The Growth Efficiency of High-Redshift Black Holes

Abstract

The observational evidence that Super-Massive Black Holes ($M_{\bullet }\sim 10^{9-10}{\mathrm{M}}_{\odot }$) are already in place less than $1\mathrm{Gyr}$ after the Big Bang poses stringent time constraints on the growth efficiency of their seeds. Among proposed possibilities, the formation of massive ($\sim 10^{3-6}{\mathrm{M}}_{\odot }$) seeds and/or the occurrence of super-Eddington ($\dot{M}>{\dot{M}}_{Edd}$) accretion episodes may contribute to the solution of this problem. In this work we analytically and numerically investigate the accretion flow onto high-redshift ($z\sim 10$) black holes to understand the physical requirements favoring rapid and efficient growth. Our model identifies a "feeding-dominated" accretion regime and a "feedback-limited" one, the latter being characterized by intermittent (duty cycles $\mathcal{D}\lesssim 0.5$) and inefficient growth, with recurring outflow episodes. We find that low-mass seeds ($\lesssim 10^{3-4}{\mathrm{M}}_{\odot }$) evolve in the feedback-limited regime, while more massive seeds ($\gtrsim 10^{5-6}{\mathrm{M}}_{\odot }$) grow very rapidly as they are found in the feeding-dominated regime. In addition to the standard accretion model with a fixed matter-energy conversion factor ($\epsilon =0.1$), we have also explored slim disk models, appropriate for super-Eddington accretion, where radiation is trapped in the disk and the radiative efficiency is reduced ($\epsilon \lesssim 0.04$), which may ensure a continuous growth with $\dot{M}\gg {\dot{M}}_{Edd}$ (up to $\sim 300{\dot{M}}_{Edd}$ in our simulations). Under these conditions, outflows play a negligible role and a black hole can accrete $80\%-100\%$ of the gas mass of the host halo ($\sim 10^7{\mathrm{M}}_{\odot }$) in $\sim 10\mathrm{Myr}$, while in feedback-limited systems we predict that black holes can accrete only up to $\sim 15\%$ of the available mass.

Accepted for publication in MNRAS

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