A new method for inspiral-to-ringdown waveforms of compact binaries: Helmholtz orbits and spherical-Bessel flux
Abstract
The waveform is obtained from one balance of energy and radiation on Helmholtz orbits of the retarded mass kernel, with a spherical-Bessel flux. That balance follows from the Dirac--Maxwell equation with a modified vertex, the single U(1) coupling being replaced by the eight operators of the source interaction. After contact that balance is the energy loss of one packet: a bounded well for a black-hole remnant and the Coulomb ladder of one star for a neutron-star remnant. Ringdown starts from the spherical projection of that end state, which contains its spin. The comparisons use model waveforms at the published parameters. For GW250114, at the Coulomb-radius contact and after a shift of −16 ms, the noise-weighted norm ratio against the NRSur7dq4 median in $100−−200\,\mathrm{Hz}$ stays between $1.36$ and $1.94$ across the published distance interval. Stopping at $2.4$ times that radius lowers the ratio to $1.11$, which the same interval moves from $0.94$ to $1.35$. With contact placed on the published merger time and with no time shift, that ratio is $3.32$ at the Coulomb radius and $2.30$ at $2.4$ times that radius. At the larger radius, the unretarded limit of this balance, with unit spherical-Bessel weights, reaches contact at 94 Hz, and in $20−−100\,\mathrm{Hz}$ the norm ratio to the Helmholtz balance is $1.12$ after a shift of +27 ms. For GW170817, |h+| near 100 Hz is 8.0×10−23, and the mismatch against the $2.5$PN inspiral is a difference in phasing.
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BibTeX
@misc{jin2026method,
title = {{A new method for inspiral-to-ringdown waveforms of compact binaries: Helmholtz orbits and spherical-Bessel flux}},
author = {Hong-Bo Jin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40168},
eprint = {2609.40168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A new method for inspiral-to-ringdown waveforms of compact binaries: Helmholtz orbits and spherical-Bessel flux
AU - Hong-Bo Jin
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40168
UR - https://arxiv.org/abs/2609.40168
AB - The waveform is obtained from one balance of energy and radiation on Helmholtz orbits of the retarded mass kernel, with a spherical-Bessel flux. That balance follows from the Dirac--Maxwell equation with a modified vertex, the single U(1) coupling being replaced by the eight operators of the source interaction. After contact that balance is the energy loss of one packet: a bounded well for a black-hole remnant and the Coulomb ladder of one star for a neutron-star remnant. Ringdown starts from the spherical projection of that end state, which contains its spin. The comparisons use model waveforms at the published parameters. For GW250114, at the Coulomb-radius contact and after a shift of −16 ms, the noise-weighted norm ratio against the NRSur7dq4 median in $100−−200\,\mathrm{Hz}$ stays between $1.36$ and $1.94$ across the published distance interval. Stopping at $2.4$ times that radius lowers the ratio to $1.11$, which the same interval moves from $0.94$ to $1.35$. With contact placed on the published merger time and with no time shift, that ratio is $3.32$ at the Coulomb radius and $2.30$ at $2.4$ times that radius. At the larger radius, the unretarded limit of this balance, with unit spherical-Bessel weights, reaches contact at 94 Hz, and in $20−−100\,\mathrm{Hz}$ the norm ratio to the Helmholtz balance is $1.12$ after a shift of +27 ms. For GW170817, |h_+| near 100 Hz is 8.0×10^−23, and the mismatch against the $2.5$PN inspiral is a difference in phasing.
ER -