A. Sedrakian et I. Wasserman, Perturbations of self-gravitating, ellipsoidal superfluid-normal fluid mixtures - art. no. 024016, PHYS REV D, 6302(2), 2001, pp. 4016
We study the perturbation modes of rotating superfluid ellipsoidal figures
of equilibrium in the framework of the two-fluid superfluid hydrodynamics a
nd Newtonian gravity. Our calculations focus on linear perturbations of bac
kground equilibria in which the two fluids move together, the total density
is uniform, and the densities of the two components are proportional to on
e another, with ratios that are independent of position. The motions of the
two fluids are coupled by mutual friction, as formulated by Khalatnikov. W
e show that there are two general classes of modes for small perturbations:
one class in which the two fluids move together and the other in which the
re is relative motion between them. The former are identical to the modes f
ound for a single fluid, except that the rate of viscous dissipation, when
computed in the secular (or "low Reynolds number") approximation under the
assumption of a constant kinematic viscosity, is diminished by a factor f(N
), the fraction of the total mass in the normal fluid. The relative modes a
re completely new, and are studied in detail for a range of values for the
phenomenological mutual friction coefficients, relative densities of the su
perfluid and normal components, and, for Roche ellipsoids, binary mass rati
os. We find that there are no new secular instabilities connected with the
relative motions of the two fluid components. Moreover, although the new mo
des are subject to viscous dissipation (a consequence of viscosity of the n
ormal matter), they do not emit gravitational radiation at all.