= Radiation-supported inner-disk height
{title2=$H(R)$}
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-thickness
$$
H(R)\simeq\frac{3\kappa_{\rm es}\dot M}{8\pi c}\left(1-\sqrt{R_{\rm in}/R}\right).
$$
The 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.
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