Snowball planets as a possible type of water-rich terrestrial planet in extrasolar planetary systems

Terrestrial planets with abundant water have multiple climate modes, including an ice-free, a partially ice-covered, and a globally ice-covered state. Recent geological studies have revealed that the Earth experienced global glaciations in its history ("snowball Earth" hypothesis). In the snowball glaciations, liquid water is thought to have existed under the ice shell because of geothermal heat flow from the Earth's interior. Here, by analogy with the snowball glaciations, I discuss the conditions for an extrasolar terrestrial planet which is covered with ice but has an internal ocean for the timescale of planetary evolution owing to geothermal heat flow from the planetary interior. I show that liquid water can exist if the planetary mass and the water abundance are comparable to the Earth, although a planet with a mass < 0.4 M-circle plus (is the Earth's mass) would not be able to maintain the internal ocean. Liquid water would be absolutely stable for a planet with a mass greater than or similar to 4 M-circle plus (i.e., super-Earth) either on its surface or beneath the ice, irrespective of planetary orbit and luminosity of the central star. Searches for terrestrial planets in extrasolar planetary systems should consider such a "snowball planet," which is a possible type of water-rich terrestrial planet other than an Earth-like "ocean planet".