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Accretion onto Intermediate Mass Black Holes Regulated by Radiative Feedback I. Parametric Study for Spherically Symmetric Accretion

We study the effect of radiative feedback on accretion onto intermediate mass black holes (IMBHs) using the hydrodynamical code ZEUS-MP with a radiative transfer algorithm. In this paper, the first of a series, we assume accretion from a uniformly dense gas with zero angular momentum and extremely low metallicity. Our 1D and 2D simulations explore how X-ray and UV radiation emitted near the black hole regulates the gas supply from large scales. Both 1D and 2D simulations show similar accretion rate and period between peaks in accretion, meaning that the hydro-instabilities that develop in 2D simulations do not affect the mean flow properties. We present a suite of simulations exploring accretion across a large parameter space, including different radiative efficiencies and radiation spectra, black hole masses, density and temperature, $T_\infty$, of the neighboring gas. In agreement with previous studies we find regular oscillatory behavior of the accretion rate, with duty cycle $\sim 6%$, mean accretion rate 3% $(T_{\infty}/10^4 {\rm K})^{2.5}$ of the Bondi rate and peak accretion $\sim 10$ times the mean for $T_{\infty}$ ranging between 3000K and 15000K. We derive parametric formulas for the period between bursts, the mean accretion rate and the peak luminosity of the bursts and thus provide a formulation of how feedback regulated accretion operates. The temperature profile of the hot ionized gas is crucial in determining the accretion rate, while the period of the bursts is proportional to the mean size of the Strömgren sphere and we find qualitatively different modes of accretion in the high vs. low density regimes. We also find that softer spectrum of radiation produces higher mean accretion rate.