Radiation-supported inner-disk height ($H(R)$)

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.