Effects of dark matter on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi></mml:math>-mode oscillations of neutron stars

The effect of dark matter (DM) on $f$-mode oscillations in DM admixed neutron stars (NSs) is investigated in a comprehensive analysis with particular attention to the role of the nuclear equation of state. Hadronic matter is modeled by the relativistic mean-field model and the DM model is based on the neutron decay anomaly. The nonradial $f$-mode oscillations for such DM admixed NSs are studied in a full general relativistic framework. We investigate the impact of DM, DM self-interaction, and DM fraction on the $f$-mode characteristics. We derive relations encoding the effect of DM on $f$-mode parameters. We then perform a systematic study by varying all the model parameters within their known uncertainty range and obtain a universal relation for the DM fraction based on the total mass of the star and DM self-interaction strength. We also perform a correlation study among model parameters, NS observables, and in particular, $f$-mode parameters. Finally, we check the $f$-mode universal relations for the case of DM admixed NSs and demonstrate the existence of a degeneracy between purely hadronic NSs and DM admixed NSs.