Local Simulations of Heating Torques on a Luminous Body in an Accretion Disk

A luminous body embedded in an accretion disk can generate asymmetric density perturbations that lead to a net torque and thus orbital migration of the body. Linear theory has shown that this heating torque gives rise to a migration term linear in the body's mass that can oppose or even reverse that arising from the sum of gravitational Lindblad and co-orbital torques. We use high-resolution local simulations in an unstratified disk to assess the accuracy and domain of applicability of the linear theory. We find agreement between analytic and simulation results to better than 10\% in the appropriate regime (low luminosity, low thermal conductivity), but measure deviations in the non-linear (high luminosity) regime and in the high thermal conductivity regime. In the non-linear regime, linear theory overpredicts the acceleration due to the heating torque, which we find to be due to the neglect of non-linear terms in the heat flux. In the high thermal conductivity regime linear theory underpredicts the acceleration, although here both non-linear and computational constraints play a role. We discuss the impact of the heating torque for the evolution of low-mass planets in protoplanetary disks, and for massive stars or accreting compact objects embedded in AGN disks. For the latter case, we show that the thermal torque is likely to be the dominant physical effect at disk radii where the optical depth drops below a critical value.