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

## TL;DR

This paper investigates how thermal effects influence the evolution of eccentricity and inclination of low-mass planets in protoplanetary discs, revealing conditions for damping or exponential growth based on planetary luminosity.

## Contribution

It introduces a linear perturbation theory framework to analyze thermal effects on planetary orbital evolution, highlighting the impact of planetary luminosity on eccentricity and inclination.

## Key findings

- Eccentricity and inclination are damped in non-luminous planets.
- High planetary luminosity causes exponential growth of eccentricity and inclination.
- Growth rate of eccentricity exceeds that of inclination at large luminosities.

## 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.