paper

Tidal Locking of Habitable Exoplanets

arXiv:1708.02981 · doi:10.1007/s10569-017-9783-7

Abstract

Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. I calculate how habitable planets evolve under two commonly-used models and find, for example, that one model predicts that the Earth's rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no satellites, and it always maintained the modern Earth's tidal properties. Lower mass stellar hosts will induce stronger tidal effects on potentially habitable planets, and tidal locking is possible for most planets in the habitable zones of GKM dwarf stars. For fast rotating planets, both models predict eccentricity growth and that circularization can only occur once the rotational frequency is similar to the orbital frequency. The orbits of potentially habitable planets of very late M dwarfs (<0.15 solar masses) are very likely to be circularized within 1 Gyr and hence those planets will be synchronous rotators. Proxima b is almost assuredly tidally locked, but its orbit may not have circularized yet, so the planet could be rotating super-synchronously today. The evolution of the isolated and potentially habitable Kepler planet candidates is computed and about half could be tidally locked. Finally, projected TESS planets are simulated over a wide range of assumptions, and the vast majority of all cases are found to tidally lock within 1 Gyr. These results suggest that the process of tidal locking is a major factor in the evolution of most of the potentially habitable exoplanets to be discovered in the near future. [abridged]

40 pages, 11 figures, 3 tables (including the online tables). Accepted to Celestial Mechanics and Dynamical Astronomy. Source code to integrate the tidal evolution equations and to generate the figures and tables are available at https://github.com/RoryBarnes

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