Thermal g-modes and unexpected convection in superfluid neutron stars

We suggest that specific thermal low-frequency g-modes can exist in superfluid neutron stars. They can be excited in the matter with a nonzero gradient of entropy per electron. We determine the Brunt-Vaisala frequency for these modes and demonstrate that they can be unstable with respect to convection. The criterion for the instability onset (analogue of the well-known Schwarzschild criterion) is derived. It is very sensitive to the equation of state and a model of nucleon superfluidity. In particular, convection may occur for both positive and negative temperature gradients. Our results may have interesting implications for neutron star cooling and seismology.