Investigating methods of fitting quasinormal-modes in numerical-relativity ringdown signals

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Abstract:: The ringdown of a black hole merger can be decomposed into quasinormal modes (QNMs), and it has been suggested that the subset of QNMs known as overtones can contribute significantly. This work aims to measure the contribution of each overtone to the ringdown via fits to numerical-relativity waveforms, which has implications for analysis of ringdown signals and tests of general relativity (GR). We employ both least-squares and Bayesian fitting methods, and use several different metrics to determine each overtoneâ€™s importance. The first metric used is the earliest time at which a model with N overtones is a good fit (i.e., the ringdown start time). Each additional overtone allows an earlier fit, however the change in start time decreases with N. The second metric introduces deviations from the GR frequency of each overtone. We found that the effect of deviations decreases rapidly with overtone index n. This implies it becomes harder to perform tests of GR with each additional overtone. The third metric is the stability of mode amplitudes between fits with different ringdown start times. It is known that least-squares fits are not optimal for studying amplitudes, and here we perform a Bayesian analysis for more robust results.

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LIGO Document T2400223-v1