Saved in:
| Main Authors: | , |
|---|---|
| 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 |