Dynamo constraints on the long-term evolution of Earth’s magnetic field strength

Abstract

Elucidating the processes in the liquid core that have produced observed paleointensity changes over the last 3.5 Gyrs is crucial for understanding the dynamics and long-term evolution of Earth’s deep interior. We combine numerical geodynamo simulations with theoretical scaling laws to investigate the variation of Earth’s magnetic field strength over geological time. Our approach follows the study of Aubert et al. (2009), adapted to include recent advances in numerical simulations, mineral physics and paleomagnetism. We first compare the field strength within the dynamo region and on the core-mantle boundary (CMB) between a suite of 314 dynamo simulations and two power-based theoretical scaling laws. The scaling laws are both based on a Quasi-Geostropic (QG) force balance at leading-order and a Magnetic, Archimedian, and Coriolis (MAC) balance at first order and differ in treating the characteristic lengthscale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the dataset is filtered to retain only simulations with magnetic to kinetic energy ratios greater than at least two we find that the internal field together with the RMS and dipole CMB fields exhibit power-law behaviour that is compatible with both scalings within uncertainties arising from different heating modes and boundary conditions. However, while the extrapolated intensity based on the QG-MAC-free scaling matches Earth’s modern CMB field, the QG-MAC-fixed prediction shoots too high and also significantly overestimates paleointensities over the last 3.5 Gyrs. We combine the QG-MAC-free scaling with outputs from 275 realisations of core-mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyrs. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation within observational uncertainties, but PINT does not contain the predicted strong increase and subsequent high TDMs during the early stages of inner core growth. The best-fit models are obtained for a present-day CMB heat flow of 11-16 TW, increasing to 17-22 TW at 4 Ga, and predict a minimum TDM at inner core nucleation.