Radial Oscillations in Neutron Stars with Delta Baryons

We investigate the effect of $\Delta$ 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 $\Delta$-inclusive nuclear (N+$\Delta$) and hyperonic matter (N+H+$\Delta$) by solving the Sturm-Liouville boundary value problem and also verifying its validity. We see that the lowest mode frequencies for N+$\Delta$ and N+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 $\Delta$s.