Relativistic entrainment matrix of a superfluid nucleon-hyperon mixture: The zero temperature limit

Abstract

We calculate the relativistic entrainment matrix ${Y}_{\mathit{ik}}$ at zero temperature for a nucleon-hyperon mixture composed of neutrons, protons, and \ensuremath{\Lambda} and ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ 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 ${Y}_{\mathit{ik}}$ is expressed through the Landau parameters of nucleon-hyperon matter. The results are illustrated with a particular example of the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$ mean-field model with scalar self-interactions. Using this model, we calculate the matrix ${Y}_{\mathit{ik}}$ and the Landau parameters. We also analyze the stability of the ground state of nucleon-hyperon matter with respect to small perturbations.