The growth efficiency of high-redshift black holes

The observational evidence that Super-Massive Black Holes (M-center dot similar to 10(9-10) M-circle dot) are already in place less than 1 Gyr after the big bang poses stringent time constraints on the growth efficiency of their seeds. Among proposed possibilities, the formation of massive (similar to 10(3-6) M-circle dot) seeds and/or the occurrence of super-Eddington ((M)over dot > (M)over dot(Edd)) accretion episodes may contribute to the solution of this problem. In this work, using a set of astrophysically motivated initial conditions, we analytically and numerically investigate the accretion flow on to high-redshift (z similar to 10) black holes to understand the physical requirements favouring 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 D less than or similar to 0.5) and inefficient growth, with recurring outflow episodes. We find that low-mass seeds (less than or similar to 10(3-4) M-circle dot) evolve in the feedback-limited regime, while more massive seeds (greater than or similar to 10(5-6) M-circle dot) 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 disc models, appropriate for super-Eddington accretion, where radiation is trapped in the disc and the radiative efficiency is reduced (epsilon less than or similar to 0.04), which may ensure a continuous growth with (M)over dot >> (M)over dot(Edd) (up to similar to 300 (M)over dot(Edd) in our simulations). Under these conditions, outflows play a negligible role and a black hole can accrete 80-100 per cent of the gas mass of the host halo (similar to 10(7) M-circle dot) in similar to 10 Myr, while in feedback-limited systems we predict that black holes can accrete only up to similar to 15 per cent of the available mass.