Critical Accretion Disk

For a supercritical accretion regime, we propose a critical accretion disk, where the mass-accretion rate is regulated just at the critical rate with the help of wind mass-loss. We first derive a critical radius, inside of which the standard picture is violated, using the condition that the radiative force is balanced by the gravity in the vertical direction. The critical radius $r_\mathrm{cr}$ is found to be $r_\mathrm{cr} = (9\sqrt{3}\sigma_\mathrm{T} / 16\pi c m_\mathrm{p}) \dot{M}_\mathrm{input} = 1.95 (\dot{M}_\mathrm{input} / \dot{M}_\mathrm{crit}) r_\mathrm{g}$, where $\dot{M}_\mathrm{input}$ is the mass-accretion rate at the outer edge of the disk, $\dot{M}_\mathrm{crit}$ the critical accretion rate, and $r_\mathrm{g}$ the Schwarzschild radius of the central object. Outside of this critical radius, the disk is in a radiation-pressure dominated standard state, while inside this radius the disk is in a critical state, where the excess mass is expelled by wind and the accretion rate is kept to be just at the critical rate at any radius inside $r_\mathrm{cr}$. In such a critical accretion disk, the disk thickness is $H \sim (1/6\sqrt{3})r$ and the surface temperature is $\sigma T^4 \sim (2/3\sqrt{3}) L_\mathrm{E} / 4\pi r^2$, where $L_\mathrm{E}$ is the Eddington luminosity. The total disk luminosity becomes $L_\mathrm{disk} \sim (2/3\sqrt{3}) [\ln (r_\mathrm{cr}/r_\mathrm{in})+1] L_\mathrm{E}$, where $r_\mathrm{in}$ is the inner radius. We apply the present model to microquasars and narrow-line Seyfert 1 galaxies, which are supposed to be under supercritical accretion.