Formation of Overheated Regions and Truncated Disks around Black Holes;
  Three-dimensional General Relativistic Radiation-magnetohydrodynamics
  Simulations
  Using three-dimensional general relativistic radiation magnetohydrodynamics
simulations of accretion flows around stellar mass black holes, we report that
the relatively cold disk ($\gtrsim 10^{7}$K) is truncated near the black hole.
Hot and less-dense regions, of which the gas temperature is $ \gtrsim 10^9$K
and more than ten times higher than the radiation temperature (overheated
regions), appear within the truncation radius. The overheated regions also
appear above as well as below the disk, and sandwich the cold disk, leading to
the effective Compton upscattering. The truncation radius is $\sim 30 r_{\rm
g}$ for $\dot{M} \sim L_{\rm Edd}/c^2$, where $r_{\rm g}, \dot M,
L_\mathrm{Edd}, c$ are the gravitational radius, mass accretion rate, Eddington
luminosity, and light speed. Our results are consistent with observations of
very high state, whereby the truncated disk is thought to be embedded in the
hot rarefied regions. The truncation radius shifts inward to $\sim 10 r_{\rm
g}$ with increasing mass accretion rate $\dot{M} \sim 100 L_{\rm Edd}/c^2$,
which is very close to an innermost stable circular orbit. This model
corresponds to the slim disk state observed in ultra luminous X-ray sources.
Although the overheated regions shrink if the Compton cooling effectively
reduces the gas temperature, the sandwich-structure does not disappear at the
range of $\dot{M} \lesssim 100L_{\rm Edd}/c^2$. Our simulations also reveal
that the gas temperature in the overheated regions depends on black hole spin,
which would be due to efficient energy transport from black hole to disks
through the Poynting flux, resulting gas heating.
