Ohmic dissipation and power requirements for dynamo generation on Mercury

Abstract:

To sustain a convectively-driven planetary core dynamo, the rate at which mechanical energy is delivered to the process of magnetic field production must exceed the rate at which this energy is lost through ohmic dissipation. The amount and importance of ohmic dissipation depends on the magnetic field strength in the core and the physical length scale over which this dissipation occurs (L_crit) — two highly uncertain parameters within planetary cores. Here, we describe a novel approach to calculate ohmic dissipation and apply it to Mercury’s core. Mercury has an internally-generated magnetic field at present and crustal magnetic field signatures indicate that an ancient dynamo was active between 4 - 3.5 Ga. We revisit the entropy budget for Mercury’s core and illustrate the importance of including ohmic dissipation. We assume core flow conditions are described to first order by a quasi-geostrophic balance, consistent with a recent consensus between experiments and numerical simulations (see Aurnou and King, 2017; Aubert, 2019). Accordingly, we take L_crit to be proportional to the Ekman number E^1/3, which depends on spin rate.

The magnitude of ohmic dissipation is governed primarily by magnetic field magnitude in the core and to a lesser extent the spin rate. A lower bound for Mercury’s core magnetic field strength is found by downward continuing the present-day surface field to the core-mantle boundary assuming an entirely poloidal field. Varying the magnitude of the core field by 2 orders of magnitude is consistent with the possibility of stable stratification in the outer core (i.e., a deeper dynamo region), as well as the partitioning of poloidal and toroidal field consistent with studies of thin shell dynamos. Mercury currently spins at a rotation rate of 1/59 days^-1. However, to enter the present 3:2 spin-orbit resonance, the planet initially rotated faster. We explore conditions for dynamo action using one-dimensional parameterized thermal history models and map conditions in which mantle heat loss (Q_mantle) leads to dynamo action (Figure 1) and is consistent with additional observational constraints of Mercury’s evolution.