Tidal obliquity evolution of potentially habitable planets

Abstract: Stellar insolation has been used as the main constraint on a planet's 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. We apply two equilibrium tide theories 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 deg to 5 deg, the 'tilt erosion time', is compared to the traditional insolation habitable zone (IHZ) as a function of semi-major axis, eccentricity, and stellar mass. We also compute tidal heating and equilibrium rotation caused by obliquity tides. The Super-Earth Gl581d and the planet candidate Gl581g are studied as examples for tidal processes. Earth-like obliquities of terrestrial planets in the IHZ around <0.25 solar mass (M_sun) stars are eroded in <0.1 Gyr. Only terrestrial planets orbiting stars with masses >0.9 M_sun experience tilt erosion times larger than 1 Gyr throughout the IHZ. Terrestrial planets in the IHZ of stars with masses <0.25 M_sun undergo significant tidal heating due to obliquity tides. The predictions of the two tidal models diverge significantly for e>0.3. In our two-body simulations, Gl581d's obliquity is eroded to 0 and its rotation period reached its equilibrium state of half its orbital period in <0.1 Gyr. Tidal surface heating on the putative Gl581g is <150 mW/m^2 as long as its eccentricity is <0.3. 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.