The curious case of Mars’ formation

Dynamical models of planet formation coupled with cosmochemical data from martian meteorites show that Mars' isotopic composition is distinct from that of Earth. Reconciliation of formation models with meteorite data require that Mars grew further from the Sun than its present position. Here, we evaluate this compositional difference in more detail by comparing output from two $N$-body planet formation models. The first of these planet formation models simulates what is termed the "Classical" case wherein Jupiter and Saturn are kept in their current orbits. We compare these results with another model based on the "Grand Tack", in which Jupiter and Saturn migrate through the primordial asteroid belt. Our estimate of the average fraction of chondrite assembled into Earth and Mars assumes that the initial solid disk consists of only sources of enstatite chondrite composition in the inner region, and ordinary chondrite in the outer region. Results of these analyses show that both models tend to yield Earth and Mars analogues whose accretion zones overlap. The Classical case fares better in forming Mars with its documented composition (29% to 68% enstatite chondrite plus 32% to 67% ordinary chondrite) though the Mars analogues are generally too massive. However, if we include the restriction of mass on the Mars analogues, the Classical model does not work better. We also further calculate the isotopic composition of $^{17} \rm O$, $^{50} \rm Ti$, $^{54} \rm Cr$, $^{142} \rm Nd$, $^{64} \rm Ni$, and $^{92} \rm Mo$ in the martian mantle from the Grand Tack simulations. We find that it is possible to match the calculated isotopic composition of all the above elements in Mars' mantle with their measured values, but the resulting uncertainties are too large to place good restriction on the early dynamical evolution and birth place of Mars.