Spin-Inversion Degeneracies in Restricted Inspiral Waveforms for LISA
Abstract
Spin inversions appear in several settings. Analytical work predicts a single spin flip during unequal-mass supermassive binary inspiral, while numerical relativity and post-Newtonian calculations show repeated flip-flop motion in comparable-mass binaries. Secular spin evolution also predicts additional cases driven by spin-induced mass quadrupoles. Whether these effects can be distinguished in gravitational-wave data is still unclear. We combine the secular spin angle equations with a quasi-circular second post-Newtonian frequency evolution and build a restricted waveform weighted by the sky-averaged LISA sensitivity. We study five near-equal-mass injections with detector-frame total mass M=2×105M⊙, including Kerr flip-flops and one quadrupole-induced case. Each injection is compared with physically evolving waveforms constrained to have no orbital-plane crossings. We search all four no-inversion sectors, vary the masses, spin magnitudes, and initial spin angles, and maximize over time, phase, and overall amplitude. Large spin motion does not by itself lead to a clearly different waveform in this restricted model. We compare configurations with different spin magnitudes, relative spin orientations, and angular excursions at eleven observer inclinations between 0∘ and 90∘. With each injection normalized to signal SNR ρ⋆=100, four of the five cases leave a residual SNR below unity for the 0∘ viewing direction along the total angular momentum. At nonzero inclinations, the residual associated with the largest match found reaches $7.07$ in the two-active-spin case at 55∘. These upper bounds on the minimum residual within the allowed template family suggest potential distinguishability of spin inversions and motivate studies with more complete waveforms and the full LISA response.
Versions
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BibTeX
@misc{karacsonyi2026spininversion,
title = {{Spin-Inversion Degeneracies in Restricted Inspiral Waveforms for LISA}},
author = {Kata Karácsonyi and László Árpád Gergely},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.20174},
eprint = {2608.20174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20174},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-Inversion Degeneracies in Restricted Inspiral Waveforms for LISA
AU - Kata Karácsonyi
AU - László Árpád Gergely
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2608.20174
UR - https://arxiv.org/abs/2608.20174
AB - Spin inversions appear in several settings. Analytical work predicts a single spin flip during unequal-mass supermassive binary inspiral, while numerical relativity and post-Newtonian calculations show repeated flip-flop motion in comparable-mass binaries. Secular spin evolution also predicts additional cases driven by spin-induced mass quadrupoles. Whether these effects can be distinguished in gravitational-wave data is still unclear. We combine the secular spin angle equations with a quasi-circular second post-Newtonian frequency evolution and build a restricted waveform weighted by the sky-averaged LISA sensitivity. We study five near-equal-mass injections with detector-frame total mass M=2×10^5M_⊙, including Kerr flip-flops and one quadrupole-induced case. Each injection is compared with physically evolving waveforms constrained to have no orbital-plane crossings. We search all four no-inversion sectors, vary the masses, spin magnitudes, and initial spin angles, and maximize over time, phase, and overall amplitude. Large spin motion does not by itself lead to a clearly different waveform in this restricted model. We compare configurations with different spin magnitudes, relative spin orientations, and angular excursions at eleven observer inclinations between 0^∘ and 90^∘. With each injection normalized to signal SNR ρ_⋆=100, four of the five cases leave a residual SNR below unity for the 0^∘ viewing direction along the total angular momentum. At nonzero inclinations, the residual associated with the largest match found reaches $7.07$ in the two-active-spin case at 55^∘. These upper bounds on the minimum residual within the allowed template family suggest potential distinguishability of spin inversions and motivate studies with more complete waveforms and the full LISA response.
ER -