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The assumed central black hole mass is $M_{\bullet }\sim 10^8{M}_{\odot }\simeq 2\times 10^{38}\mathrm{kg}$. A mass alone does not fix radiated energy: specify a formation mechanism and its radiative efficiency of black-hole accretion. For radiatively efficient accretion, if a fraction $ϵ$ of the supplied rest-mass energy escapes and the remainder increases the black hole mass, then $M_{\bullet }=(1-ϵ)M_{\mathrm{supplied}}$ andTaking the customary order-of-magnitude efficiency $ϵ\sim 0.1$ givesThe coeval accretion phase would be a quasar-scale source, hundreds of times brighter than a typical present $L_{\ast }$ galaxy. Compared directly with the preceding gravitational-collapse estimate,Despite its small mass fraction, black-hole accretion extracts a fraction of rest-mass energy, while galactic collapse releases only an energy scale $M{\sigma }^2\ll M{c}^2$. The numerical luminosity is conditional: a radiatively inefficient accretion flow, direct collapse or assembly by mergers need not radiate this amount over the galactic clock, and the question supplies no unique efficiency.

The specific orbital energy released in a black-hole accretion flow reaching an inner radius $r_{\mathrm{in}}$ is of order $GM/r_{\mathrm{in}}$. For a circular Keplerian orbit, the binding energy is more precisely $GM/(2r_{\mathrm{in}})$, with the other half of the potential-energy decrease retained as orbital kinetic energy. Multiplying by the mass accretion rate gives the accretion luminosity scaleFor an inner radius of order the Schwarzschild radius, $r_{\mathrm{in}}\sim 2GM/c^2$, this becomesThis is an energy-release scaling, not unit radiative efficiency of black-hole accretion. The actual inner orbit, stresses and advected energy determine the coefficient and the emitted luminosity; the innermost stable circular orbit of a Schwarzschild black hole lies outside its horizon.