Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 581d

TL;DR

This study analyzes the long-term orbital and rotational dynamics of GJ 581d, a potentially habitable exoplanet, revealing its likely spin-orbit resonance states and system stability, which are crucial for assessing its habitability.

Contribution

The paper provides a detailed dynamical analysis of GJ 581d, including re-analysis of radial velocities, stability assessment of the system, and modeling of the planet's spin-orbit resonances considering tidal effects.

Findings

The GJ 581 system is dynamically stable with bounded chaos.

GJ 581d is likely trapped in a 2:1 or higher spin-orbit resonance.

The planet probably did not reach a 1:1 resonance, favoring habitability.

Abstract

GJ 581d is a potentially habitable super-Earth in the multiple system of exoplanets orbiting a nearby M dwarf. We investigate this planet's long-term dynamics, with an emphasis on its probable final rotation states acquired via tidal interaction with the host. The published radial velocities for the star are re-analysed with a benchmark planet detection algorithm, to confirm that there is no evidence for the recently proposed two additional planets (f and g). Limiting the scope to the four originally detected planets, we assess the dynamical stability of the system and find bounded chaos in the orbital motion. For the planet d, the characteristic Lyapunov time is 38 yr. Long-term numerical integration reveals that the system of four planets is stable, with the eccentricity of the planet d changing quasi-periodically in a tight range around 0.27, and with its semimajor axis varying only a little. The spin-orbit interaction of GJ 581d with its host star is dominated by the tides exerted by the star on the planet. We model this interaction, assuming a terrestrial composition of the mantle. Besides the customarily included secular parts of the triaxiality-caused and tidal torques, we also include these torques' oscillating components. It turns out that, dependent on the mantle temperature, the planet gets trapped into the 2:1 or an even higher spin-orbit resonance. It is very improbable that the planet could have reached the 1:1 resonance. This enhances the possibility of the planet being suitable for sustained life.