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 ($\sim 10–1000\mathrm{s}$) 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.

Figure 1

The plot on the left is the background distribution for the seedless clustering algorithm cluster SNR defined in Eq. (4). Monte Carlo denotes Gaussian colored noise. Time-shift denotes real time-shifted data with vetoes to limit the effects of instrumental artifacts. The theoretical line corresponds to the Gaussian approximation to the distribution given by Eq. (8). The plot on the right is the standard deviation of ${\mathrm{SNR}}_{\mathrm{tot}}$ as a function of track length. The standard deviation differs on the order of a few percent across the track lengths considered. In our analysis, we approximate the standard deviation of ${\mathrm{SNR}}_{\mathrm{tot}}$ across track length as constant.

Figure 2

Background distributions computed for the seedless clustering algorithm using both Bézier and chirp-like templates. The distributions are generated from time-shifted initial LIGO data. The top row corresponds to the Bézier templates and the bottom row chirp-like templates. The left column corresponds to a directed search (in a specific sky direction) and the right to an all-sky search performed looping over 40 time-delays for each template. The theoretical line corresponds to using Gaussian distributions with standard deviations presented in Fig. 3. The dotted lines correspond to $1\sigma$ error bars on the analytic approximation. These are derived from simulating the p-value vs. SNR distribution using many random seeds, in essence creating thousands of p-value vs SNR distributions consistent with the measured distributions, and computing the median and $1\sigma$ error bar for each p-value. The analytical background distributions for the directed searches are consistent with the measured background (within $1\sigma$). The distributions for the all-sky searches, however, are not generally within $1\sigma$. This is due to the assumption in the analytic-model that the loop over time-delays creates more independent trials, which is not the case and biases the result (please see the text for more details).

Figure 3

The plot on the left is the cumulative density function of the standard deviation of the ${\mathrm{SNR}}_{\mathrm{tot}}$ for the two parametrizations. Distribution is significantly broader for chirp-like templates due to track correlations. The plot on the right is the background distribution using the analytic approximation for the cases considered here. It shows the $\mathrm{Max}[{\mathrm{SNR}}_{\mathrm{tot}}]$ required for a $3\sigma$, $4\sigma$, and $5\sigma$ gravitational-wave detection using seedless clustering in dotted horizontal lines. The four different lines corresponds to the four-different seedless analysis types considered in this paper (a directed and all-sky Bézier template search and a directed and all-sky compact binary search), which each have significantly different distributions of $\mathrm{Max}[{\mathrm{SNR}}_{\mathrm{tot}}]$.

Figure 4

The plot on the left is the p-value vs ${\mathrm{SNR}}_{\mathrm{tot}}$ distribution for three different cases (for a single map): a directional search, a search looping over 40 sky-directions, and a search using 40 different tracks. As is expected, a search searching over 40 sky-directions results in higher background values for ${\mathrm{SNR}}_{\mathrm{tot}}$ than the directional case. Similarly, a search using 40 different tracks is conservative relative to the 40 sky-direction case, indicating that it is appropriate to consider such a method conservative. The plot on the right is the overlap between the templates used in the compact binary search algorithm. In general, there is significant overlap between templates, which biases the computation of the theoretical ${\mathrm{SNR}}_{\mathrm{tot}}$ distribution.