Numerical simulations of rotating axisymmetric sunspots

TL;DR

This paper presents a numerical MHD model simulating rotating, axisymmetric sunspots, revealing vortex structures and magnetic flow patterns influenced by rotation, with implications for understanding sunspot dynamics.

Contribution

It introduces a new axisymmetric MHD simulation of rotating sunspots, capturing vortex flows and magnetic structures not previously modeled in this detail.

Findings

Formation of Rankine vortex with rigid body rotation in flux tube

Azimuthal velocity peaks near flux tube edge

Flow and magnetic structures decay without imposed rotation

Abstract

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the nonlinear MHD equations, with density and temperature gradients simulating the upper layer of the sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow are prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.