Differentiation of planetesimals and the thermal consequences of melt migration

We model the heating of a primordial planetesimal by decay of the short-lived radionuclides Al and Fe to determine (1) the time scale on which melting will occur, (2) the minimum size of a body that will produce silicate melt and differentiate, (3) the migration rate of molten material within the interior, and (4) the thermal consequences of the transport of Al in partial melt. Our models incorporate results from previous studies of planetary differentiation and are constrained by petrologic (i.e., grain-size distributions), isotopic (e.g., Pb-Pb and Hf-W ages), and mineralogical properties of differentiated achondrites. We show that formation of a basaltic crust via melt percolation was limited by the formation time of the body, matrix grain size, and viscosity of the melt. We show that low viscosity (<1 Pa Æ s) silicate melt can buoyantly migrate on a time scale comparable to the mean life of Al. The equilibrium partitioning of Al into silicate partial melt and the migration of that melt acts to dampen internal temperatures. However, subsequent heating from the decay of Fe generated melt fractions in excess of 50%, thus completing differentiation for bodies that accreted within 2 Myr of CAI formation (i.e., the onset of isotopic decay). Migration and concentration of Al into a crust results in remelting of that crust for accretion times less than 2 Myr and for bodies >100 km in size. Differentiation would be most likely for planetesimals larger than 20 km in diameter that accreted within approximately 2.7 Myr of CAI formation.