We examine a new family of global analytic solutions for optically thick accretion disks , which includes the supercritical accretion regime .
We found that the ratio of the advection cooling rate , Q _ { adv } , to the viscous heating rate , Q _ { vis } , i.e. , f = Q _ { adv } / Q _ { vis } , can be represented by an analytical form dependent on the radius and the mass accretion rate .
The new analytic solutions can be characterized by the photon-trapping radius , r _ { trap } , inside which the accretion time is less than the photon diffusion time in the vertical direction ; the nature of the solutions changes significantly as this radius is crossed .
Inside the trapping radius , f approaches f \propto r ^ { 0 } , which corresponds to the advection-dominated limit ( f \sim 1 ) , whereas outside the trapping radius , the radial dependence of f changes to f \propto r ^ { -2 } , which corresponds to the radiative-cooling-dominated limit .
The analytical formula for f derived here smoothly connects these two regimes .
The set of new analytic solutions reproduces well the global disk structure obtained by numerical integration over a wide range of mass accretion rates , including the supercritical accretion regime .
In particular , the effective temperature profiles for our new solutions are in good agreement with those obtained from numerical solutions .
Therefore , the new solutions will provide a useful tool not only for evaluating the observational properties of accretion flows , but also for investigating the mass evolution of black holes in the presence of supercritical accretion flows .