The difference between the inactive surface of Mimas and the active surface of Enceladus is puzzling. We investigate the conditions under which both have a thick subsurface ocean and the thermal lithosphere of Mimas is thicker than that of Enceladus by using a one-dimensional simulation of thermal evolution. We adopt the initial core temperature, initial methane concentration, and tidal heating rate as free parameters in the calculation. The initial methane concentration and tidal heating rate greatly affect the current ocean thickness, although the initial core temperature does not affect the thickness. Methane hydrate forms at the base of the icy shell if the initial methane concentration is not 0. The methane hydrate layer plays an insulative role in an icy shell. When the initial methane concentration is 1000 , ∼2 GW is needed to achieve more than 50 km of the subsurface ocean on Mimas and ∼7.5 GW is needed to achieve more than 25 km of the subsurface ocean on Enceladus. These values are smaller than those needed when the initial methane concentration is 0 . The existence of the methane hydrate layer promotes the survival of the subsurface ocean because it insulates internal heat. In addition, it is found that the surface heat flux is depressed if the methane hydrate layer exists, which is consistent with the unrelaxed craters in Mimas. Methane hydrate may explain the thick oceans in Mimas and Enceladus and the inactive shell of Mimas.
