Search algorithm for the detection of long-duration narrow-band transients in GW interferometers

The recent observation of quasi-periodic oscillations (QPOs) in the x-ray light curve of soft gamma-ray repeaters, which fall within LIGO's sensitivity band, prompted us to search for gravitational waves associated with them. We describe the corresponding search algorithm that is based on the energy measurement in a single detector signal stream. We analytically derive the search sensitivity and compare it to the numerical sensitivity provided by the analysis pipeline with simulated detector noise. We found excellent agreement between the two approaches, reassuring us that the analysis method is well understood and implemented properly. The detector noise is approximated as white Gaussian with a strain equivalent spectral noise density of 10−22 strain Hz−1/2, similar to the noise floor of the H1 LIGO detector at the time of the SGR 1806–20 hyperflare event of 27 December 2004. As a trial model, we use a hypothetical 100 Hz QPO lasting for 50s. The corresponding energy sensitivity is found to be Esens = 3.63 × 10−43 strain2 Hz−1 which, in terms of amplitude, is hsensrss-det = 6.06 × 10−22 strain Hz−1/2. We show that, besides being simple and flexible, the algorithm is sensitive to a wide range of waveforms obeying the time and bandwidth requirements.