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Instability of Superfluid Flow in the Neutron Star Inner Crust

Pinning of superfluid vortices to the nuclear lattice of the inner crust of a neutron star supports a velocity difference between the superfluid and the solid as the star spins down. Under the Magnus force that arises on the vortex lattice, vortices undergo {\em vortex creep} through thermal activation or quantum tunneling. We examine the hydrodynamic stability of this situation. Vortex creep introduces two low-frequency modes, one of which is unstable above a critical wavenumber for any non-zero flow velocity of the superfluid with respect to the solid. For typical pinning parameters of the inner crust, the superfluid flow is unstable over length scales $\lap 10$ m and over timescales as fast as months. The vortex lattice could degenerate into a tangle, and the superfluid flow could become turbulent. Unexpectedly large dissipation would suppress this instability.