Fundamental Oscillation Modes in Neutron Stars with Hyperons and Delta Baryons

For a new parameterization of the modified effective chiral model, developed primarily to regulate the density content of the symmetry energy and its higher order terms, equations of state (EoSs) for hyperon-rich matter ($H$) and delta baryon matter ($\Delta$) were obtained. The models were used to investigate the emission of gravitational waves (GWs) through $f$-mode oscillations in the corresponding neutron stars. We obtained the stellar structure, $f$-mode frequency and tidal deformability $\Lambda$ for our models. We report that the $\Delta$ EoS is stiffer compared to the $H$ EoS. We also analyzed the velocity of sound in these media. The corresponding mass--radius relationships were obtained and compared with various observations. We studied the dependence of $f$-mode frequencies on the stellar mass, redshift and tidal deformability. We employed the well known Cowling approximation to obtain the $f$-mode frequencies for $l=2,\,3$ and $4$ modes of oscillation. We found that the $f$-mode frequencies of the $H$ and $\Delta$ EoSs were almost the same in the lower mass region, while we observed a substantial difference between them in the high-mass region. We also obtained an empirical relation for the EoSs considered. The various attributes obtained for our models showed close agreement with various observational constraints from pulsars and GW events.