Gravitational wave asteroseismology limits from low density nuclear matter and perturbative QCD

TL;DR

This paper constrains the fundamental mode frequencies and damping times of non-radial oscillations in neutron stars using combined low and high density equations of state, providing model-independent bounds relevant for gravitational wave asteroseismology.

Contribution

It introduces a method to connect low-density chiral EFT and high-density perturbative QCD EOSs through interpolating polytropes, deriving universal constraints on neutron star oscillation properties.

Findings

$f$-mode frequency and damping time are tightly constrained.

Empirical relations for $f$-mode properties are analyzed for robustness.

Constraints are largely model-independent within the considered EOS family.

Abstract

We investigate the fundamental mode of non-radial oscillations of non-rotating compact stars in general relativity using a set of equations of state (EOS) connecting state-of-the-art calculations at low and high densities. Specifically, a low density model based on the chiral effective field theory (EFT) and high density results based on perturbative Quantum Chromodynamics (QCD) are matched through different interpolating polytropes fulfilling thermodynamic stability and subluminality of the speed of sound, together with the additional requirement that the equations of state support a two solar mass star. We employ three representative models (EOS I, II and III) presented in Ref. [1] such that EOS I gives the minimum stellar radius, EOS II the maximum stellar mass, and EOS III the maximum stellar radius. Using this family of equations of state, we find that the frequency and the damping time of the $f$-mode are constrained within narrow quite model-independent windows. We also analyze some proposed empirical relations that describe the $f$-mode properties in terms of the average density and the compactness of the neutron star. We discuss the stringency of these constrains and the possible role of physical effects that cannot be encoded in a mere interpolation between low and high density EOSs.