Blackbody dust sublimation radius
= Blackbody dust sublimation radius
{title2=$r_{\rm sub}\propto L^{1/2}T_{\rm sub}^{-2}$}
A spherical black grain of <radius> $a$ absorbs luminosity $L$ through projected area $\pi a^2$ and emits over $4\pi a^2$. Radiative balance at sublimation <temperature> gives $r_{\rm sub}=[L/(16\pi\sigma_{\rm SB}T_{\rm sub}^4)]^{1/2}$. Grain size cancels only under the stated unit-efficiency approximation; shielding and wavelength-dependent emissivity change the result.