Tidal heating of Earth-like exoplanets around M stars: Thermal, magnetic, and orbital evolutions

The internal thermal and magnetic evolution of rocky exoplanets is critical to their habitability. We focus on the thermal-orbital evolution of Earth-mass planets around low mass M stars whose radiative habitable zone overlaps with the "tidal zone". We develop a thermal-orbital evolution model calibrated to Earth that couples tidal dissipation, with a temperature-dependent Maxwell rheology, to orbital circularization and migration. We illustrate thermal-orbital steady states where surface heat flow is balanced by tidal dissipation and cooling can be stalled for billions of years until circularization occurs. Orbital energy dissipated as tidal heat in the interior drives both inward migration and circularization, with a circularization time that is inversely proportional to the dissipation rate. We identify a peak in the internal dissipation rate as the mantle passes through a visco-elastic state at mantle temperatures near 1800 K. Planets orbiting a 0.1 solar-mass star within $0.07$ AU circularize before 10 Gyr, independent of initial eccentricity. Once circular, these planets cool monotonically and maintain dynamos similar to Earth. Planets forced into eccentric orbits can experience a super-cooling of the core and rapid core solidification, inhibiting dynamo action for planets in the habitable zone. We find that tidal heating is insignificant in the habitable zone around $0.45$ (or larger) solar mass stars because tidal dissipation is a stronger function of orbital distance than stellar mass, and the habitable zone is further from larger stars. Suppression of the planetary magnetic field exposes the atmosphere to stellar wind erosion and the surface to harmful radiation. In addition to weak magnetic fields, massive melt eruption rates and prolonged magma oceans may render eccentric planets in the habitable zone of low mass stars inhospitable for life.