Artigo aceito para publicação no MNRAS Letters.
http://arxiv.org/abs/1108.3745
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 $z\sim 0.6-3.0$ 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 accretion regime to produce the growth of the black hole seeds. The present scenario is consistent with the formation of black hole seeds $\sim 10^3{\rm M}_\odot$ at $z\sim 20$.
http://arxiv.org/abs/1108.3745
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 $z\sim 0.6-3.0$ 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 accretion regime to produce the growth of the black hole seeds. The present scenario is consistent with the formation of black hole seeds $\sim 10^3{\rm M}_\odot$ at $z\sim 20$.
