ISSN:
1365-246X
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Geosciences
Notes:
bThe Earth is found to equilibrate thermally after a giant impact melts a significant portion of the planet on a time-scale of a few million years. A simple thermal evolution model for the cooling of a terrestrial planet, a prescribed fraction of which is melted during a giant impact, is presented. Two model geometries are considered. The first has a laterally inhomogeneous distribution of melt and solid through a mega-crater geometry and the second has a global magma ocean. The model assumes convective heat transfer in the melt and, in the case of the mega-crater geometry, convection in the solid part of the planet. In the magma-ocean case the solid interior is not convecting. The melt region may cool due to heat transfer to the planet's surface and to the solid region and due to melting of solid. The solid region cools by heat transfer to the planet's surface in the mega-crater model. The viscosities of the melt and the solid are assumed to be dependent on the exponential of the inverse absolute temperature. Convective heat transfer is parametrized by using semi-empirical boundary layer thickness scaling laws. Most model parameters including planetary size are absorbed into a cooling time-scale. Of the remaining parameters of the scaled model, the rate of change of melt viscosity with temperature, the surface temperature and, for small melt fractions, the melt region geometry are most important in determining the cooling time. The initial melt temperature, the heat capacities of the solid and the melt, and the Stefan number, a measure of the latent heat of melting, determine the proportion of the solid that is melted during cooling of the impact melt. It is found that almost the whole planet may melt if the impact originally melted half of the planet and if the initial melt temperature was twice a representative planet melting temperature. For reasonable choices of parameter values it is found that thermal equilibration of the Earth occurs on a time-scale of 1 to 10 million years.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1365-246X.1991.tb01164.x
