Search for gravitational waves associated with 39 gamma-ray bursts using data from the second, third, and fourth LIGO runs

We present the results of a search for short-duration gravitational-wave bursts associated with 39 gamma-ray bursts (GRBs) detected by gamma-ray satellite experiments during LIGO’s S2, S3, and S4 science runs. The search involves calculating the crosscorrelation between two interferometer data streams surrounding the GRB trigger time. We search for associated gravitational radiation from single GRBs, and also apply statistical tests to search for a gravitational-wave signature associated with the whole sample. For the sample examined, we find no evidence for the association of gravitational radiation with GRBs, either on a single-GRB basis or on a statistical basis. Simulating gravitational-wave bursts with sine-Gaussian waveforms, we set upper limits on the root-sum-square of the gravitational-wave strain amplitude of such waveforms at the times of the GRB triggers. We also demonstrate how a sample of several GRBs can be used collectively to set constraints on population models. The small number of GRBs and the significant change in sensitivity of the detectors over the three runs, however, limits the usefulness of a population study for the S2, S3, and S4 runs. Finally, we discuss prospects for the search sensitivity for the ongoing S5 run, and beyond for the next generation of detectors.

Figure 1

Progression of LIGO sensitivities from S2 to S4 science runs. For each run, the corresponding curve gives the magnitude of the noise spectral density, in strain-equivalent units, for one of the IFOs during a representative time interval within the run. The solid curve gives the initial LIGO design sensitivity goal as given in LIGO’s Science Requirements Document (SRD).

Figure 2

(a) Example of a crosscorrelation post-trials distribution for the 25-ms crosscorrelation window, for the H1-H2 IFO pair. Data from off-source segments for GRB 050318 was used. (b) Cumulative distribution of (a), normalized to the total number of entries in the distribution. Both distributions with and without time shifts are shown, including the statistical errors. The arrow points to the largest crosscorrelation found in the on-source segment for GRB 050318. In this example, the largest crosscorrelation of 0.36 has a local probability of 0.57.

Figure 3

Cumulative local probability distribution resulting from the search of 59 IFO-IFO on-source pairs using a 25-ms crosscorrelation length. The most significant excess is indicated by the arrow. The expected distribution under the null hypothesis is indicated by the bold, dashed line. The excess needed for a $\sim 1\%$ confidence in the null hypothesis is indicated by the solid line. The maximum excess indicated by this line is 15 events because only the 15 most significant events in the actual distribution are tested.

Figure 4

Similar to Fig. 3, but using a 100-ms crosscorrelation length.

Figure 5

The cumulative distributions of the on-source (solid black with $+$ marker) and off-source (solid gray) largest H1-H2 crosscorrelations from the 100-ms search. The vertical lines denote the locations of the medians of the off-source (gray) and on-source (black, dashed) samples.

Figure 6

Plot of the cumulative distribution function of the off-source values of the sum-max statistic $\chi$. The dashed line shows the best fit normal distribution. The solid horizontal and vertical lines indicate the location of the on-source values of ${\chi }_{\mathrm{on}}$ and the corresponding cumulative probability. The on-source value was ${\chi }_{\mathrm{on}}=0.1753$, which yields a cumulative probability of 0.64 or an empirical significance of $1-0.64=0.36$.

Figure 7

Examples of upper limit curves that were used to set upper limits on $h_{\mathrm{rss}}$ using linear and circular polarizations. These were the upper limit curves for the H1-H2 IFO pair, for GRB 050306, using sine-Gaussians with $\mathrm{Q}=8.9$ and $f_0=150\mathrm{Hz}$. The shaded regions indicate the total $1\sigma$ uncertainty in the $h_{\mathrm{rss}}$ value.

Figure 8

Progression of $h_{\mathrm{rss}}$ upper limits from the S2 to S4 LIGO runs for linearly polarized sine-Gaussian waveforms; 25-ms crosscorrelation.

Figure 9

Progression of $h_{\mathrm{rss}}$ upper limits from the S2 to S4 LIGO runs for circularly polarized sine-Gaussian waveforms; 25-ms crosscorrelation.

Figure 10

Upper limit confidence belts at 90% confidence level on ${\rho }_0$, the SNR at the most probable redshift for Swift GRBs given in [63]. The solid line is the curve for all S2, S3, S4 GRBs that were used in the H1-H2 search (on-source $\chi =0.1753$). The dashed line is the curve when only the last 10 GRBs from the above set are selected (on-source $\chi =0.1702$). The line with filled circles is for a hypothetical scenario with 35 GRBs, all with an optimal sky location, and two identical and constant sensitivity detectors. The shifting of the curves horizontally is due to the change in the variance of $\chi$ as the number of GRBs is changed. For each value of ${\rho }_0$, 10 000 values of $\chi$ were drawn from its marginal distribution.