Impact of anti-symmetric contributions to signal multipoles in the measurement of black-hole spins

Many current models for the gravitational-wave signal from precessing black-hole binaries neglect an asymmetry in the $\pm m$ multipoles. The asymmetry is weak, but is responsible for out-of-plane recoil, which for the final black hole can be several thousand km/s. In this work we show that the multipole asymmetry is also necessary to accurately measure the black-hole spins. We consider synthetic signals calculated from the numerical relativity surrogate model NRSur7dq4, which includes the multipole asymmetry, and measure the signal parameters using two versions of the same model, one with and one without the multipole asymmetry included. We find that in high signal-to-noise-ratio observations where the spin magnitude and direction can in principle be measured accurately, neglecting the multipole asymmetry can result in biased measurements of these quantities. Measurements of the black-hole masses and the standard aligned-spin combination $\chi_{\rm eff}$ are not in general strongly affected. As an illustration of the impact of the multipole asymmetry on a real signal we consider the LVK observation GW200129_065458, and find that the inclusion of the multipole asymmetry is necessary to identify the binary as unequal-mass and a high in-plane spin in the primary.