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

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, ${\delta }_{\max }\sim 0.09-0.22$ depending on the CSFR. The mean radiative efficiency, $\bar{\eta }(z)$, peaks at $z\sim 0.1-1.3$ with ${\bar{\eta }}_{\max }\sim 0.10-0.46$ depending on the specific CSFR used. Our results also show that is not necessary a supercritical Eddington accret

accepted for publication in MNRAS Letters (5 pages, 6 figures), Some typos fixed; MNRAS Letters 17 Aug 2011

References in corpus (5)

• An Observational Determination of the Bolometric Quasar Luminosity Function
• Quasars Are Not Light-Bulbs: Testing Models of Quasar Lifetimes with the Observed Eddington Ratio Distribution
• Evidence for Rapidly Spinning Black Holes in Quasars
• Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors
• Cosmological Evolution of the Duty Cycle of Quasars

Cited by in corpus (5)

• Two-phase galaxy evolution: the cosmic star-formation histories of spheroids and discs
• What triggers black-hole growth? Insights from star formation rates
• Probing a cosmological model with a $\Lambda ={\Lambda }_0+3\beta H^2$ decaying-vacuum
• Connecting the Cosmic Star Formation Rate with the Local Star Formation
• Stochastic backgrounds of gravitational waves from cosmological sources - The role of dark energy