Protoplanetary disks including radiative feedback from accreting planets

Abstract

While recent observational progress is converging on the detection of compact regions of thermal emission due to embedded protoplanets, further theoretical predictions are needed to understand the response of a protoplanetary disk to the planet formation radiative feedback. This is particularly important to make predictions for the observability of circumplanetary regions. In this work we use 2D hydrodynamical simulations to examine the evolution of a viscous protoplanetary disk in which a luminous Jupiter-mass planet is embedded. We use an energy equation which includes the radiative heating of the planet as an additional mechanism for planet formation feedback. Several models are computed for planet luminosities ranging from $10^{-5}$ to $10^{-3}$ Solar luminosities. We find that the planet radiative feedback enhances the disk's accretion rate at the planet's orbital radius, producing a hotter and more luminous environement around the planet, independently of the prescription used to model the disk's turbulent viscosity. We also estimate the thermal signature of the planet feedback for our range of planet luminosities, finding that the emitted spectrum of a purely active disk, without passive heating, is appreciably modified in the infrared. We simulate the protoplanetary disk around HD 100546 where a planet companion is located at about 68 au from the star. Assuming the planet mass is 5 Jupiter masses and its luminosity is $\sim 2.5 \times 10^{-4} \, L_\odot$, we find that the radiative feedback of the planet increases the luminosity of its $\sim 5$ au circumplanetary disk from $10^{-5} \, \rm L_\odot$ (without feedback) to $10^{-3} \, \rm L_\odot$, corresponding to an emission of $\sim 1 \, \rm mJy$ in $L^\prime$ band after radiative transfer calculations, a value that is in good agreement with HD 100546b observations.