[Paper Review] Potassium influence on Earth's mantle convection and Borexino data

I. S. Karpikov|arXiv (Cornell University)|Feb 17, 2026

High-pressure geophysics and materials0 citations

TL;DR

The paper investigates whether a large potassium-40 content in Earth's mantle is plausible by modeling two-dimensional mantle convection with internal heating from 40K and comparing implications with Borexino data.

ABSTRACT

High flux of geoantineutrinos $^{40}$K and geoneutrinos $^{40}$K ($^{40}$K-geo-($\barν + ν$)) can be obtained from reanalysis of the Borexino Phase III data. Large amounts of $^{40}$K should produce a significant heat flow that should affect Earth's internal processes. We present the results of the modeling of mantle convection taking into account the excess heat from $^{40}$K.

Motivation & Objective

• Motivate the study by linking Earth's internal heat to mantle convection and potential high 40K content.
• Quantify how 40K radiogenic heat could influence mantle dynamics under plausible rheology.
• Assess consistency between Borexino geoneutrino data analyses and a high-40K Earth model.
• Provide qualitative convection simulations to test feasibility of substantial mantle potassium.
• Outline future work to refine viscosity and diffusivity dependencies on temperature and pressure.

Proposed method

• Solve dimensionless governing equations for mass, momentum, and energy in a two-dimensional spherical ring using the Boussinesq approximation.
• Use non-dimensionalization with scales x=X/D, t=t'κ0/D^2, T=T'/ΔT, v=VD/κ0, P=P' D^2/(κ0 η0).
• Assume η and κ equal to one for qualitative evaluation and set T0=ΔT, v0=0 as initial conditions.
• Impose no-slip velocity boundaries at r=0 and r=D and fixed temperature boundaries with T|r=0=0.12ΔT and T|r=D=1.12ΔT.
• Model four cases with Ra=10^5 or Ra=10^6 and two internal heating scenarios: Hnow=5×10^-12 and Hnow=15×10^-12 W/kg.
• Incorporate time-dependent internal heating H(t)=H0 exp(-t/t40K) with H0=Hnow·exp(tmax/t40K) and tmax=4.5 Gyr, t40K=1.8 Gyr.

Experimental results

Research questions

• RQ1 Can a large 40K content in Earth's mantle be compatible with observed mantle convection patterns under plausible viscosity contrasts?
• RQ2 How does the inclusion of 40K-derived internal heating affect mantle temperature and flow fields in 2D convection models?
• RQ3 Do Borexino geoneutrino analyses support a substantial potassium-40 budget when interpreted alongside mantle convection constraints?
• RQ4 What parameter regimes (Ra, H) allow cooling to compete with radiogenic heating over geological timescales?

Key findings

• High-viscosity model (Ra=10^5) heats up strongly and may not cool to present-day conditions within the modeled timescale.
• Low-viscosity model (Ra=10^6) cools faster as thermal energy converts to kinetic energy of mantle flow.
• In high-viscosity cases, heat from 40K can raise mantle temperatures above core temperature; in low-viscosity cases, there is more time for cooling.
• Borexino analyses suggest substantial 40K content; the study qualitatively demonstrates that under certain mantle parameters, such a potassium-rich Earth is possible.