The hydrodynamics, describing dynamical effects in superfluid neutron stars, essentially differs from the standard one-fluid hydrodynamics. In particular, we have four bulk viscosity coefficients in the theory instead of one. In this paper we calculate these coefficients, for the first time, assuming they are due to non-equilibrium beta-processes (such as modified or direct Urca process). The results of our analysis are used to estimate characteristic damping times of sound waves in superfluid neutron stars. It is demonstrated that all four bulk viscosity coefficients lead to comparable dissipation of sound waves and should be considered on the same footing.Comment: 11 pages, 1 figure, this version with some minor stylistic changes is published in Phys. Rev.
We examine radial oscillations of superfluid neutron stars at finite internal temperatures. For this purpose we generalize the description of relativistic superfluid hydrodynamics to the case of superfluid mixtures. We show that in a neutron star at hydrostatic and beta-equilibrium the red-shifted temperature gradient is smoothed out by neutron superfluidity (but not by proton superfluidity). We calculate radial oscillation modes of neutron stars assuming "frozen" nuclear composition in the pulsating matter. The resulting pulsation frequencies show a strong temperature dependence in the temperature range (0.1-1) T_cn, where T_cn is the critical temperature of neutron superfluidity. Combining our results with thermal evolution, we obtain a significant evolution of the pulsation spectrum, associated with highly efficient Cooper pairing neutrino emission, for 20 years after superfluidity onset.Comment: 29 pages, 1 table, 4 figure
Abstract. We simulate cooling of superfluid neutron stars with nucleon cores where the direct Urca process is forbidden. We adopt density-dependent critical temperatures T cp (ρ) and T cn (ρ) of singlet-state proton and triplet-state neutron pairing in a stellar core and consider strong proton pairing (with maximum T max cp > ∼ 5 × 10 9 K) and moderate neutron pairing (T max cn ∼ 6 × 10 8 K). When the internal stellar temperature T falls below T max cn , the neutrino luminosity L CP due to Cooper pairing of neutrons behaves ∝T 8 , just as that produced by the modified Urca process (in a non-superfluid star) but is higher by about two orders of magnitude. In this case the Cooper-pairing neutrino emission acts like an enhanced cooling agent. By tuning the density dependence T cn (ρ) we can explain observations of cooling isolated neutron stars in the scenario in which the direct Urca process or a similar process in kaon/pion condensed or quark matter are absent.
The entrainment matrix (also termed the Andreev-Bashkin matrix or the massdensity matrix) for a neutron-proton mixture is derived at a finite temperature in a neutron star core. The calculation is performed in the frame of the Landau Fermiliquid theory generalized to account for superfluidity of nucleons. It is shown, that the temperature dependence of the entrainment matrix is described by a universal function independent on an actual model of nucleon-nucleon interaction employed. The results are presented in the form convenient for their practical use. The entrainment matrix is important, e.g., in kinetics of superfluid nucleon mixtures or in studies of the dynamical evolution of neutron stars (in particular, in the studies of star pulsations and pulsar glitches).One of the key ingredients of hydrodynamics and kinetics of superfluid mixtures is the entrainment matrix ρ αα ′ (also termed the Andreev-Bashkin matrix or the mass-density matrix). Implying, for simplicity, that the only baryons in a neutron star core are neutrons and protons, the matrix ρ αα ′ can be defined as [13]:(2)Here ρ α = m α n α ; n α and m α are the number density and the mass of nucleon species α = n or p; J J J α and V V V αs are the mass current density and the superfluid velocity; V V V qp is the normal velocity of thermal excitations (see, e.g., Refs. [14,15]). We assume that V V V qp is the same for nucleons of both species. Eqs.(1) and (2) differ from a "natural" expression for the mass current density J J J α = ρ α V V V α (with V V V α being the momentum per unit mass of nucleon species α) for two reasons.First, three independent motions can exist in a mixture of two superfluids, each carrying a mass (see, e.g., Ref.[16]). They are the motion of thermal excitations with the velocity V V V qp and two superfluid motions with the velocities V V V ns and V V V ps .Second, the superfluid flow of one component of the mixture entrains a flow
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