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

Christopher J Davies,Julien Aubert,Andrew J Biggin,Samuel Greenwood,Domenico G Meduri,Richard K Bono

doi:10.1093/gji/ggab342

Abstract

SUMMARY Elucidating the processes in the liquid core that have produced observed palaeointensity changes over the last 3.5 Gyr 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., adapted to include recent advances in numerical simulations, mineral physics and palaeomagnetism. 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 length scale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the data set 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 root-mean-square 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 palaeointensities over the last 3.5 Gyr. We combine the QG-MAC-free scaling with outputs from 275 realizations of core–mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyr. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation (ICN) 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-fitting 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 ICN.

Highlights

Earth has sustained a global magnetic field over most of its history
We present the palaeointensity data set and calculate true dipole moment (TDM) for 275 thermal history models that span a wide range of plausible evolutionary scenarios for the core
For the QG-MAC-fixed scaling, we consider the lowest estimate of c = 0.0749 across all filters, which still produces TDMs that far exceed those from PINT as we show below

Summary

Introduction

Databases of palaeointensity estimates indicate no hiatuses in the geodynamo back to 3.55 Ga (Biggin et al 2008; Tarduno et al 2010; Tauxe & Yamazaki 2015; Biggin et al 2015; Bono et al 2019), while records of a field extending back to 4.2 Ga (Tarduno et al 2015) are currently under debate (Tang et al 2019; Tarduno et al 2020). These observations provide a unique probe of otherwise unobservable processes in the liquid iron core where the field is generated by a hydromagnetic dynamo.

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Conclusion