Nonlinearities in Black Hole Ringdowns

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain’s $(\mathrm{\ell },m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic $(4,4)$ mode’s amplitude exhibits quadratic scaling with the fundamental $(2,2)$ mode – its parent mode. The nonlinear mode’s amplitude is comparable to or even larger than that of the linear $(4,4)$ mode. Therefore, correctly modeling the ringdown of higher harmonics – improving mode mismatches by up to 2 orders of magnitude – requires the inclusion of nonlinear effects.