Core and mantle thermal evolution constraints on the onset of plate tectonics and a long-lived geodynamo

Abstract

Earth's long-lived geodynamo is difficult to reconcile with recent high estimates of the core thermal conductivity, a problem known as the new core paradox. At the same time, the long-term thermal evolution of the mantle remains uncertain, largely due to the poorly constrained onset of modern-style plate tectonics, which marks the transition to efficient cooling of the interior through mobile-lid convection. Because core cooling -- and thus magnetic field generation -- depends on the efficiency with which the mantle extracts heat from the core, these two problems are closely linked. Here, we investigate the coupled thermal evolution of mantle and core using a 1D model that incorporates a parametrized transition transition from stagnant- to mobile-lid convection, defined by its onset time and with a prescribed duration. This framework allows us to assess how different tectonic histories influence Earth's thermal and magnetic evolution. We perform a Bayesian inversion using constraints from the palaeomagnetic record, mantle cooling history, and present-day thermal state. Our results favour a transition from stagnant- to mobile-lid convection during the Archean, which promotes core cooling and enables a geodynamo throughout Earth's history, even for core thermal conductivities in excess of 100 W/m/K. A delayed onset of mobile-lid convection provides thus a viable solution to the new core paradox.

Figures (10)

• Figure 1: Radial profiles within the core: (a) isentropic temperature ($T_{ct} = 8400$ K) for different numerical computation methods (solid lines) and corresponding temperature gradient (dashed lines); (b) thermal conductivity end-members (solid lines) and resulting isentropic heat flux (dashed lines); (c) PREM density PREM, and polynomial-based density profile for the inner (solid red line) and outer core (solid blue line) at the present-day, and initial density profile (grey dashed line); (d) pure-iron melting curve (red line), crystallisation entropy (blue line), ICB temperature at present-day (blue diamond) and central melting temperature (red diamond).
• Figure 2: Scheme of inner core growth during secular cooling. The inner core size is given by the intersection of the temperature profile (black lines) and the melting curve (red lines). The melting temperature decreases as the inner core grows because of the enrichment of the outer core in light elements. The inner core radius growth rate ($\frac{\mathrm{d}r_{ic}}{\mathrm{d}t}$) depends on the difference between the isentropic gradient ($\frac{\mathrm{d}T_a}{\mathrm{d}r}$) and the melting temperature gradient ($\frac{\mathrm{d}T_m}{\mathrm{d}r}$), and on the drop in melting temperature ($\frac{\mathrm{d}T_m}{\mathrm{d}t}$).
• Figure 3: Stratified layer growth method from greenwood2021stable. The thermally stratified layer growth rate depends only on the difference between the cooling rate of the isentropic temperature profile and the cooling rate at the base of the conductive profile in the thermally stratified layer. This method preserves the continuity of the temperature profile but not of the heat flux.
• Figure 4: Benchmark for core thermal evolution for three cases: our model (solid lines), greenwood2021stable model (dashed lines), and our model modified to use the polynomial fit for the isentropic temperature profile from G21 (dotted lines). Time evolution of (a) central core temperature (orange), CMB temperature (red), and ICB temperature (blue); (b) CMB heat flow (red), isentropic heat flow (grey), secular cooling (black), and heat flows due to latent heat and gravitational energy release upon inner core freezing (blue); (c) inner-core radius (blue) and thickness of the thermally stratified layer (grey); and (d) Joule entropy (black), entropy sink trough conduction (red), and entropy sources due to inner core freezing (blue) and secular cooling (grey).
• Figure 5: (a) Mobile-lid efficiency factor $\gamma_{eff}$ as a function of time (eq. \ref{['eq:gamma_eff']}), for two different times and durations of the transition. (b) Mantle internal heat production (eq. \ref{['eq:Qradt']}) as a function of time for two different enrichment factors: $\Lambda_m = 1$ and 0.66 over 4.5 Gyr (dashed and dotted lines, respectively, transition from $\Lambda_m = 1$ to 0.66 following the two mobile-lid efficiency evolutions of panel a (blue and red solid lines). Mantle thermal conductivity as a function of depth and temperature based on eq. \ref{['eq:thermal_cond']}tosi2013mantle.