Radial oscillations in neutron stars with delta baryons

Abstract

We investigate the effect of $\mathrm{\ensuremath{\Delta}}$ baryons on the radial oscillations of neutron and hyperon stars, employing a density-dependent relativistic mean-field model. The spin-$3/2$ baryons are described by the Rarita-Schwinger Lagrangian density. The baryon-meson coupling constants for the spin-$3/2$ decuplet and the spin-$1/2$ baryonic octet are calculated using a unified approach relying on the fact that the Yukawa couplings present in the Lagrangian density of the mean-field models must be invariant under the SU(3) and SU(6) group transformations. We calculate the 20 lowest eigenfrequencies and corresponding oscillation functions of $\mathrm{\ensuremath{\Delta}}$-inclusive nuclear ($\mathrm{N}+\mathrm{\ensuremath{\Delta}}$) and hyperonic matter ($\mathrm{N}+\mathrm{H}+\mathrm{\ensuremath{\Delta}}$) by solving the Sturm-Liouville boundary value problem and also verifying its validity. We see that the lowest mode frequencies for $\mathrm{N}+\mathrm{\ensuremath{\Delta}}$ and $\mathrm{N}+\mathrm{H}$ EoSs are higher as compared to the pure nucleonic matter because of the deltas and hyperons present. Furthermore, the separation between consecutive modes increases with the addition of hyperons and $\mathrm{\ensuremath{\Delta}}$s.