Quasinormal-mode filters: A new approach to analyze the gravitational-wave ringdown of binary black-hole mergers

We propose two frequency-domain filters to analyze ringdown signals of binary black hole mergers. The first rational filter is constructed based on a set of (arbitrary) quasinormal modes (QNMs) of the remnant black holes, whereas the second full filter comes from the transmissivity of the remnant black holes. The two filters can remove corresponding QNMs from original time-domain ringdowns, while changing early inspiral signals in a trivial way---merely a time and phase shift. After filtering out dominant QNMs we can visualize the existence of various subdominant effects. For example, by applying our filters to a GW150914-like numerical relativity (NR) waveform, we find second-order effects in the $(l=4,m=4),(l=5,m=4)$, and $(l=5,m=5)$ harmonics; the spherical-spheroidal mixing mode in the $(l=2,m=2)$ harmonic; and a mixing mode in the $(l=2,m=1)$ harmonic due to a gravitational recoil. In another NR simulation where two component spins are antialigned with the orbital angular momentum we also find retrograde modes. The filters are sensitive to the remnant properties (i.e., mass and spin) and thus have a potential application to future data analyses and parameter estimations. We also investigate the stability of the full filter. Its connection to the instability of QNM spectra is discussed.