Accounting for Ringdown Mode-Mixing in Black-Hole Merger Waveforms

With rapid progress in numerical relativity recent years, the merger of comparable-mass black-hole binaries has become a reliable source of gravitational waveforms. The dominant harmonic modes $(l,m) = (2,\pm 2)$ are readily extracted and agree across research groups to high precision, making them suitable as raw material for high-accuracy template construction. However, examination of leading subdominant gravitational harmonic modes has revealed more complex behavior that impedes full modeling. For example, the $(3,\pm 2)$ mode, usually comparable to the $(4,4)$ in power content near merger, shows a complex frequency oscillation after merger, when the system should be ringing down to a Kerr end-state with constant quasi-normal mode (QNM) frequencies. Analysis indicates some kind of mode-mixing between the nominal $(3,2)$ mode and the dominant $(2,2)$ mode. We discuss the possible sources of this mode-mixing in numerical wave-extraction algorithms, and how to mitigate it to produce better-behaved waveforms that can be used for parameter estimation in gravitational-wave data analysis.