The robustness of quasinormal modes extracted from black-hole merger simulation

In the regime of linear perturbation theory, the ring-down phase of a gravitational wave signal is described by a linear combination of quasinormal modes (QNMs). In studies of ring-down fitting, extracting QNM coefficients accurately and robustly is a crucial aspect of analyzing the gravitational-wave signal. In our work, we use a greedy algorithm within which we fix certain QNM coefficients and apply this approach to linear fitting, and to nonlinear fitting where the properties of the remnant black hole are treated as unknown variables. This approach can help us understand the robustness of QNM coefficients by lowering the degrees of freedom for the fitting problem. We have found that only the fundamental mode (2,2,0,+) and the first overtone (2,2,1,+) can be extracted robustly with reasonable accuracy when we are fitting only the spherical harmonic multipole (l,m) = (2,2). The modes (3,2,0,+), (4,2,0,+), and (3,2,1,+) can also be extracted robustly when spherical-spheroidal mixing is considered and multimode fitting is applied to the spherical harmonic multipoles (l,m) = (2,2), (3,2), (4,2). Beyond that, the other subdominant QNMs can only be extracted with large uncertainties.