General Relativistic Simulations of the Nonlinear Evolution of r-modes in Rapidly Rotating Neutron Stars
Abstract
The r-modes in rotating neutron stars are a promising source of continuous gravitational waves, and may grow or be excited to amplitudes α≲1. We perform general relativistic simulations of nonlinear l=|m|=2 r-modes in a rapidly rotating neutron star with spin frequency fspin≈792 Hz, relaxing the Cowling and small-α approximations. The star is idealised as an unmagnetised, one-component, perfect fluid with a polytropic equation of state. The r-mode frequency is measured to be fr−mode=1014 Hz for initial amplitude α0=0.2. The dimensionless frequency κ≈0.7197 agrees with an estimate from linear perturbation theory to within 1.7%. fr−mode increases quadratically with amplitude, and κ decreases by 3.4% across simulations where α0 is varied through the range 0.2≤α0≤1.2. The gravitational wave strain calculated from the Newman-Penrose scalar implies hr−mode≈9.7×10−22 at $10$ kpc for α0=0.2, which agrees with Einstein's quadrupole formula to within 35%. We also report on nonlinear phenomena observed in our simulations, e.g. differential rotation, amplitude decay, and signatures of nonlinear mode coupling in the spacetime oscillations.
Versions
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BibTeX
@misc{yu2026general,
title = {{General Relativistic Simulations of the Nonlinear Evolution of r-modes in Rapidly Rotating Neutron Stars}},
author = {Justin K. Yu and Andrew Melatos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29259},
eprint = {2610.29259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29259},
}
RIS
TY - UNPB
TI - General Relativistic Simulations of the Nonlinear Evolution of r-modes in Rapidly Rotating Neutron Stars
AU - Justin K. Yu
AU - Andrew Melatos
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29259
UR - https://arxiv.org/abs/2610.29259
AB - The r-modes in rotating neutron stars are a promising source of continuous gravitational waves, and may grow or be excited to amplitudes α≲1. We perform general relativistic simulations of nonlinear l=|m|=2 r-modes in a rapidly rotating neutron star with spin frequency f_spin≈792 Hz, relaxing the Cowling and small-α approximations. The star is idealised as an unmagnetised, one-component, perfect fluid with a polytropic equation of state. The r-mode frequency is measured to be f_r−mode=1014 Hz for initial amplitude α_0=0.2. The dimensionless frequency κ≈0.7197 agrees with an estimate from linear perturbation theory to within 1.7%. f_r−mode increases quadratically with amplitude, and κ decreases by 3.4% across simulations where α_0 is varied through the range 0.2≤α_0≤1.2. The gravitational wave strain calculated from the Newman-Penrose scalar implies h_r−mode≈9.7×10^−22 at $10$ kpc for α_0=0.2, which agrees with Einstein's quadrupole formula to within 35%. We also report on nonlinear phenomena observed in our simulations, e.g. differential rotation, amplitude decay, and signatures of nonlinear mode coupling in the spacetime oscillations.
ER -