Impact of thermal effects on the evolution of eccentricity and inclination of low-mass planets

Abstract

Using linear perturbation theory, we evaluate the time-dependent force exerted on an eccentric and inclined low-mass planet embedded in a gaseous protoplanetary disc with finite thermal diffusivity $\chi$. We assume the eccentricity and inclination to be small compared to the size of the thermal lobes $\lambda \sim (\chi /\Omega {)}^{1/2}$, itself generally much smaller than the scalelength of pressure $H$. When the planet is non-luminous, we find that its eccentricity and inclination are vigorously damped by the disc, over a timescale shorter by a factor $H/\lambda$ than the damping timescale in adiabatic discs. On the contrary, when the luminosity-to-mass ratio of the planet exceeds a threshold that depends on the disc's properties, its eccentricity and inclination undergo an exponential growth. In the limit of a large luminosity, the growth rate of the eccentricity is 2.5~times larger than that of the inclination, in agreement with previous numerical work. Depending on their luminosity, planetary embryos therefore exhibit much more diverse behaviours than the mild damping of eccentricity and inclination considered hitherto.

16 pages, 4 figures. Minor amendments to match the version published by MNRAS

References in corpus (6)

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• Density waves in protoplanetary discs excited by eccentric planets: linear theory
• Accreting luminous low-mass planets escape from migration traps at pressure bumps
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• Evolution of the eccentricity and inclination of low-mass planets subjected to thermal forces: a numerical study
• On the evolution of pebble-accreting planets in evolving protoplanetary discs
• Estimating the depth of gaps opened by planets in eccentric orbit