# Triaxial Deformation and Asynchronous Rotation of Rocky Planets in the Habitable Zone of Low-Mass Stars

## TL;DR

This paper investigates how rocky planets in the habitable zones of M-dwarf stars can maintain asynchronous rotation states due to their intrinsic triaxial deformation, which affects their spin-orbit resonance capture.

## Contribution

It derives an analytic expression for the maximum triaxiality of rocky planets, considering various physical parameters, to assess their potential for asynchronous rotation.

## Key findings

- Maximum triaxiality aligns with observed terrestrial planets.
- Rocky planets in M-dwarf habitable zones can sustain asynchronous spin states.
- Analytic model supports the possibility of non-synchronous rotation due to triaxiality.

## Abstract

Rocky planets orbiting M-dwarf stars in the habitable zone tend to be driven to synchronous rotation by tidal dissipation, potentially causing difficulties for maintaining a habitable climate on the planet. However, the planet may be captured into asynchronous spin-orbit resonances, and this capture may be more likely if the planet has a sufficiently large intrinsic triaxial deformation. We derive the analytic expression for the maximum triaxiality of a rocky planet, with and without a liquid envelope, as a function of the planet's radius, density, rigidity and critical strain of fracture. The derived maximum triaxiality is consistent with the observed triaxialities for terrestrial planets in the solar system, and indicates that rocky planets in the habitable zone of M-dwarfs can in principle be in a state of asynchronous spin-orbit resonances.