Feedback-regulated accretion onto the first black holes

We study radiation-regulated gas accretion onto black holes (BHs) from galactic scales emphasizing the role of thermal and radiation pressures in limiting gas supply to the BH. We explore how the gas accretion depends on free parameters such as radiative efficiency, BH mass, ambient gas density/temperature, and the spectrum of the emitted radiation assuming simple initial conditions, as in the Bondi-Hoyle-Lyttleton problem. Our numerical simulations show an oscillatory behavior of the accretion rate, and thus the luminosity from the BH. We present a model for the feedback loop and provide analytical relationships for the accretion rate and the period of the accretion bursts. For stationary BHs the mean accretion rate is always less than 1% of the Bondi rate, and the period of the luminosity bursts is proportional to the average size of the ionized hot bubble. We discover that there are two distinct modes of oscillations with very different duty cycles (6% and 50%), governed by two different depletion proc...