Pressure-opacity zones of a Shakura--Sunyaev thin disk

The standard thin-disk solution separates approximately into an inner radiation-pressure and electron-scattering zone, a middle gas-pressure and electron-scattering zone, and an outer gas-pressure and free-free-opacity zone.

The inner Shakura--Sunyaev thin disk is supported mainly by radiation pressure and has nearly constant electron-scattering opacity. Equating radiative diffusion with local dissipation and imposing vertical hydrostatic equilibrium gives the characteristic half-thicknessThe radiation-supported height approaches a plateau away from the inner boundary. The formal zero at that boundary is outside the reliable radiation-dominated approximation. At an Eddington accretion rate defined using efficiency $0.1$, this height can make the inner flow only marginally thin.