Extending the Love-Q Relation to Rapidly Rotating Neutron Stars for Gravitational-Waveform Modelling
Abstract
Gravitational-wave observations of binary neutron star mergers probe the neutron star equation of state through finite-size effects on the waveform. These include the tidal deformation of the stars due to their respective companion, but for spinning neutron stars also include the spin-induced quadrupole moment of the stars. Typically, to avoid introducing additional equation of state dependent parameters, waveform models relate this quadrupole moment to the tidal deformability through so-called quasi-universal relations. These are derived under the slow-rotation approximation, which at larger spins, i.e., for millisecond pulsars, becomes unreliable. We attempt to extend the existing quasi-universal relations by explicitly accounting for the spin, calibrating it against numerically computed quadrupole moments across a broad set of equations of state and spins 0.15 ≤ |χ| ≤ 0.6 with the χ→ 0 limit enforced by construction. The resulting spin-extended relation reduces the median absolute percentage error relative to the slow-rotation relation by 66\% across this range. Parameter estimation using the spin-extended relation reduces biases in recovered intrinsic parameters in some cases, though biases from mass-spin degeneracies dominate largely when a population is considered. These results provide a more accurate description of the spin-induced quadrupole moment for spinning neutron star binaries, relevant for waveform modelling with third-generation gravitational-wave detectors.
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BibTeX
@misc{williams2026extending,
title = {{Extending the Love-Q Relation to Rapidly Rotating Neutron Stars for Gravitational-Waveform Modelling}},
author = {Natalie Williams and Tim Dietrich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19975},
eprint = {2609.19975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19975},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extending the Love-Q Relation to Rapidly Rotating Neutron Stars for Gravitational-Waveform Modelling
AU - Natalie Williams
AU - Tim Dietrich
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19975
UR - https://arxiv.org/abs/2609.19975
AB - Gravitational-wave observations of binary neutron star mergers probe the neutron star equation of state through finite-size effects on the waveform. These include the tidal deformation of the stars due to their respective companion, but for spinning neutron stars also include the spin-induced quadrupole moment of the stars. Typically, to avoid introducing additional equation of state dependent parameters, waveform models relate this quadrupole moment to the tidal deformability through so-called quasi-universal relations. These are derived under the slow-rotation approximation, which at larger spins, i.e., for millisecond pulsars, becomes unreliable. We attempt to extend the existing quasi-universal relations by explicitly accounting for the spin, calibrating it against numerically computed quadrupole moments across a broad set of equations of state and spins 0.15 ≤ |χ| ≤ 0.6 with the χ→ 0 limit enforced by construction. The resulting spin-extended relation reduces the median absolute percentage error relative to the slow-rotation relation by 66\% across this range. Parameter estimation using the spin-extended relation reduces biases in recovered intrinsic parameters in some cases, though biases from mass-spin degeneracies dominate largely when a population is considered. These results provide a more accurate description of the spin-induced quadrupole moment for spinning neutron star binaries, relevant for waveform modelling with third-generation gravitational-wave detectors.
ER -