Gravitational wave echoes from strange stars for various equations of state

TL;DR

This paper investigates gravitational wave echoes from strange stars using various equations of state, finding that certain models can produce high-frequency echoes, with frequencies depending on specific model parameters.

Contribution

It compares GWE frequencies from strange stars modeled with MIT bag, linear, and polytropic EoSs, highlighting the model-dependent nature of the echoes.

Findings

Polytropic EoS cannot emit GWE due to low stiffness.

MIT bag and linear EoSs can produce GWE at tens of kilohertz.

GWE frequency increases with bag constant B and decreases with linear constant b.

Abstract

The tentative Gravitational Wave Echo (GWE) at a frequency of about $72\,Hz$ has been recently claimed at $4.2\sigma$ significance level in the GW170817 event. GWEs can be used as a tool to study the characteristics of ultra-compact stellar objects. Considering the final ultra-compact, post-merger object as a strange star, the GWE frequency can be calculated. However, GWEs are observed for only those compact stellar structures whose compactness lies in between 0.33 and 0.44. Alternatively, GWE can be obtained for those compact stars which feature a photon sphere and compactness not crossing the Buchdahl's limit radius $R_{B}=9/4M$. A photon sphere is a surface located at $R=3M$, $R$ being the radius and $M$ is the total mass of the ultra-compact object. Recently using the simplest MIT Bag model Equation of State (EoS) it has been reported that strange stars can produce GWEs with frequencies of tens of kilohertz. In view of this, for a comparative study, we have calculated the respective echo frequencies associated with strange stars by considering three models of strange star EoSs, viz., MIT bag model, linear and polytropic EoSs \cite{JB}. We found that, not being too stiff the polytropic EoS can not emit GWE, whereas the MIT Bag model and the linear EoSs can emit GWEs at a frequency range of about tens of kilohertz. Also, GWE frequency increases with the increase in values of bag constant $B$ and decreases with the increasing values of linear constant $b$. So a model-dependent nature of GWE frequencies is observed.