General-relativistic treatment of tidal $g$-mode resonances in coalescing binaries of neutron stars. I. Theoretical framework and crust breaking

TL;DR

This paper develops a relativistic framework to analyze tidal g-mode resonances in neutron star binaries, showing that certain mode excitations can cause crust failure shortly before merger.

Contribution

It introduces a comprehensive theoretical model incorporating realistic equations of state, post-Newtonian effects, and magnetic fields to study mode resonances and crust breaking in neutron stars.

Findings

Certain g-modes can induce crust failure seconds before coalescence.

Mode excitation depends on the equation of state, stratification, and magnetic field.

Resonant excitations may influence gravitational wave signals and neutron star crust integrity.

Abstract

During the final stages of a neutron-star binary coalescence, stellar quasi-normal modes can become resonantly excited by tidal fields. If the strain exerted by the excited modes exceeds the extent to which the crust can respond linearly, localised crustal failures may occur. In this work, we re-examine resonant $g$-mode excitations of relativistic neutron stars in the last $\sim$ 10 seconds of an inspiral. We adopt realistic equations of state that pass constraints from GW170817, include 3rd order post-Newtonian terms for the conservation orbital motion, and employ a 2.5 post-Newtonian scheme for gravitational back-reaction. Frequency modulations of the modes due to tidal fields, Lorentz forces, and (slow) rotation are also considered to investigate the maximal strain achievable by resonantly-excited $g$-modes. Depending on the equation of state, degree of stratification, and stellar magnetic field, we find that certain $g$-modes excitations may be able to break the crust some seconds prior to coalescence.