ergs/s/Mpc^{3}. By integrating W_{tot} over red-shift, we determine the total energy density deposited by jets as e_{tot} ~ 2x10^{58} ergs/Mpc^{3}. Both W_{tot} and e_{tot} are dominated by low luminosity sources. Comparing e_{tot} to the local black hole mass density rho_{BH} gives an average jet production efficiency of epsilon_{jet} = e_{jet}/rho_{BH}c^2 ~ 3%. Since black hole mass is accreted mainly during high luminosity states, epsilon_{jet} is likely much higher during low luminosity states.