Did the cessation of convection in Mercury's mantle allow for a dynamo supporting increase in heat loss from its core?

Abstract

Mercury's large core generates a magnetic field and harbors a solidified inner component. These features constrain models of the planet's thermal history. The mantle provides the boundary condition on Mercury's core that determines heat loss. Recent studies suggest Mercury's mantle may have a higher thermal diffusivity than the silicate shells of other rocky bodies due to iron depletion. Considering the role of diffusivity, we model Mercury's mantle starting from a post magma-ocean state by calculating core-mantle boundary heat flow and the ratio of inner-core boundary radius to core-mantle boundary radius, fc, for periods comparable to the age of the solar system. Core-mantle boundary (CMB) heat flow is calculated using 3D mantle convection simulations for thermal diffusivities, κ, ranging from 1.0 - 3.0 ×10−6 m2/s and initial radiogenic uniform mantle heating rates, χ, of 0 - 40 pW/kg (that decay with a 3 Gyr half-life). Several scenarios can unfold for the range of parameters considered: these include cases featuring both the cessation of mantle convection and its continuation at 4.5 Gyr. We map a trend in κ - χ space and find that for some parameters present-day core heat flux and inner-core size estimates are satisfied for a Mercurian mantle that is cooling by conduction. The influence of initial sulfur fraction in the core was examined for a subset of cases. For a sulfur fraction of 0.10, fc falls between 0.1 and 0.55 which corresponds to planetary radius contractions below 7 km (since the Late Heavy Bombardment). However, fc exceeds 0.55 for a lower initial sulfur fraction and results in planetary contraction in excess of 7 km. In general, we find that the mean core heat flux reaches a temporal local minimum when the mantle transitions from a convective to a conductive regime and subsequently climbs before decreasing. The transition to conduction is delayed with increased mantle internal heating rate but the maximum mean heat flux from the core into the conducting and cooling mantle is always greater than the heat flux observed at the cessation of the stagnant-lid convection. We find that for an initially more vigorously convecting mantle the onset of inner-core growth is earlier while the basal heat flux is marginally reduced at present day. In general, we find that current-day conductive cooling of the Mercurian mantle can satisfy estimates on Mercury's core heat loss inferred from the strength of its magnetic field while also satisfying the limits on the present-day size of its inner core.