Effects of Heat Conduction on Blocking off the Super-Eddington Growth of Black Holes at High Redshift

We investigate the effect of conductive heating of the gas surrounding a geometrically thick accretion disk on the growth of a black hole (BH) at high redshift. If a BH is accreting the surrounding gas at a super-Eddington rate, the X-ray radiation from the vicinity of the BH would be highly anisotropic due to the self-shielding of a geometrically thick accretion disk, and then the radiative feedback on the surrounding medium would be suppressed in the equatorial region, within which super-Eddington accretion can continue. However, if this region is sufficiently heated via thermal conduction from the adjacent region that is not shielded and heated by the X-ray irradiation, the surrounding gas becomes isotropically hot, and the Bondi accretion rate would be suppressed and become sub-Eddington. We evaluate the condition under which such isotropic heating is realized and derive new criteria required for super-Eddington accretion.