Upper limits on gravitational wave bursts in LIGO’s second science run

We perform a search for gravitational wave bursts using data from the second science run of the LIGO detectors, using a method based on a wavelet time-frequency decomposition. This search is sensitive to bursts of duration much less than a second and with frequency content in the 100–1100 Hz range. It features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by LIGO. Improvements in the search method allow exploring weaker signals, relative to the detector noise floor, while maintaining a low false alarm rate, $O(0.1)$ $\mu \mathrm{Hz}$. The sensitivity in terms of the root-sum-square (rss) strain amplitude lies in the range of $h_{\mathrm{rss}}\sim {10}^{-20}-{10}^{-19}{\mathrm{Hz}}^{-1/2}$. No gravitational wave signals were detected in 9.98 days of analyzed data. We interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level. We combine this limit with measurements of the detection efficiency for selected waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order-of-magnitude distance sensitivity to certain modeled astrophysical sources. Both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad-band search for untriggered and unmodeled gravitational wave bursts to date.

Figure 1

Typical LIGO strain sensitivities in units of ${\mathrm{Hz}}^{-1/2}$ during the second science run (S2), compared to the most sensitive detector (L1) during the S1 science run. The solid line denotes the design goal for the 4 km instruments.

Figure 2

Block diagram of the WaveBurst analysis pipeline for the three LIGO detectors, H1, H2 and L1 as applied in the S2 data.

Figure 3

The significance distribution of the triple coincident WaveBurst events for individual detectors (L1, H1, H2) and the combined significance of their triple coincidences (L1xH1xH2) for the S2 data set. Solid histograms reflect the zero-lag events, while the points represent background (time-lag) events as produced with unphysical time shifts between the Livingston and Hanford detectors (and normalized to the S2 live-time). The change in the significance distribution for the individual detectors around significance equal to four is attributed to the onset of single pixel clusters (for which a higher threshold was applied).

Figure 4

Time between consecutive WaveBurst events (prior to the application of the $r$-statistic test). The top two panels show the distributions for double-coincidence H1-H2 and H1-L1 triggers, respectively. The triple-coincidence events, shown in the bottom panel, are reasonably well described by a Poisson process of constant mean. The exponential fits are performed for time delays greater than 4 s.

Figure 5

WaveBurst event count (prior to the $r$-statistic test) versus lag time (in seconds) of the L1 interferometer with respect to H1 and H2. The zero-lag measurement, i.e., the only coincidence measurement that is physical, is also shown. Because of the fragmentation of the data set, each time-lag has a slightly different live-time; for this reason, the event count is corrected so that they all correspond to the zero-lag live-time. A projection of the event counts to a one-dimensional histogram with a Poisson fit is also shown in the adjacent panel.

Figure 6

Circles: histogram of $r$-statistic confidence value ($\Gamma$) for zero-lag events passing the WaveBurst analysis. Stair-step curve: mean background per bin, estimated from time lags, for an observation time equal to that of the zero-lag analysis. The black error bars indicate the statistical uncertainty on the mean background. The shaded bars represent the expected root-mean-square statistical fluctuations on the number of background events in each bin.

Figure 7

Circles: histogram of $r$-statistic confidence value ($\Gamma$) for zero-lag events passing the WaveBurst analysis and surviving the acoustic veto. The background estimated from time-lag events surviving the acoustic veto is shown in the same manner as in Fig. 6.

Figure 8

Detection efficiency of the analysis pipeline as a function of the signal strength for sine-Gaussian waveforms of $Q=8.9$ and central frequencies of 100, 153, 235, 361, 554 and 849 Hz. The efficiencies plotted reflect averaging over random sky positions and polarization angles for injections covering the entire S2 data set. The $x$ axis reflects the $h_{\mathrm{rss}}$ as defined in Eq. (8.2).

Figure 9

Same plot as in Fig. 8 but for Gaussian injections of $\tau =0.1$, 0.5, 1.0, 2.5, 4.0 and 6.0 ms.

Figure 10

Timing error of the WaveBurst algorithm in the three LIGO instruments during S2 when sine-Gaussian injections of varying frequency and strength were injected. For comparison, the time separation between the two LIGO sites is 10 ms and the coincidence time window used in this analysis is 20 ms.

Figure 11

Detected versus injected root-sum-square (rss) signal strength for $Q=8.9$ sine-Gaussian injections. The vertical bars indicate one-sigma spread of the reconstructed values.

Figure 12

Rate versus $h_{\mathrm{rss}}$ exclusion plots at the 90% confidence level derived from the LIGO burst search using the S2 data. The top plot corresponds to burst events modeled by sine-Gaussians of $Q=8.9$ and frequencies ranging from 100 Hz to 849 Hz, while the bottom plot corresponds to ones events modeled by Gaussians of the $\tau$’s shown. For comparison, the corresponding curves resulting from the S1 analysis are superimposed.

Figure 13

Signal strength $h_{\mathrm{rss}}$ at the detectors versus central frequency for the 176 supernovae waveforms from the three models described in references [14, 15, 16]: the hydrodynamical model of Ref. [14], labeled “ZM”, the relativistic effects considered in Ref. [15] and labeled “DFM”, and finally the hydrodynamical model employing realistic nuclear equation of state of Ref. [16], labeled “OBLW”. In all cases, the supernova events are positioned in optimal orientation and polarization at 100 pc from the detectors. The strain sensitivity of the L1 detector during the S2 run is shown for comparison.

Figure 14

Rate versus $h_{\mathrm{rss}}$ exclusion curves at the 95% confidence level for optimally oriented Gaussians of $\tau =0.1\mathrm{ms}$. The solid curve displays the 95% confidence level measurement obtained by LIGO with this search. The shaded area is the IGEC exclusion region, adapted from Fig. 13 of [47]. If the comparison were performed using $Q=8.9$, 849 Hz sine-Gaussians, the LIGO and IGEC curves would move to smaller amplitudes by factors of 1.1 and $\sim 3$, respectively.