Tidal evolution of Earth-like planets in the habitable zone of low-mass stars

Abstract

Earth-like planets in the habitable zone of low-mass stars undergo strong tidal effects that modify their spin states. These planets are expected to host dense atmospheres that can also play an important role in the spin evolution. On one hand, gravitational tides tend to synchronise the rotation with the orbital mean motion, but on the other hand, thermal atmospheric tides push the rotation away and may lead to asynchronous equilibria. Here, we investigate the complete tidal evolution of Earth-like planets by taking into account the effect of obliquity and eccentric orbits. We adopted an Andrade rheology for the gravitational tides and benchmarked the unknown parameters with the present rotation of Venus. We then applied our model to Earth-like planets, and we show that asynchronous rotation can be expected for planets orbiting stars with masses between 0.4 and 0.9 $M_ and semi-major axes between 0.2 and 0.7 au. Interestingly, we find that Earth-like planets in the habitable zone of stars with masses $ 0.8$ $M_ may end up with an equilibrium rotation of 24 hours. We additionally find that these planets can also develop high obliquities, which may help sustain temperate environments.