  Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it
possible to study accretion dynamics in detail. However, special effort is
required to connect inflow dynamics (dependent largely on angular momentum
transport) to radiation (dependent largely on thermodynamics and photon
diffusion). To this end we extend the flux-conservative, general relativistic
MHD code HARM from axisymmetry to full 3D. The use of an energy conserving
algorithm allows the energy dissipated in the course of relativistic accretion
to be captured as heat. The inclusion of a simple optically thin cooling
function permits explicit control of the simulated disk's geometric thickness
as well as a direct calculation of both the amplitude and location of the
radiative cooling associated with the accretion stresses. Fully relativistic
ray-tracing is used to compute the luminosity received by distant observers.
For a disk with aspect ratio H/r ~ 0.1 accreting onto a black hole with spin
parameter a/M = 0.9, we find that there is significant dissipation beyond that
predicted by the classical Novikov-Thorne model. However, much of it occurs
deep in the potential, where photon capture and gravitational redshifting can
strongly limit the net photon energy escaping to infinity. In addition, with
these parameters and this radiation model, significant thermal and magnetic
energy remains with the gas and is accreted by the black hole. In our model,
the net luminosi ty reaching infinity is 6% greater than the Novikov-Thorne
prediction. If the accreted thermal energy were wholly radiated, the total
luminosity of the accretion flow would be ~20% greater than the Novikov-Thorne
value.
