Causal and Stable Superfluid Hydrodynamics

We investigate the linearized stability and causality properties of relativistic viscous superfluid hydrodynamics. The Landau-Lifshitz-Clark-Putterman formulation for the theory of relativistic viscous superfluids suffers from the same instability and acausality issues as the relativistic Navier-Stokes equation for normal fluids when written in the formulations of Eckart or Landau and Lifshitz. We show that conditions to ensure stability and causality can be satisfied with judicious redefinitions of the hydrodynamic variables. The conditions we obtain hold at non-zero superfluid velocity as well.