A new method for inspiral-to-ringdown waveforms of compact binaries: Helmholtz orbits and spherical-Bessel flux

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, 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, 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 times10-23, and the mismatch against the 2.5 PN inspiral is a difference in phasing.