Saved in:
Bibliographic Details
Main Authors: Pitre, Tristan, Poisson, Eric
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.08722
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910998838902784
author Pitre, Tristan
Poisson, Eric
author_facet Pitre, Tristan
Poisson, Eric
contents The tidal deformation of a neutron star in a binary inspiral driven by the emission of gravitational waves affects the orbital dynamics and produces a measurable modulation of the waves. Late in the inspiral, a regime of dynamical tides takes over from a prior regime of static tides. A recent analysis by Yu et al. [M.N.R.A.S. 519, 4325 (2022)] reveals that nonlinear aspects of the tidal interaction are important during the regime of dynamical tides. Their theoretical framework is grounded in Newtonian gravity and fluid mechanics, and relies on a representation of the tidal deformation in terms of the star's normal modes of vibration. We confirm their observation in a general relativistic treatment of the tidal deformation of a neutron star, without relying on a mode representation of this deformation. The starting point of our description is a simultaneous time-derivative and nonlinear expansion of the tidal deformation, expressed in terms of three encapsulating constants, the static $k_2$, dynamic $\ddot{k}_2$, and nonlinear $p_2$ tidal constants. We describe the neutron star's deformation in terms of a well-defined quadrupole moment tensor, which is related to the tidal quadrupole moment through a frequency-domain response function $\tilde{k}_2(ω)$. In a pragmatic extension of our simultaneous expansion, we express this in a form proportional to $(1-ω^2/ω_*^2)^{-1}$, the characteristic response of a harmonic oscillator subjected to a driving force of frequency $ω$, with a natural-frequency parameter $ω_*$ constructed from the tidal constants. We compute these for polytropic stellar models, and show that the nonlinear constant $p_2$ lowers the frequency parameter by as much as 15% relative to an estimation based on a purely linear treatment of the tidal deformation.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08722
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Impact of nonlinearities on relativistic dynamical tides in compact binary inspirals
Pitre, Tristan
Poisson, Eric
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
The tidal deformation of a neutron star in a binary inspiral driven by the emission of gravitational waves affects the orbital dynamics and produces a measurable modulation of the waves. Late in the inspiral, a regime of dynamical tides takes over from a prior regime of static tides. A recent analysis by Yu et al. [M.N.R.A.S. 519, 4325 (2022)] reveals that nonlinear aspects of the tidal interaction are important during the regime of dynamical tides. Their theoretical framework is grounded in Newtonian gravity and fluid mechanics, and relies on a representation of the tidal deformation in terms of the star's normal modes of vibration. We confirm their observation in a general relativistic treatment of the tidal deformation of a neutron star, without relying on a mode representation of this deformation. The starting point of our description is a simultaneous time-derivative and nonlinear expansion of the tidal deformation, expressed in terms of three encapsulating constants, the static $k_2$, dynamic $\ddot{k}_2$, and nonlinear $p_2$ tidal constants. We describe the neutron star's deformation in terms of a well-defined quadrupole moment tensor, which is related to the tidal quadrupole moment through a frequency-domain response function $\tilde{k}_2(ω)$. In a pragmatic extension of our simultaneous expansion, we express this in a form proportional to $(1-ω^2/ω_*^2)^{-1}$, the characteristic response of a harmonic oscillator subjected to a driving force of frequency $ω$, with a natural-frequency parameter $ω_*$ constructed from the tidal constants. We compute these for polytropic stellar models, and show that the nonlinear constant $p_2$ lowers the frequency parameter by as much as 15% relative to an estimation based on a purely linear treatment of the tidal deformation.
title Impact of nonlinearities on relativistic dynamical tides in compact binary inspirals
topic General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
url https://arxiv.org/abs/2506.08722