On detection of black hole quasinormal ringdowns: Detection efficiency and waveform parameter determination in matched filtering

Gravitational radiation from a slightly distorted black hole with ringdown waveform is well understood in general relativity. It provides a probe for direct observation of black holes and determination of their physical parameters, masses and angular momenta (Kerr parameters). For ringdown searches using data of gravitational wave detectors, matched filtering technique is useful. In this paper, we describe studies on problems in matched filtering analysis in realistic gravitational wave searches using observational data. Above all, we focus on template constructions, matches or signal-to-noise ratios (SNRs), detection probabilities for Galactic events, and accuracies in evaluation of waveform parameters or black hole hairs. In template design for matched filtering, search parameter ranges and template separations are determined by requirements from acceptable maximum loss of SNRs, detection efficiencies, and computational costs. In realistic searches using observational data, however, effects of nonstationary noises cause decreases of SNRs, and increases of errors in waveform parameter determinations. These problems will potentially arise in any matched filtering searches for any kind of waveforms. To investigate them, we have performed matched filtering analysis for artificial ringdown signals which are generated with Monte-Carlo technique and injected into the TAMA300 observational data. We employed an efficient method to construct a bank of ringdown filters recently proposed by Nakano et al., and use a template bank generated from a criterion such that losses of SNRs of any signals do not exceed 2%. We found that this criterion is fulfilled in ringdown searches using TAMA300 data, by examining distribution of SNRs of simulated signals. It is also shown that with TAMA300 sensitivity, the detection probability for Galactic ringdown events is about 50% for black holes of masses greater than 20M_⊙ with SNR>10. The accuracies in waveform parameter estimations are found to be consistent with the template spacings, and resolutions for black hole masses and the Kerr parameters are evaluated as a few % and ∼40%, respectively. They can be improved up to <0.9% and <24% for events of SNR≥10 by using fine-meshed template bank in the hierarchical search strategy.