Search for gravitational wave ringdowns from perturbed black holes in LIGO S4 data

According to general relativity a perturbed black hole will settle to a stationary configuration by the emission of gravitational radiation. Such a perturbation will occur, for example, in the coalescence of a black hole binary, following their inspiral and subsequent merger. At late times the waveform is a superposition of quasinormal modes, which we refer to as the ringdown. The dominant mode is expected to be the fundamental mode, $l=m=2$. Since this is a well-known waveform, matched filtering can be implemented to search for this signal using LIGO data. We present a search for gravitational waves from black hole ringdowns in the fourth LIGO science run S4, during which LIGO was sensitive to the dominant mode of perturbed black holes with masses in the range of $10{M}_{\ensuremath{\bigodot}}$ to $500{M}_{\ensuremath{\bigodot}}$, the regime of intermediate-mass black holes, to distances up to 300 Mpc. We present a search for gravitational waves from black hole ringdowns using data from S4. No gravitational wave candidates were found; we place a 90%-confidence upper limit on the rate of ringdowns from black holes with mass between $85{M}_{\ensuremath{\bigodot}}$ and $390{M}_{\ensuremath{\bigodot}}$ in the local universe, assuming a uniform distribution of sources, of $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}=1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}{L}_{10}^{\ensuremath{-}1},$where ${L}_{10}$ is ${10}^{10}$ times the solar blue-light luminosity.