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 (ℓ,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.
@article{arxiv.2208.07380,
title = {Nonlinearities in Black Hole Ringdowns},
author = {Keefe Mitman and Macarena Lagos and Leo C. Stein and Sizheng Ma and Lam Hui and Yanbei Chen and Nils Deppe and François Hébert and Lawrence E. Kidder and Jordan Moxon and Mark A. Scheel and Saul A. Teukolsky and William Throwe and Nils L. Vu},
journal= {arXiv preprint arXiv:2208.07380},
year = {2023}
}
Comments
6+2 pages, 4 figures, 1 table. Matches PRL version