Numerical study of coorbital thermal torques on cold or hot satellites

Abstract

We evaluate the thermal torques exerted on low-mass planets embedded in gaseous protoplanetary discs with thermal diffusion, by means of high-resolution three-dimensional hydrodynamics simulations. We confirm that thermal torques essentially depend on the offset between the planet and its corotation, and find a good agreement with analytic estimates when this offset is small compared to the size of the thermal disturbance. For larger offsets that may be attained in discs with a large pressure gradient or a small thermal diffusivity, thermal torques tend toward an asymptotic value broadly compatible with results from a dynamical friction calculation in an unsheared medium. We perform a convergence study and find that the thermal disturbance must be resolved over typically 10 zones for a decent agreement with analytic predictions. We find that the luminosity at which the net thermal torque changes sign matches that predicted by linear theory within a few percents. Our study confirms that thermal torques usually supersede Lindblad and corotation torques by almost an order of magnitude for low mass planets. As we increase the planetary mass, we find that the ratio of thermal torques to Lindblad and corotation torques is progressively reduced, and that the thermal disturbance is increasingly distorted by the horseshoe flow. Overall, we find that thermal torques are dominant for masses up to an order of magnitude larger than implemented in recent models of planetary population synthesis. We finally briefly discuss the case of stellar or intermediate-mass objects embedded in discs around AGNs.

Eccentricity driving of pebble accreting low-mass planets

“…Therefore, the quoted asymptotic eccentricities here on present a slight overestimation. We note that the requirement that the size of the heated region being of the order of ten cells is in agreement with the study of (Chametla & Masset 2021), who obtain a similar value for thermal forces exerted on planets on circular orbits.…”

“…We summarise here only the results relative to an eccentric planet. Those relative to a planet on a circular orbit can be found in Masset (2017) or Chametla & Masset (2021).…”

“…We have validated our implementation of the heat release and the disc's thermal diffusion by running a low-mass planet on a circular orbit and checking that the perturbation induced in the gas by the heat released has the shape and amplitude predicted by Masset (2017). This validation procedure, presented in Appendix A, is similar to that of Hankla et al (2020) or that of Chametla & Masset (2021).…”

“…These contributions are generically referred to as thermal forces or thermal torques. While they have important consequences even in the case of a planet on a circular orbit (Lega et al 2014;Benítez-Llambay et al 2015;Masset 2017) as they can modify considerably the speed and even the direction of migration (Guilera et al 2019;Chametla & Masset 2021), they play an even more important role on the ‹ E-mail: david.velasco@icf.unam.mx evolution of the eccentricity and inclination (Chrenko et al 2017;Eklund & Masset 2017). Eklund & Masset (2017) have found that non-luminous planets embedded in radiative discs (hence subjected to some form of heat diffusion) have their eccentricity and inclination damped much more vigorously than if the disc is adiabatic.…”

The importance of thermal torques on the migration of planets growing by pebble accretion

“…If discs are neither isothermal nor adiabatic, thermal diffusion introduces an additional torque, called the thermal torque (e.g. Masset 2017;Velasco Romero & Masset 2020;Hankla et al 2020;Chametla & Masset 2021). If the planet is not luminous, the thermal torque is known as the cold torque because the surrounding gas is cooler and denser than it would be if it behaved adiabatically, generating an additional torque (Lega et al 2014;Masset 2017) that is in general negative.…”