Abstract
We develop a simple evolutionary scenario for the growth of supermassive black holes (BHs), assuming growth due to accretion only, to learn about the evolution of the BH mass function from $z=3$ to 0 and from it calculate the energy budgets of different modes of feedback. We tune the parameters of the model by matching the derived X-ray luminosity function (XLF) with the observed XLF of active galactic nuclei. We then calculate the amount of comoving kinetic and bolometric feedback as a function of redshift, derive a kinetic luminosity function and estimate the amount of kinetic feedback and $PdV$ work done by classical double Fanaroff-Riley II (FR II) radio sources. We also derive the radio luminosity function for FR IIs from our synthesized population and set constraints on jet duty cycles. Around 1/6 of the jet power from FR II sources goes into $PdV$ work done in the expanding lobes during the time the jet is on. Anti hierarchical growth of BHs is seen in our model due to addition of an amount of mass being accreted on to all BHs independent of the BH mass. The contribution to the total kinetic feedback by active galaxies in a low accretion, kinetically efficient mode is found to be the most significant at $z<1.5$. FR II feedback is found to be a significant mode of feedback above redshifts $z\sim 1.5$, which has not been highlighted by previous studies.
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