Eddington accretion rate (${\dot{M}}_{\mathrm{Edd}}$)

An Eddington accretion rate converts the Eddington luminosity into a mass supply rate using an adopted reference efficiency ${\eta }_0$: ${\dot{M}}_{\mathrm{Edd}}=L_{\mathrm{Edd}}/({\eta }_0{c}^2)$. The common choice ${\eta }_0=0.1$ gives ${\dot{M}}_{\mathrm{Edd}}=10L_{\mathrm{Edd}}/c^2$.

For radiatively efficient release of Newtonian surface binding energy, $L\sim GM\dot{M}/R_{\ast }$ and $L_E=4\pi GMc/\kappa$ imply the displayed rate. Its efficiency is $\eta \sim GM/(R_{\ast }{c}^2)$, so at fixed opacity the maximum rate scales with stellar radius. This differs from defining an Eddington supply rate with an arbitrarily fixed reference efficiency. Geometry, advection and mass loss can modify the simple limit.