The role of Compton heating in radiation-regulated accretion on to black holes

We investigate the role of Compton heating in radiation-regulated accretion on to black holes from a neutral dense medium using 1D radiation-hydrodynamic simulations. We focus on the relative effects of Compton-heating and photo-heating as a function of the spectral slope {\alpha}, assuming a power-law spectrum in the energy range of 13.6 eV--100 keV. While Compton heating is dominant only close to the black hole, it can reduce the accretion rate to 0.1 % ($l \propto \dot{m}^2$ model)--0.01 % ($l \propto \dot{m}$ model) of the Bondi accretion rate when the BH radiation is hard ({\alpha} ~ 1), where $l$ and $\dot{m}$ are the luminosity and accretion rate normalised by Eddington rates, respectively. The oscillatory behaviour otherwise typically seen in simulations with {\alpha} > 1, become suppressed when {\alpha} ~ 1 only for the $l \propto \dot{m}$ model. The relative importance of the Compton heating over photo-heating decreases and the oscillatory behaviour becomes stronger as the spectrum softens. When the spectrum is soft ({\alpha} > 1.5), photo-heating prevails regardless of models making the effect of Compton heating negligible. On the scale of the ionization front, where the gas supply into the Str\"omgren sphere from large scale is regulated, photo-heating dominates. Our simulations show consistent results with the advection-dominated accretion flow ($l \propto \dot{m}^2$) where the accretion is inefficient and the spectrum is hard ({\alpha} ~ 1).