Tidal obliquity evolution of potentially habitable planets

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 degrees to 5 degrees, 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 M-s. 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 less than or similar to 0.25 M-circle dot are eroded in less than 0.1 Gyr. Only terrestrial planets orbiting stars with masses greater than or similar to 0.9 M-circle dot 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 less than or similar to 10 Gyr. Terrestrial planets in the IHZ of stars with masses less than or similar to 0.25 M-circle dot undergo significant tidal heating due to obliquity tides, whereas in the IHZ of stars with masses greater than or similar to 0.5 M-circle dot they require additional sources of heat to drive tectonic activity. The predictions of the two tidal models diverge significantly for e greater than or similar to 0.3. In our two-body simulations, Gl581 d's obliquity is eroded to 0 degrees and its rotation period reached its equilibrium state of half its orbital period in <0.1 Gyr. Tidal surface heating on the putative Gl581 g is less than or similar to 150 mW/m(2) as long as its eccentricity is smaller than 0.3. Conclusions. Obliquity tides modify the concept of the habitable zone. Tilt erosion of terrestrial planets orbiting LMSs should be included by atmospheric modelers. Tidal heating needs to be considered by geologists.