Impacts of dark matter on the $f$-mode oscillation of hyperon star

Abstract

We investigate the $f$-mode oscillation of the dark matter admixed hyperon star within the relativistic Cowling approximation. The macroscopic properties are calculated with the relativistic mean-field equation of states by assuming that the dark matter particles are inside the star. The $f$-mode oscillation frequencies (only for $l=2$) are calculated with four different neutron star equation of states. We also check the effects of hyperons/dark matter and hyperons with dark matter equation of states on the $f$-mode oscillations varying with different astrophysical quantities such as mass ($M$), radius ($R$), compactness ($M/R$), surface red-shift ($Z_s$), average density ($\bar{\rho}$), dimensionless tidal deformability ($\Lambda$) of the neutron star. Significant changes have been seen in the $f$-mode frequencies with and without hyperons/dark matter or hyperons+dark matter. Substantial correlations are observed between canonical frequencies and $\Lambda$ ($f_{1.4}-\Lambda_{1.4}$) and maximum frequencies and canonical $\Lambda$ ( $f_{max}-\Lambda_{1.4}$).