Accretion luminosity as a function of BH mass. The solid blue line shows the locally emitted luminosity ﹩{L}_{\mathrm{emitted}}=\eta {\dot{M}}_{{\rm{B}}}{c}^{2}﹩ (Section 3.2). The black dashed line is L_Edd ∝ M, the dotted black line is the M. C. Begelman (1979) cap 0.6L_Edd, and the green dashed–dotted line is the saturated-convection floor ﹩{L}_{\mathrm{conv},\mathrm{sat}}=4\pi {r}_{{\rm{B}}}^{2}{\rho }_{{\rm{\infty }}}{c}_{{\rm{\infty }}}^{3}﹩. The red thick line is the total escaping (radiative plus convective) luminosity ﹩{L}_{{\rm{esc}},{\rm{tot}}}={\rm{\max }}\left({L}_{{\rm{esc}}},\,(1-{f}_{{\rm{geom}}})\,{L}_{{\rm{conv}},{\rm{sat}}}\right)﹩, where ﹩{L}_{\mathrm{esc}}={f}_{\mathrm{geom}}\min ({L}_{\mathrm{emitted}},0.6{L}_{\mathrm{Edd}})﹩ is the radiative escape defined in Section 3.3 and ﹩{f}_{{\rm{geom}}}={\rm{\max }}(0,\,1-{r}_{{\rm{trap}}}/{r}_{{\rm{B}}})﹩; it is capped by the Begelman bound in the partial-trapping window and asymptotes to L_conv,sat once r_trap ≥ r_B. The vertical dashed and dotted lines mark τ(r_B) = 1 and r_trap = r_B, respectively. Background shading marks the three accretion regimes. The solar luminosity L_⊙ is shown for reference.