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We have numerically studied the thermal evolution of various-mass terrestrialplanets in habitable zones, focusing on duration of dynamo activity to generatetheir intrinsic magnetic fields, which may be one of key factors inhabitability on the planets. In particular, we are concerned with super-Earths,observations of which are rapidly developing. We calculated evolution oftemperature distributions in planetary interior, using Vinet equations ofstate, Arrhenius-type formula for mantle viscosity, and the astrophysicalmixing length theory for convective heat transfer modified for mantleconvection. After calibrating the model with terrestrial planets in the Solarsystem, we apply it for 0.1--$10M_{\oplus}$ rocky planets with surfacetemperature of $300~\mbox{K}$ (in habitable zones) and the Earth-likecompositions. With the criterion for heat flux at the CMB (core-mantleboundary), the lifetime of the magnetic fields is evaluated from the calculatedthermal evolution. We found that the lifetime slowly increases with theplanetary mass ($M_p$) independent of initial temperature gap at thecore-mantle boundary ($\Delta T_{\rm CMB}$) but beyond a critical value$M_{c,p}$ ($\sim O(1)M_{\oplus}$) it abruptly declines by the mantle viscosityenhancement due to the pressure effect. We derived $M_{c,p}$ as a function of$\Delta T_{\rm CMB}$ and a rheological parameter (activation volume, $V^*$).Thus, the magnetic field lifetime of super-Earths with $M_p > M_{p,c}$sensitively depends on $\Delta T_{\rm CMB}$, which reflects planetaryaccretion, and $V^*$, which has uncertainty at very high pressure. Moreadvanced high-pressure experiments and first-principle simulation as well asplanetary accretion simulation are needed to discuss habitability ofsuper-Earths.

Thermal evolution and lifetime of intrinsic magnetic fields of Super Earths in habitable zones