On Detection of Black Hole Quasi-Normal Ringdowns: Detection Efficiency and Waveform Parameter Determination in Matched Filtering

TL;DR

This paper evaluates the effectiveness of matched filtering techniques in detecting black hole ringdown signals and accurately estimating their parameters using observational gravitational wave data, focusing on realistic detection scenarios.

Contribution

It presents a detailed analysis of detection probabilities and parameter estimation accuracies for black hole ringdowns using TAMA300 data, including strategies to improve resolution with hierarchical searches.

Findings

Detection probability for Galactic events is about 50% for black holes >20 M_sun with SNR > 10.

Waveform parameter estimation accuracy is within a few percent for mass and about 40% for Kerr parameters.

Hierarchical search strategies can improve parameter resolution to below 0.9% for mass and 24% for Kerr parameters.

Abstract

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. We have performed matched filtering analysis for artificial ringdown signals which are generated with Monte-Carlo technique and injected into the TAMA300 observational data. It is shown that with TAMA300 sensitivity, the detection probability for Galactic ringdown events is about 50% for black holes of masses greater than $20 M_{\odot}$ 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 $\sim 40 %$, respectively. They can be improved up to $< 0.9 %$ and $< 24 %$ for events of ${\rm SNR} \ge 10$ by using fine-meshed template bank in the hierarchical search strategy.