Approximate helical symmetry in compact binaries

The inspiral of a circular, nonprecessing binary exhibits an approximate helical symmetry. The effects of eccentricity, precession, and radiation reaction break the exact symmetry. We estimate the failure of this symmetry using the flux of the Bondi–van der Burg–Metzner–Sachs (BMS) charge corresponding to helical symmetry carried away by gravitational waves. We analytically compute the helical flux for binaries moving on eccentric orbits and quasicircular orbits without precession using post-Newtonian theory. The helical flux is nonvanishing at the 0PN order for eccentric orbits as expected. We analytically predict the helical flux to be at a relative 5PN order for quasicircular nonprecessing binaries. This prediction is compared with 113 quasicircular nonprecessing numerical relativity waveforms from the SXS catalog. We find good agreement between analytical and numerical results for quasicircular nonprecessing binaries establishing that helical symmetry starts to break at 5PN for these binaries.