Probing Dark Star Parameters Through $f$-Mode Gravitational Wave Signals

TL;DR

This paper explores how gravitational wave signals from $f$-mode oscillations can be used to determine the physical parameters of dark matter compact stars, offering a new method to probe dark matter properties.

Contribution

It introduces a universal relation for $f$-mode oscillations of dark stars and proposes a scheme to infer their physical parameters from gravitational wave data.

Findings

$f$-mode frequencies relate to stellar mass, radius, and moment of inertia.

Universal functions enable parameter inference from gravitational wave signals.

Dark star properties can be constrained using $f$-mode gravitational wave observations.

Abstract

Theoretical models of self-interacting dark matter offer a promising solution to several unresolved issues within the collisionless cold dark matter framework. For asymmetric dark matter, these self-interactions may encourage gravitational collapse, potentially leading to the creation of compact objects primarily composed of dark matter. By considering both fermionic and bosonic equations of state, we analyze the equilibrium structure of non-rotating dark stars, examining their bulk properties and comparing them with baryonic neutron stars. We show that the frequency and damping rate of $f$-mode oscillations of dark compact stars can be expressed in terms of universal functions of stellar mass, radius and moment of inertia. Finally, by employing the universality in the $f$-mode, we propose a scheme to infer accurate values of the physical parameters of dark compact stars from their $f$-mode gravitational wave signal.