Impacts of dark matter on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi></mml:math>-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 ($\overline{\ensuremath{\rho}}$), and dimensionless tidal deformability ($\mathrm{\ensuremath{\Lambda}}$) of the neutron star. Significant changes have been seen in the $f$-mode frequencies with and without hyperons/dark matter or $\mathrm{hyperons}+\mathrm{dark}$ matter. Substantial correlations are observed between canonical frequencies and $\mathrm{\ensuremath{\Lambda}}$ (${f}_{1.4}\ensuremath{-}{\mathrm{\ensuremath{\Lambda}}}_{1.4}$) and maximum frequencies and canonical $\mathrm{\ensuremath{\Lambda}}$ (${f}_{\mathrm{max}}\ensuremath{-}{\mathrm{\ensuremath{\Lambda}}}_{1.4}$).