The first generation of interferometric gravitational wave detectors have now collected data at their design strain sensitivities [1,2,3,4,5,6], and an improved generation of detectors [7,8] is already under development. Even at this unprecedented level of sensitivity, potentially detectable signals from astrophysical sources are expected to be at or near the limits of detectability, requiring carefully designed search algorithms in order to identify and distinguish them from the background detector noise. In this study, we focus on the problem of detecting the specific class of gravitational wave signals known as gravitational-wave bursts (GWBs). These are signals lasting from a few milliseconds to a few seconds, for which we do not have sufficient theoretical understanding or reliable models to predict a waveform. This includes signals from the merger of binary compact objects, asymmetric core collapse supernovae, the progenitors of gamma ray bursts, and possibly unexpected sources.
Since accurate waveform predictions do not exist for GWBs, the typical method to identify them is to project the data under test onto a convenient basis of abstract waveforms that are chosen to cover a targeted region of the time-frequency plane, and then identify regions of this search space with statistically significant excess signal energy [9]. In this study, we focus on one such burst search algorithm, the QPipeline [10], which first projects the data under test onto an overlapping basis of Gaussian enveloped sinusoids characterized by their center time, center frequency, and quality factor. A trigger is recorded whenever this projection exceeds a threshold value, with the magnitude of the projection indicating the significance of the trigger. Since the triggers are considered separately, the existing algorithm currently under-reports the total energy and true significance of those signals that are extended in time and/or frequency, since they have a significant projection onto multiple independent basis functions. Since GWB signals with such extended features are commonly observed in simulations of core collapse supernovae, the mergers of binary compact objects, and instabilities of spinning neutron stars, there are good reasons to try to improve the sensitivity of the search algorithm to such sources.
To improve the sensitivity of the QPipeline to signals that are extended in time and/or frequency, we have investigated extensions to the QPipeline that also consider the combined statistical significance of arbitrarily shaped clusters of projections in the time-frequency plane. Although a number of clustering algorithms are commonly available [11], this work focuses on a density based clustering algorithm due to its ability to also decrease the false detection probability of GWB searches by rejecting isolated single projection events associated with noise fluctuations. In this paper we present the details of a density based clustering algorithm implementation as an extension to the QPipeline, and demonstrate the resulting improved performance of the QPipeline for signals that are extended in time and/or frequency.
The paper is structured as follows. Section 2 briefly describes the QPipeline burst search algorithm. Section 3 considers the motivations for clustering and surveys some of the available approaches. Section 4 presents the details of the proposed density based clustering algorithm. Section 5 demonstrates the benefit of the proposed approach for detecting simulated gravitational wave bursts of various waveforms. Finally, in section 6, we present our conclusions and discuss possible future investigations.