Thermal-Orbital Coupled Tidal Heating and Habitability of Martian-sized Extrasolar Planets around M Stars

M-type stars are good targets in the search for habitable extrasolar planets. Due to their low effective temperatures, the habitable zone of M stars is very close to the stars themselves. For planets that are close to their stars, tidal heating plays an important role in thermal and orbital evolutions, especially when the planet's orbit has a relatively large eccentricity. Although tidal heating interacts with the thermal state and the orbit of the planet, such coupled calculations for extrasolar planets around M stars have not been conducted. We perform coupled calculations using simple structural and orbital models and analyze the thermal state and habitability of a terrestrial planet. Considering this planet to be Martian-sized, the tide heats up and partially melts the mantle, maintaining an equilibrium state if the mass of the star is less than 0.2 times the mass of the Sun and the initial eccentricity of the orbit is more than 0.2. The reduction of heat dissipation due to the melted mantle allows the planet to stay in the habitable zone for more than 10 Gyr even though the orbital distance is small. The surface heat flux at the equilibrium state is between that of Mars and Io. The thermal state of the planet mainly depends on the initial value of the eccentricity and the mass of the star.