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Register a new userThe relativistic entrainment matrix of a superfluid nucleon-hyperon mixture. II. Effect of finite temperatures
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M.E. Gusakov Ioffen Institute
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We calculate the important quantity of superfluid hydrodynamics, the relativistic entrainment matrix for a nucleon-hyperon mixture at arbitrary temperature. In the nonrelativistic limit this matrix is also termed the Andreev-Bashkin or mass-density matrix. Our results can be useful for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores and for studies of the kinetic properties of superfluid baryon matter.
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We calculate the relativistic entrainment matrix Y_ik at zero temperature for nucleon-hyperon mixture composed of neutrons, protons, Lambda and Sigma^- hyperons, as well as of electrons and muons. This matrix is analogous to the entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix) of non-relativistic theory. It is an important ingredient for modelling 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 sigma-omega-rho mean-field model with scalar self-interactions. Using this model we calculate the matrix Y_ik and the Landau parameters. We also analyze stability of the ground state of nucleon-hyperon matter with respect to small perturbations.
We analyse the oscillations of general relativistic superfluid hyperon stars, following the approach suggested by Gusakov & Kantor and Gusakov et al. and generalizing it to the nucleon-hyperon matter. We show that the equations governing the oscillations can be split into two weakly coupled systems with the coupling parameters $s_{rm e}$, $s_{rm mu}$, and $s_{rm str}$. The approximation $s_{rm e} = s_{rm mu} = s_{rm str} = 0$ (decoupling approximation) allows one to drastically simplify the calculations of stellar oscillation spectra. An efficiency of the presented scheme is illustrated by the calculation of sound speeds in the nucleon-hyperon matter composed of neutrons (n), protons (p), electrons (e), muons ($mu$), as well as $rm Lambda$, ${rm Xi}^-$, and ${rm Xi}^0$-hyperons. However, the gravity oscillation modes (g-modes) cannot be treated within this approach, and we discuss them separately. For the first time we study the composition g-modes in superfluid hyperon stars with the $rm npemuLambda$ core and show that there are two types of g-modes (`muonic and `$Lambda$--hyperonic) in such stars. We also calculate the g-mode spectrum and find out that the eigenfrequencies $ u$ of the superfluid g-modes can be exceptionally large (up to $ u approx 742~{rm Hz}$ for a considered stellar model).
We investigate the tidal deformability of a superfluid neutron star. We calculate the equilibrium structure in the general relativistic two-fluid formalism with entrainment effect where we take neutron superfluid as one fluid and the other fluid is comprised of protons and electrons, making it a charge neutral fluid. We use a relativistic mean field model for the equation of state of matter where the interaction between baryons is mediated by the exchange $sigma$, $omega$ and $rho$ mesons. Then, we study the linear, static $l=2$ perturbation on the star to compute the electric-type Love number following Hinderers prescription.
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.
In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results of low-density pure neutron matter calculations. When entrainment is included at the level suggested by recent microscopic calculations and the core is fully coupled to the crust, the model is only able to account for the Vela glitch activity for a 1.4$M_{odot}$ star if the equation of state is particularly stiff $L>100$ MeV. However, an uncertainty of about 10% in the crust-core transition density and pressure allows for the Vela glitch activity to be marginally accounted for in the range $Lapprox30-60$MeV consistent with a range of experimental results. Alternatively, only a small amount of core neutrons need be involved. If less than 50% of the core neutrons are coupled to the crust during the glitch, we can also account for the Vela glitch activity using crustal neutrons alone for EOSs consistent with the inferred range of $L$. We also explore the possibility of Vela being a high-mass neutron star, and of crustal entrainment being reduced or enhanced relative to its currently predicted values.
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