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

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 $\mathcal{M}>0.98$ 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.

Corrected typos and updated timing model coefficients

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Cited by in corpus (7)

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• Detecting gravitational-wave bursts from black hole binaries in the Galactic Center with LISA
• Inferring Interference: Identifying a Perturbing Tertiary with Eccentric Gravitational Wave Burst Timing
• Deep learning to detect gravitational waves from binary close encounters: Fast parameter estimation using normalizing flows
• Eccentric Catastrophes & What To Do With Them
• Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries
• Importance of relativistic pericenter precession in identifying the presence of a third body near eccentric binaries