Timing of Martian Core Formation from Models of Hf-W Evolution Coupled with N-body Simulations

Determining how and when Mars formed has been a long-standing challenge for planetary scientists. The size and orbit of Mars are difficult to reproduce in classical simulations of planetary accretion, and this has inspired models of inner solar system evolution that are tuned to produce Mars-like planets. However, such models are not always coupled to geochemical constraints. Analyses of Martian meteorites using the extinct hafnium-tungsten (Hf-W) radioisotopic system, which is sensitive to the timing of core formation, have indicated that the Martian core formed within a few million years of the start of the solar system itself. This has been interpreted to suggest that, unlike Earth's protracted accretion, Mars grew to its modern size very rapidly. These arguments, however, generally rely on simplified growth histories for Mars. Here, we combine likely accretionary histories from a large number of N-body simulations with calculations of metal-silicate partitioning and Hf-W isotopic evolution during core formation to constrain the range of conditions that could have produced Mars. We find that there is no strong correlation between the final masses or orbits of simulated Martian analogs and their ¹⁸²W anomalies, and that it is readily possible to produce Mars-like Hf-W isotopic compositions for a variety of accretionary conditions. The Hf-W signature of Mars is very sensitive to the oxygen fugacity (fO₂) of accreted material because the metal-silicate partitioning behavior of W is strongly dependent on redox conditions. The average fO₂ of Martian building blocks must fall in the range of 1.3-1.6 log units below the iron-wüstite buffer to produce a Martian mantle with the observed Hf/W ratio. Other geochemical properties (such as sulfur content) also influence Martian ¹⁸²W signatures, but the timing of accretion is a more important control. We find that while Mars must have accreted most of its mass within ~5 million years of solar system formation to reproduce the Hf-W isotopic constraints, it may have continued growing afterwards for over 50 million years. There is a high probability of simultaneously matching the orbit, mass, and Hf-W signature of Mars even in cases of prolonged accretion if giant impactor cores were poorly equilibrated and merged directly with the proto-Martian core.