The relativistic entrainment matrix of a superfluid nucleon-hyperon mixture at zero temperature

TL;DR

This paper computes the relativistic entrainment matrix for a superfluid nucleon-hyperon mixture at zero temperature, essential for modeling neutron star pulsations, using relativistic Landau Fermi-liquid theory and mean-field models.

Contribution

It introduces a relativistic calculation of the entrainment matrix for nucleon-hyperon matter, extending non-relativistic concepts and providing a basis for neutron star pulsation models.

Findings

Calculated the entrainment matrix Y_ik for nucleon-hyperon matter.

Expressed Y_ik through Landau parameters in a relativistic framework.

Analyzed the stability of the nucleon-hyperon ground state.

Abstract

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.