Neutron Stars in the Effective Fly-By Framework: $f$-Mode Re-summation

TL;DR

This paper develops an analytic model for gravitational wave signals from neutron stars in eccentric binaries during close fly-bys, capturing f-mode excitations and enabling better detection and understanding of neutron star properties.

Contribution

It introduces a re-summed harmonic oscillator model for f-mode gravitational wave emission in eccentric binaries, improving accuracy over previous harmonic decompositions.

Findings

Re-summed f-mode waveform matches numerical results with >98% accuracy.

Model accurately predicts timing of pericenter passages and mode excitation across multiple orbits.

Applicable to high-eccentricity systems with specific orbital parameters.

Abstract

Eccentric compact binaries pose not only a challenge for gravitational wave detectors, but also provide a probe into the nuclear equation of state if one of the objects is a neutron star. At the short pericenter passage, tidal interactions excite f-modes on the star, which in turn emit their own gravitational waves. We derive an analytic waveform for these stellar oscillations within the effective fly-by framework, modeling the emission to leading post-Newtonian order. At this order, the f-mode response can be written in a Fourier decomposition in terms of orbital harmonics, with the amplitudes of each harmonic depending on Hansen coefficients. Re-summing the harmonics of the f-mode results in a simple decaying harmonic oscillator, with the amplitude now determined by a Hansen coefficient of complex harmonic number. We compute the match between the re-summed f-mode and numerical integrations of the tidal response, and find ${\cal{M}} > 0.98$ for systems with high orbital eccentricity $(e > 0.8)$ and low semi-latus rectum $(p < 15M)$ for three equations of state. We further compare our model to modes generated from subsequent pericenter passages under the effect of radiation reaction, and develop an accurate model to time pericenter passages. We show how the timing model can be used to specify initial conditions to accurately track the f-mode excitation across multiple pericenter passages.