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We present a geometrical derivation of the relativistic dynamics of thesuperfluid inner crust of a neutron star. The resulting model is analogous tothe Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-componentsuperfluid at finite temperature, but particular attention should be paid tothe fact that some fraction of the neutrons are locked to the motion of theprotons in nuclei. This gives rise to an ambiguity in the definition of the twocurrents (the normal and the superfluid one) on which the model is built, aproblem that manifests itself as a chemical gauge freedom of the theory. Toensure chemical gauge covariance of the hydrodynamic model, thephenomenological equation of motion for a quantized vortex should contain anextra transverse force, that is the relativistic version of the Iordanskiiforce discussed in the context of superfluid Helium. Hence, we extend themutual friction model of Langlois et al. (1998) to account for the possiblepresence of this Iordanskii-like force. Furthermore, we propose that a betterunderstanding of the (still not completely settled) controversy around thepresence of the Iordanskii force in superfluid Helium, as well as in neutronstars, may be achieved by considering that the different incompatible resultspresent in the literature pertain to two, opposite, dynamical regimes of thefluid system.

Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance