Estimating the Radiative Efficiency of Magnetized Accretion Disks Around   Black Holes
  Simulations of black hole accretion have shown that magnetic stresses are present near and inside the innermost stable circular orbit (ISCO). This finding suggests that such flows may be more luminous than predicted by the standard accretion disk model. Here we apply a prescription for heat dissipation within the simulated accretion flows to estimate their implied radiative efficiency. We assume that dissipation is proportional to the current density squared, and find that the resulting azimuthally-averaged and shell-integrated radial profile is well-matched to the radial heat dissipation profile of the standard disk model for the region outside the ISCO, particularly when it is adjusted to account for additional stress at the ISCO. In contrast to the standard model, however, the dissipation profile derived from the current density continues past the ISCO and through the plunging region. The total predicted dissipation rate is between $\simeq 30%$ and $\simeq 100%$ greater than that predicted by the standard model, depending on the black hole spin. Most of the additional dissipation takes place just outside the ISCO. To predict luminosities, we assume instantaneous radiation and zero optical depth, but allow for photon capture. The net radiative efficiency seen by a distant observer is increased relative to the standard model by $\simeq 25%$--80%, with the largest fractional increase for intermediate black hole spins because the increase in dissipation from enhanced stress that occurs for rapid spin is partially offset by the increased likelihood that the additional photons will be captured by the hole. 
Kris Beckwith, John F. Hawley and Julian H. Krolik