Cooling of the magma ocean due to accretional disruption of the surface insulating layer

Planetary accretion has been considered as a process to heat planets. Some fraction of the kinetic energy of incoming planetesimals is trapped to heat the planetary interior (Kaula, 1979; Davies, 1984). Moreover, blanketing effect of a primary atmosphere (Hayashi et al., 1979; Sasaki, 1990) or a degassed atmosphere (Abe and Matsui, 1986; Zahnle et al., 1988) would raise the surface temperature of the Earth-size planets to be higher than the melting temperature. The primordial magma ocean was likely to be formed during accretion of terrestrial planets. In the magma ocean, if crystallized fractions were heavier than melt, they would sink. But if solidified materials were lighter than the melt (like anorthosite of the lunar early crust) they would float to form a solid shell surrounding the planet. (In an icy satellite, solidified water ice should easily float on liquid water because of its small density.) The surface solid lid would prevent efficient convective heat transfer and slow the interior cooling. Consider that the accretion of planetesimals still continues in this cooling stage. Shock disruption at planetesimal impact events may destroy the solid insulating layer. Even if the layer survives impacts, the surface layer is finally overturned by Rayleigh-Taylor instability, since accreting materials containing metals are heavier than the surface solidified lid of silicates.