Spin-Inversion Degeneracies in Restricted Inspiral Waveforms for LISA
arXiv:2608.20174
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 , 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. A weak spin that sweeps through leaves a residual SNR of at reference signal SNR . A case where both spins cross the orbital plane many times gives the largest residual, . The quadrupole case has a secondary-spin range of with five crossings, yet the best no-inversion candidate found leaves a residual SNR of only . All largest matches found exceed . Within this restricted model, the spin inversion cases are therefore strongly degenerate with no-inversion binaries at . More complete waveforms, including observer-frame precession modulations, higher harmonics, separate polarizations, and the full LISA response, are needed to test whether this degeneracy can be broken.
20 pages, 4 figures. Submitted to Universe. Data and code: https://doi.org/10.5281/zenodo.22025538