Matched filtering and parameter estimation of ringdown waveforms

Abstract

Using recent results from numerical relativity simulations of nonspinning binary black hole mergers, we revisit the problem of detecting ringdown waveforms and of estimating the source parameters, considering both LISA and Earth-based interferometers. We find that Advanced LIGO and EGO could detect intermediate-mass black holes of mass up to $\ensuremath{\sim}{10}^{3}{M}_{\ensuremath{\bigodot}}$ out to a luminosity distance of a few Gpc. For typical multipolar energy distributions, we show that the single-mode ringdown templates presently used for ringdown searches in the LIGO data stream can produce a significant event loss ($>10%$ for all detectors in a large interval of black hole masses) and very large parameter estimation errors on the black hole's mass and spin. We estimate that more than $\ensuremath{\sim}{10}^{6}$ templates would be needed for a single-stage multimode search. Therefore, we recommend a ``two-stage'' search to save on computational costs: single-mode templates can be used for detection, but multimode templates or Prony methods should be used to estimate parameters once a detection has been made. We update estimates of the critical signal-to-noise ratio required to test the hypothesis that two or more modes are present in the signal and to resolve their frequencies, showing that second-generation Earth-based detectors and LISA have the potential to perform no-hair tests.