Prospect of unraveling the first-order phase transition in neutron stars with $f$ and $p_1$ modes

TL;DR

This paper investigates how neutron star oscillation modes, specifically $f$ and $p$ modes, can potentially distinguish between different internal compositions, including the presence of a first-order phase transition, despite current detection limitations.

Contribution

The study constructs two equation of state ensembles to analyze the potential of $f$ and $p$ modes in identifying phase transitions in neutron stars.

Findings

Exclusion regions in frequency-damping time relations differ between ensembles.

Higher-order modes show more prominent exclusion regions.

Current detectors cannot observe the high-frequency modes discussed.

Abstract

Quasi-normal modes of neutron stars are an exciting prospect for analyzing the internal composition of NSs and studying matter at high densities. In this work, we focus on studying the $f$- and $p$- quadrupolar oscillation modes, which couple with gravitational waves. We construct two different equation of state ensembles, one without and one with a first-order phase transition, and examine how $f$- and $p$-modes might help us differentiate them. We find ensemble specific exclusion regions in the $65\%$ and $95\%$ confidence contours of the frequency-damping time relations. The exclusion regions become more prominent for the higher-order oscillation modes. However, these modes have higher frequencies, which are beyond the detection capabilities of present gravitational wave detectors. The quasi-universal relations of dimensionless quantities prove to be ineffective in differentiating the equation of state ensembles, as they obscure the details of the equation of state.