Thermal evolution of the core with a high thermal conductivity

Abstract

The rate at which heat is extracted across the core mantle boundary (CMB) is constrained by the requirement of dynamo action in the core. This constraint can be computed explicitly using the entropy balance of the core and depends on the thermal conductivity, whose value has been revised upwardly. A high order model (fourth degree polynomial of the radial position) for the core structure is derived and the implications for the core cooling rate and thermal evolution obtained, using the recent values of the thermal conductivity. For a thermal conductivity increasing with depth as proposed by some of these recent studies, a CMB heat flow equal to the isentropic value (13.25TW at present) leads to a 700 km thick layer at the top of the core where a downward convective heat flow is necessary to maintain an isentropic and well mixed average state. Considering a CMB heat flow larger than the well mixed isentropic value leads to an inner core less than 700 Myr old and the thermal evolution of the core is largely constrained by the conditions for dynamo action without an inner core. Analytical calculations for that period show that a CMB temperature larger than 7000 K must have prevailed 4.5 Gyr ago if the geodynamo has been driven by thermal convection for that whole time. This raises questions regarding the onset of the geodynamo and its continuous operation for the last 3.5 Gyr. Implications regarding the evolution of a basal magma ocean are also considered.

Constraints from material properties on the dynamics and evolution of Earth’s core

“…prior to inner core formation, after which Q cmb is set constant to ensure the outer core remains just superadiabatic. Results from other recent studies are shown in yellow 68 , pink 63 , orange 80 and maroon 69 . The inverted triangle denotes that ∆ρ did not enter into this formulation.…”

“…Recent calculations with the new (high) conductivities find that 1) The inner core age is less than 500-600 Ma 24,59,63,80 ; 2) high early CMB heat flow and corresponding core temperatures that significantly exceeded present estimates of the lower mantle solidus temperature 59,63,68,94 imply partial melting of the lowermost mantle in the past; 3) the present-day core is subadiabatic at the top and may be stably stratified 24,26,80 . Prior to the high conductivity estimates, models predicted inner core nucleation 1 billion years ago 8 , early core temperatures comparable to the lower mantle solidus 9 , and superadiabatic conditions throughout the core at the present-day.…”

“…The depth increase of k opens up the possibility that the very top of the core is superadiabatic, with a stable layer directly beneath 26,80 . The conditions required to form such a layer are sensitive to the T a (r) and k(r) profiles; the models in this review do not produce such an effect.…”

The solubility of heat-producing elements in Earth’s core

“…The present day geodynamo is mainly driven by compositional buoyancy, due to light element release by the crystallisation of the inner core. A core with large thermal conductivity (e.g., Pozzo et al, 2012;Ohta et al, 2016) yields a young age (less than 1 Gyr) for the inner core (Labrosse, 2015;Nimmo, 2015a), which is in apparent contradiction with palaeomagnetic evidence for an old geodynamo dating back to at least 3.5 Ga (Tarduno et al, 2010). Even with a low core thermal conductivity (Konôp-ková et al, 2016), the problem is partially mitigated, in that a dynamo can be sustained for 3.5 Gyr (e.g., Labrosse, 2003;Nimmo, 2015a), but initial core temperatures are very high, above 7000 K, which implies a fully molten Earth for extended periods of time.…”

“…Because radionuclide abundance decreases with time, the process is dominant very early in Earth's history and vanishes with time. Potassium and uranium are the main sources of heat in the Earth, and their incorporation in the core has been thoroughly examined through the years (e.g., Buffett, 2002;Gubbins et al, 2003;Labrosse, 2003Labrosse, , 2015Nimmo et al, 2004), and it was shown that the incorporation of ~100s of ppm K in the core would mitigate the young inner core/early geodynamo/hot initial core conundrum.…”