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

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.

💡 Research Summary

The paper presents a comprehensive calculation of the relativistic entrainment matrix Yₖᵢ for a zero‑temperature superfluid mixture composed of neutrons, protons, Λ hyperons, and Σ⁻ hyperons, together with electrons and muons. In non‑relativistic superfluid hydrodynamics the entrainment (or Andreev‑Bashkin) matrix quantifies how the flow of one superfluid component drags another; it appears as a mass‑density matrix in the equations of motion. Extending this concept to the extreme densities of massive neutron‑star cores requires a relativistic treatment, which the authors achieve by generalizing Landau’s Fermi‑liquid theory to relativistic, multi‑component superfluids.

The theoretical framework starts from the quasiparticle energy \