Supermassive Black Holes: Connecting the Growth to the Cosmic Star Formation Rate

TL;DR

This paper models the connection between cosmic star formation rate and supermassive black hole growth, revealing how black hole accretion and quasar activity evolve with redshift, especially during the Universe's reionization epoch.

Contribution

It introduces a probabilistic model linking CSFR to black hole growth and derives the evolution of quasar duty-cycle and radiative efficiency across redshifts.

Findings

Quasar duty-cycle peaks at redshift 8.5-11.

Radiative efficiency peaks at redshift 0.1-1.3.

Black hole growth correlates with cosmic star formation history.

Abstract

In this Letter, we present a model connecting the cosmic star formation rate (CSFR) to the growth of supermassive black holes. Considering that the evolution of the massive black hole is dominated by accretion (Soltan's argument) and that the accretion process can be described by a probabilistic function directly regulated by the CSFR, we obtain the evolution of the black hole mass density. Then using the quasar luminosity function, we determine both the functional form of the radiative efficiency and the evolution of the quasar duty-cycle as functions of the redshift. We analyze four different CSFRs showing that the quasar duty-cycle, $\delta(z)$, peaks at $z\sim 8.5-11$ and so within the window associated with the reionization of the Universe. In particular, $\delta_{\rm max}\sim 0.09-0.22$ depending on the CSFR. The mean radiative efficiency, $\bar\eta(z)$, peaks at $z\sim 0.1-1.3$ with $\bar\eta_{\rm max}\sim 0.10-0.46$ depending on the specific CSFR used. Our results also show that is not necessary a supercritical Eddington accret