# Evolution of eccentricity and inclination of hot protoplanets embedded in radiative discs

## TL;DR

This study investigates how the eccentricity and inclination of low-mass protoplanets evolve within radiative protoplanetary discs, revealing that planetary luminosity influences orbital excitation and damping processes over thousands of years.

## Contribution

It provides new insights into the coupled evolution of eccentricity and inclination of protoplanets considering radiative effects, which was not thoroughly explored before.

## Key findings

- Luminosity-driven growth of eccentricity and inclination occurs within a few thousand years.
- Eccentricity growth rate is about three times that of inclination.
- Radiative discs dampen eccentricity and inclination more effectively than isothermal discs.

## Abstract

We study the evolution of the eccentricity and inclination of protoplanetary embryos and low-mass protoplanets (from a fraction of an Earth mass to a few Earth masses) embedded in a protoplanetary disc, by means of three dimensional hydrodynamics calculations with radiative transfer in the diffusion limit. When the protoplanets radiate in the surrounding disc the energy released by the accretion of solids, their eccentricity and inclination experience a growth toward values which depend on the luminosity to mass ratio of the planet, which are comparable to the disc's aspect ratio and which are reached over timescales of a few thousand years. This growth is triggered by the appearance of a hot, under-dense region in the vicinity of the planet. The growth rate of the eccentricity is typically three times larger than that of the inclination. In long term calculations, we find that the excitation of eccentricity and the excitation of inclination are not independent. In the particular case in which a planet has initially a very small eccentricity and inclination, the eccentricity largely overruns the inclination. When the eccentricity reaches its asymptotic value, the growth of inclination is quenched, yielding an eccentric orbit with a very low inclination. As a side result, we find that the eccentricity and inclination of non-luminous planets are damped more vigorously in radiative discs than in isothermal discs.