Ultimate large-$Rm$ regime of the solar dynamo

Abstract

For more than 40 years the quest to understand how large-scale magnetic fields emerge from turbulent flows in rotating astrophysical systems, such as the Sun, has been a major focus of computational astrophysics research. Using a parameter scan and phenomenological analysis of maximally simplified three-dimensional cartesian magnetohydrodynamic simulations of large-scale non-linear helical turbulent dynamos, I present results in this Letter that strongly point to an asymptotic ultimate regime of the large-scale solar dynamo at large magnetic Reynolds numbers, $Rm$, involving helicity fluxes between hemispheres. I obtained corresponding numerical solutions at both $Pm>1$ and $Pm<1$, and show that they can currently only be achieved in clean, simplified numerical set-ups. The analysis further strongly suggests that all global simulations to date lie in non-asymptotic turbulent magnetohydrodynamic regimes highly sensitive to changes in kinetic and magnetic Reynolds numbers. Ideas are presented to attempt to reach the ultimate regime in such 'realistic' global spherical models at a reasonable numerical cost. Overall, the results clarify the current state, and some hard limitations of the brute-force numerical modelling approach applied to this, and other similar astrophysical turbulence problems.