Seedless clustering in all-sky searches for gravitational-wave transients

The problem of searching for unmodeled gravitational-wave bursts can be thought of as a pattern recognition problem: how to find statistically significant clusters in spectrograms of strain power when the precise signal morphology is unknown. In a previous publication, we showed how “seedless clustering” can be used to dramatically improve the sensitivity of searches for long-lived ($\sim 10–1000\mathrm{s}$) gravitational-wave transients. To manage the computational costs, this initial analysis focused on externally triggered searches where the source location and emission time are both known to some degree of precision. In this paper, we show how the principle of seedless clustering can be extended to facilitate computationally feasible, all-sky searches where the direction and emission time of the source are entirely unknown. We further demonstrate that it is possible to achieve a considerable reduction in computation time by using graphical processor units, thereby facilitating more sensitive searches.

Figure 1

The effect of filter mismatch. Top left: signal-to-noise ratio (SNR) spectrogram showing an accretion disk instability signal (ADI 2) in Advanced LIGO simulated Monte Carlo noise and obtained using the correct filter. The signal appears as a whitish-yellow track indicating positive SNR. The signal has been made very loud ($d=50\mathrm{Mpc}$) for illustrative purposes. The black horizontal lines are notches due to instrumental artifacts. Top right: the same signal using an incorrect filter; i.e., the search direction does not match the source direction. The mismatch causes alternating stripes of positive (yellow) and negative (reddish black) SNR. At the turning points, where the SNR switches from positive to negative, the filtered cross-power signal is imaginary, and so the SNR (proportional to the real part of the filtered cross power) is approximately zero. Bottom left: the same signal using a different incorrect filter. In this case, the signal appears as purely negative. Bottom right: the same signal, using the correct filter, but much farther away ($D=340\mathrm{Mpc}$). It is all but impossible to see the track with the naked eye, but it can nonetheless be detected by all-sky stochtrack with $\mathrm{FAP}<0.1\%$ without knowledge of the true direction or the signal morphology.

Figure 2

Left: SNR spectrogram for a (very loud) binary neutron star signal in Monte Carlo noise. Right: the signal recovered by stochtrack. The stochtrack algorithm can detect binary neutron star signals in Advanced LIGO Monte Carlo noise with with $\mathrm{FAP}=0.1\%$ and $\mathrm{FDP}=50\%$ at a distance of 160 Mpc. Note that all-sky stochtrack does not do a good job of catching the beginning of the signal. This is not due to a lack of templates, but rather because the binary neutron star signal is not especially well described with a second-order Bézier curve.