  The Dawn mission confirms predictions that the asteroid 4 Vesta is
differentiated with an iron-rich core, a silicate mantle and a basaltic crust,
and confirms Vesta as the parent body of the HED meteorites. To better
understand its early evolution, we perform numerical calculations of the
thermo-chemical evolution adopting new data obtained by the Dawn mission such
as mass, bulk density and size of the asteroid. We have expanded the model of
Neumann et al. (2012) that includes accretion, compaction, melting and
associated changes of material properties and partitioning of 26Al, advective
heat transport, and differentiation by porous flow, to include convection and
effective cooling in a magma ocean. Depending on the melt fraction, the heat
transport by melt segregation is modelled either by porous flow or by
convection and heat flux of a magma ocean with a high effective thermal
conductivity. We show that partitioning of 26Al and its transport with the
silicate melt is crucial for the formation of a magma ocean. Due to the
accumulation of 26Al in the sub-surface (for formation times t0<1.5 Ma), a
shallow magma ocean with a thickness of 1 to a few tens of km (depending on the
silicate melt viscosity) forms. The lifetime of the shallow magma ocean is
O(10^4)-O(10^6) years and convection in this layer is accompanied by the
extrusion of 26Al at the surface. The interior differentiates from the outside
inward with a mantle that is depleted in 26Al and core formation is completed
within ~0.3 Ma. The lower mantle experiences melting below 45% suggesting a
harzburgitic to dunitic composition. Our results support the formation of
eucrites by the extrusion of early partial melt and cumulative eucrites and
diogenites may form from the crystallizing shallow magma ocean. Silicate melt
is present for up to 150 Ma, and core convects for ~100 Ma, supporting the idea
of an early magnetic field.
