2011ApJ...726...70T

We have numerically studied the thermal evolution of different-mass terrestrial planets in habitable zones, focusing on the duration of dynamo activity to generate their intrinsic magnetic fields, which may be one of the key factors in habitability of the planets. In particular, we are concerned with super-Earths, observations of which are rapidly developing. We calculated the evolution of temperature distributions in the planetary interior using Vinet equations of state, the Arrhenius-type formula for mantle viscosity, and the astrophysical mixing-length theory for convective heat transfer modified for mantle convection. After calibrating the model with terrestrial planets in the solar system, we apply it for 0.1-10 M_⊕ rocky planets with a surface temperature of 300 K (in habitable zones) and Earth-like compositions. With the criterion of heat flux at the core-mantle boundary (CMB), the lifetime of the magnetic fields is evaluated from the calculated thermal evolution. We found that the lifetime slowly increases with planetary mass (M_p), independent of the initial temperature gap at the CMB (ΔT_CMB), but beyond the critical value M_c,p(∼O(1) M_⊕) it abruptly declines from the mantle viscosity enhancement due to the pressure effect. We derived M_c,p as a function of ΔT_CMBand a rheological parameter (activation volume, V*). Thus, the magnetic field lifetime of super-Earths with M_p >M_p,c sensitively depends on ΔT_CMB, which reflects planetary accretion, and V*, which has uncertainty at very high pressure. More advanced high-pressure experiments and first-principle simulation, as well as planetary accretion simulation, are needed to discuss the habitability of super-Earths.