  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 (GONG) 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 (MHD) 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 theta less than 53 degrees. 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 Omega, 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.
