Three-temperature radiation hydrodynamics with PLUTO: Thermal and kinematic signatures of accreting protoplanets

In circumstellar disks around young stars, the gravitational influence of nascent planets produces telltale patterns in density, temperature, and kinematics. To better understand these signatures, we first performed 3D hydrodynamical simulations of a 0.012 $M_{\odot}$ disk, with a Saturn-mass planet orbiting circularly in-plane at 40 au. We tested four different disk thermodynamic prescriptions (in increasing order of complexity, local isothermality, $\beta$-cooling, two-temperature radiation hydrodynamics, and three-temperature radiation hydrodynamics), finding that $\beta$-cooling offers a reasonable approximation for the three-temperature approach when the planet is not massive or luminous enough to substantially alter the background temperature and density structure. Thereafter, using the three-temperature scheme, we relaxed this assumption, simulating a range of different planet masses (Neptune-mass, Saturn-mass, Jupiter-mass) and accretion luminosities (0, $10^{-3} L_{\odot}$) in the same disk. Our investigation revealed that signatures of disk-planet interaction strengthen with increasing planet mass, with circumplanetary flows becoming prominent in the high-planet-mass regime. Accretion luminosity, which adds pressure support around the planet, was found to weaken the midplane Doppler-flip, potentially visible in optically thin tracers like C$^{18}$O, while strengthening the spiral signature, particularly in upper disk layers sensitive to thicker lines, like those of $^{12}$CO.