We calculate the relativistic entrainment matrix Y ik at zero temperature for a nucleon-hyperon mixture composed of neutrons, protons, and and − hyperons, as well as electrons and muons. This matrix is analogous to the entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix) of nonrelativistic theory. It is an important ingredient for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores. The calculation is done in the frame of the relativistic Landau Fermi-liquid theory generalized to the case of superfluid mixtures; the matrix Y ik is expressed through the Landau parameters of nucleon-hyperon matter. The results are illustrated with a particular example of the σ -ω-ρ mean-field model with scalar self-interactions. Using this model, we calculate the matrix Y ik and the Landau parameters. We also analyze the stability of the ground state of nucleon-hyperon matter with respect to small perturbations. DOI: 10.1103/PhysRevC.79.055806 PACS number(s): 26.60.Kp, 97.60.Jd, 47.37.+q, 97.10.Sjwhere m i is the mass of a free particle species i. The nonrelativistic expressions for the mass current density of neutrons J n and protons J p have the form (see, e.g., )Here ρ n and ρ p are the neutron and proton density, respectively; ρ ik = ρ ki is the symmetric 2 × 2 entrainment matrix, also termed Andreev-Bashkin or mass-density matrix (i, k = n, p). It follows from Eqs. (2) and (3) that superfluid motion of, for example, neutrons contributes not only to J n but also to J p (and the same for protons). For the first time this effect was predicted, as applied to superfluid solutions of 3 He in 4 He, by Andreev and Bashkin [19]. The prefactors in front of V qp in Eqs. (2) and (3) can be interpreted as the densities of normal neutrons and protons, respectively. Since at zero temperature (T = 0) all particles are paired, these densities vanish, and we have [16][17][18]

Observations of massive (M ≈ 2.0 M ⊙ ) neutron stars (NSs), PSRs J1614-2230 and J0348+0432, rule out most of the models of nucleon-hyperon matter employed in NS simulations. Here we construct three possible models of nucleon-hyperon matter consistent with the existence of 2 M ⊙ pulsars as well as with semi-empirical nuclear matter parameters at saturation, and semi-empirical hypernuclear data. Our aim is to calculate for these models all the parameters necessary for modelling dynamics of hyperon stars (such as equation of state, adiabatic indices, thermodynamic derivatives, relativistic entrainment matrix, etc.), making them available for a potential user. To this aim a general non-linear hadronic Lagrangian involving σωρφσ * meson fields, as well as quartic terms in vector-meson fields, is considered. A universal scheme for calculation of the ℓ = 0, 1 Landau Fermi-liquid parameters and relativistic entrainment matrix is formulated in the mean-field approximation. Use of this scheme allow us to obtain numerical tables with the equation of state, Landau quasiparticle effective masses, adiabatic indices, the ℓ = 0, 1 Landau Fermi-liquid parameters, and the relativistic entrainment matrix for the selected models of nucleon-hyperon matter. These data are available on-line and suitable for numerical implementation in computer codes modelling various dynamical processes in NSs, in particular, oscillations of superfluid NSs and their cooling.

We propose a general method to self-consistently study the quasistationary evolution of the magnetic field in the cores of neutron stars. The traditional approach to this problem is critically revised. Our results are illustrated by calculation of the typical timescales for the magnetic field dissipation as functions of temperature and the magnetic field strength.

We consider an instability of rapidly rotating neutron stars in low-mass x-ray binaries (LMXBs) with respect to excitation of r modes (which are analogous to Earth's Rossby waves controlled by the Coriolis force). We argue that finite temperature effects in the superfluid core of a neutron star lead to a resonance coupling and enhanced damping (and hence stability) of oscillation modes at certain stellar temperatures. Using a simple phenomenological model we demonstrate that neutron stars with high spin frequency may spend a substantial amount of time at these "resonance" temperatures. This finding allows us to explain puzzling observations of hot rapidly rotating neutron stars in LMXBs and to predict a new class of hot, nonaccreting, rapidly rotating neutron stars, some of which may have already been observed and tentatively identified as quiescent LMXB candidates. We also impose a new theoretical limit on the neutron star spin frequency, which can explain the cutoff spin frequency ∼730  Hz, following from the statistical analysis of accreting millisecond x-ray pulsars. In addition to explaining the observations, our model provides a new tool to constrain superdense matter properties by comparing measured and theoretically predicted resonance temperatures.

We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordinary one-fluid hydrodynamics is a good approximation, for most of the stellar temperatures, if one is interested in calculation of the damping times of normal f -modes; (ii) for radial and p-modes such an approximation is poor; (iii) the temperature dependence of damping times undergoes a set of rapid changes associated with resonance coupling of neighboring oscillation modes. The latter effect can substantially accelerate viscous damping of normal modes in certain stages of neutron-star thermal evolution.