The role of the magnetorotational instability in the sun

We calculate growth rates for nonaxisymmetric instabilities including the magnetorotational instability (MRI) throughout the Sun. We first derive a dispersion relation for nonaxisymmetric instability including the effects of shear, convective buoyancy, and three diffusivities (thermal conductivity, resistivity, and viscosity). We then use a solar model evolved with the stellar evolution code MESA and angular velocity profiles determined by Global Oscillations Network Group helioseismology to determine the unstable modes present at each location in the Sun and the associated growth rates. The overall instability has unstable modes throughout the convection zone and also slightly below it at middle and high latitudes. It contains three classes of modes: large-scale hydrodynamic convective modes, large-scale hydrodynamic shear modes, and small-scale magnetohydrodynamic shear modes, which may be properly called MRI modes. While large-scale convective modes are the most rapidly growing modes in most of the convective zone, MRI modes are important in both stably stratified and convectively unstable locations near the tachocline at colatitudes θ < 53°. Nonaxisymmetric MRI modes grow faster than the corresponding axisymmetric modes; for some poloidal magnetic fields, the nonaxisymmetric MRI growth rates are similar to the angular rotation frequency Ω, while axisymmetric modes are stabilized. We briefly discuss the saturation of the field produced by MRI modes, finding that the implied field at the base of the convective zone in the Sun is comparable to that derived based on dynamos active in the tachocline and that the saturation of field resulting from the MRI may be of importance even in the upper convection zone.