Universal relation involving fundamental modes in two-fluid dark matter admixed neutron stars

TL;DR

This study reveals a universal relation between the fundamental oscillation frequencies and the compactness of dark matter admixed neutron stars, providing potential observational signatures of dark matter effects.

Contribution

It introduces a two-fluid relativistic Cowling approximation model to analyze oscillation frequencies in dark matter admixed neutron stars, uncovering a universal frequency-compactness relation.

Findings

Mass-scaled frequencies correlate tightly with stellar compactness.

Universality persists across dark matter parameters and nuclear equations of state.

Breakdown of universality observed when using tidal deformability.

Abstract

We systematically investigate the fundamental oscillation frequencies of dark matter admixed neutron stars, focusing on models with self-interacting fermionic dark matter that couples to normal matter solely through gravity. The analysis is carried out within a two-fluid formalism under the relativistic Cowling approximation, where the perturbation equations follow from the linearized energy-momentum conservation laws of both components. We find that the mass-scaled fundamental frequencies of the nuclear (dark) fluid in dark core (halo) configurations exhibit a remarkably tight correlation with the total stellar compactness. This universality persists across the dark matter parameter space explored in this study and is largely insensitive to the choice of nuclear equation of state. In contrast, we also find the breakdown of such universality with the tidal deformability, i.e, the same frequencies show substantial deviations from universality when expressed in terms of the tidal deformability. These contrasting behaviors highlight possible observational imprints of dark matter in neutron star interiors.