The minimum mantle viscosity of an accreting earth

The minimum mantle viscosity in an earth accreting from planetesimals is estimated. A plausible distribution of planetesimal sizes deposits enough energy to melt the outer nine-tenths of earth's mass; however, vigorous convection keeps temperatures near the solidus. Viscosity is significantly lower than prevails now. The temperature-dependent viscosity provides self-regulation so there is a continuing balance between accretional energy input and heat transfer out. This allows calculation of the minimum viscosity necessary to transfer out heat by a Nu/Ra-number relation. Typical viscosities are 0.1 to a million sq m/sec, lowest at mid-accretion when the mass growth rate is largest. Terrestrial planets are compared, and minimum iron descent times to central lithospheres are calculated.