Nonaxisymmetric instabilities of convection around magnetic flux tubes

On the surface of the Sun, magnetic flux elements collect in regions of converging flow, grow in field strength and become pores, which have been observed to exhibit nonaxisymmetric structure over a range of scales. Around a fully developed sunspot, as well as the fine scale of the penumbra, the moat sometimes shows clearly observable spoke-like structure at low azimuthal wavenumbers. We investigate the formation of azimuthal structure by computing the linear stability properties of fully nonlinear axisymmetric magnetoconvection, which takes the form of a central flux tube surrounded by a convecting field-free region. We find steady and oscillatory instabilities with a preferred azimuthal wavenumber. The unstable modes are concentrated in the convecting region close to the outer edge of the flux tube. The instability is driven by convection, and is not a magnetic fluting instability.