Context. Stellar insolation has been used as the main constraint on a planet’s potential habitability. However, as more Earth-like planets are discovered around low-mass stars (LMSs), a re-examination of the role of tides on the habitability of exoplanets has begun. Those studies have yet to consider the misalignment between a planet’s rotational axis and the orbital plane normal, i.e. the planetary obliquity. Aims. This paper considers the constraints on habitability arising from tidal processes due to the planet’s spin orientation and rate. Since tidal processes are far from being understood we seek to understand differences between commonly used tidal models. Methods. We apply two equilibrium tide theories – a constant-phase-lag model and a constant-time-lag model – to compute the obliquity evolution of terrestrial planets orbiting in the habitable zones around LMSs. The time for the obliquity to decrease from an Earth-like obliquity of 23.5° to 5°, the “tilt erosion time”, is compared to the traditional insolation habitable zone (IHZ) in the parameter space spanned by the semi-major axis a, the eccentricity e, and the stellar mass Ms. We also compute tidal heating and equilibrium rotation caused by obliquity tides as further constraints on habitability. The Super-Earth Gl581?d and the planet candidate Gl581?g are studied as examples for these tidal processes. Results. Earth-like obliquities of terrestrial planets in the IHZ around stars with masses ??0.25?M⊙ are eroded in less than 0.1?Gyr. Only terrestrial planets orbiting stars with masses ??0.9?M⊙ experience tilt erosion times larger than 1?Gyr throughout the IHZ. Tilt erosion times for terrestrial planets in highly eccentric orbits inside the IHZ of solar-like stars can be ??10?Gyr. Terrestrial planets in the IHZ of stars with masses ??0.25?M⊙ undergo significant tidal heating due to obliquity tides, whereas in the IHZ of stars with masses ??0.5?M⊙ they require additional sources of heat to drive tectonic activity. The predictions of the two tidal models diverge significantly for e ? 0.3. In our two-body simulations, Gl581?d’s obliquity is eroded to 0° and its rotation period reached its equilibrium state of half its orbital period in
展开▼
