Differential rotation, inertial waves, and magnetism in simulations of the deep Solar interior

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics

Abstract

It has been known for more than a century that the Sun rotates "differentially": its equator rotates more rapidly than regions near the pole, and parts of its interior spin at different rates, too. This differential rotation is thought to play a major role in building the Sun's organised magnetic fields, which ultimately drive Solar activity that can impact our technological society. But we still don't have a good theoretical understanding of how this differential rotation arises. For the past several decades, most models have suggested it comes ultimately from the action of convection -- the roiling motions of plasma that occur in the outer third of the Sun. These transport heat, in much the same way as a boiling pot of water on a hob, and they can also transport angular momentum. But recent observational and theoretical developments have called this view partly into question: for example, observations indicate that the convective motions are weaker than expected (so they might have a tough time generating the observed rotation profiles); meanwhile the latest supercomputer simulations have suggested that small-scale magnetic fields in the Sun are much stronger than previously believed, so that their transport might "win out" over the convection.

Here, we propose to use a series of carefully-constructed numerical simulations to determine whether the Sun's observed equatorial acceleration is driven primarily by the convection or (directly or indirectly) by the magnetism. It isn't possible to simulate all aspects of the problem at the same time, even on the largest supercomputers available today: the range of scales (of motion and magnetic field) present in the Sun is simply too large. In particular, we can't self-consistently capture the generation of the magnetic fields and their feedback on the flow in the limit of "small magnetic Prandtl number" -- the limit that applies in the Sun. But one of the key ideas in our work is that it is possible to model the angular momentum transport specifically -- which gives rise to the differential rotation -- by solving a slightly simpler problem, called "magnetoconvection," in which magnetic fields of varying strength are essentially imposed amidst a simulation of turbulent convection. This method doesn't tell you how strong the magnetic fields actually get, but it can tell you what fields of a particular strength will do, and how they will affect the convection. We will use a combination of local simulations, which model a small portion of the Sun and can be run in extreme parameter regimes, alongside global spherical-shell models, to determine how the combination of convection and magnetic fields gives rise to the Sun's differential rotation. In parallel, we will use our simulations to determine how the properties of "inertial waves" amidst the convection -- which have recently been observed at the Solar surface -- depend on the flows and imposed magnetic fields, providing a new window into dynamics in the deep Solar interior.

Publications

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