# Overstable Convective Modes of Rotating Hot Jupiters

## TL;DR

This study investigates overstable convective modes in rotating hot Jupiters, revealing their stabilization by rotation, their ability to excite gravity waves, and their limited impact on planetary inflation.

## Contribution

It provides the first detailed analysis of overstable convective modes in rotating hot Jupiters and their role in gravity wave excitation and planetary heating.

## Key findings

- Convective modes are stabilized by rapid rotation.
- Convective modes can excite gravity waves in the radiative envelope.
- Heating from these modes is insufficient to inflate hot Jupiters in linear regime.

## Abstract

We calculate overstable convective modes of uniformly rotating hot Jupiters, which have a convective core and a thin radiative envelope. Convective modes in rotating planets have complex frequency $\omega$ and are stabilized by rapid rotation so that their growth rates $\propto\omega_{\rm I}={\rm Im}(\omega)$ are much smaller than those for the non-rotating planets. The stabilized convective modes excite low frequency gravity waves in the radiative envelope by frequency resonance between them. We find that the convective modes that excite envelope gravity waves remain unstable even in the presence of non-adiabatic dissipations in the envelope. We calculate the heating rates due to non-adiabatic dissipations of the oscillation energy of the unstable convective modes and find that the magnitudes of the heating rates cannot be large enough to inflate hot Jupiters sufficiently so long as the oscillation amplitudes remain in the linear regime.