Prospects for searches for long-duration gravitational-waves without time slides

The detection of unmodeled gravitational-wave transients by ground-based interferometric gravitational-wave detectors is an important goal for the advanced detector era. These searches are commonly cast as pattern recognition problems, where the goal is to identify statistically significant clusters indicating the presence of gravitational-wave transients in spectrograms of detector strain power when the precise signal morphology is unknown. In previous work, we have introduced a clustering algorithm referred to as seedless clustering, and shown that it is a powerful tool for detecting weak and long-lived (∼10-1000s) gravitational-wave transients. However, as the algorithm is currently conceived, in order to carry out a search on approximately a year of data, significant computational resources may be required for estimating background events. Currently, the use of the algorithm is limited by the computational resources required for performing background studies to assign significance to events identified by the algorithm. In this paper, we present an analytic method for estimating the background generated by the seedless clustering algorithm and compare the performance to both Monte Carlo Gaussian noise and time-shifted gravitational-wave data from a week of LIGO's 5th Science Run. We demonstrate qualitative agreement between the model and measured distributions and argue that the approximation will be useful to supplement conventional background estimation techniques for advanced detector searches for long-duration gravitational-wave transients.