Search for gravitational waves associated with the gamma ray burst GRB030329 using the LIGO detectors

We have performed a search for bursts of gravitational waves associated with the very bright gamma ray burst GRB030329, using the two detectors at the LIGO Hanford Observatory. Our search covered the most sensitive frequency range of the LIGO detectors (approximately $80–-2048\mathrm{Hz}$), and we specifically targeted signals shorter than $\simeq 150\mathrm{ms}$. Our search algorithm looks for excess correlated power between the two interferometers and thus makes minimal assumptions about the gravitational waveform. We observed no candidates with gravitational-wave signal strength larger than a predetermined threshold. We report frequency-dependent upper limits on the strength of the gravitational waves associated with GRB030329. Near the most sensitive frequency region, around $\simeq 250\mathrm{Hz}$, our root-sum-square (RSS) gravitational-wave strain sensitivity for optimally polarized bursts was better than $h_{\mathrm{RSS}}\simeq 6\times {10}^{-21}{\mathrm{Hz}}^{-1/2}$. Our result is comparable to the best published results searching for association between gravitational waves and gamma ray bursts.

Figure 1

The GRB030329 light curve as measured by the HETE-2 FREGATE B instrument. The arrow indicates the HETE trigger time. The signal region analyzed in this study is indicated by the horizontal bar at the top. This figure is the courtesy of the HETE Collaboration.

Figure 2

Typical LIGO Hanford sensitivity curves during the S2 Run [strain ${\mathrm{Hz}}^{-1/2}$] (black and gray lines). The LIGO design sensitivity goal (SRD) is also indicated (dashed line).

Figure 3

The schematic of the analysis pipeline.

Figure 4

Examples of corrgram images. The horizontal axes are time (linearly scaled) and the vertical axes are integration length (logarithmically scaled). The color axis, an indicator of the excess correlation, is independently autoscaled for each quadrant for better visibility, therefore the meaning of colors differ from quadrant to quadrant. The time ticks also change from quadrant to quadrant for better visibility. The rainbow type color scale goes from blue to red, dark red marking the most significant points within a quadrant. The upper two quadrants show the corrgram image of injected sine Gaussians (250 Hz, $Q=8.9$). The bottom quadrants are examples of noise. The maximum of the intensity scale is significantly higher for both quadrants with injections, when compared to the noise examples. The top left injection is strong enough to be significantly above the preset detection threshold, while the top right injection is weak enough to fall significantly below the detection threshold.

Figure 5

False alarm rate as a function of the event strength threshold as determined from background data. The error bars reflect 90% C.L. Poisson errors, based on the number of events within the given bin. The pointer indicates the event strength threshold used for the analysis, which corresponds to an interpolated false alarm rate of less than $5\times {10}^{-4}\mathrm{Hz}$. Note that the signal region data is not included in this calculation. The position of symbols correspond to the center of the bins.

Figure 6

Efficiency of the detection algorithm for a sample waveform as a function of signal strength ($h_{\mathrm{RSS}}$); in this case a sine Gaussian of $f_0=250\mathrm{Hz}$ and $Q=8.9$. To extract this curve numerous simulated waveforms were embedded in a representative fraction of the background data at random times with randomly varying signal strength. The plot shows the fraction of signals detected as the function of amplitude and a sigmoid function fit. The reconstructed signal onset times were required to fall within $\pm$60 ms of the true onsets, which also explains why the low $h_{\mathrm{RSS}}$ end of the curve falls near zero. This is a typical plot and in general, the agreement between the measured values, and the fit is better than $\simeq 5\%$. We relied on the fit to extract our upper limits for an optimally oriented and polarized source. Section 6e below describes the corrections due to nonoptimal source direction and polarization.

Figure 7

Detected event strength versus $h_{\mathrm{RSS}}$ of the injected Sine-Gaussian waveform with $f_0=250\mathrm{Hz}$ and $Q\approx 8.9$. The dots indicate the scatter of the distribution of raw measurements. The gray band shows the quadratic polynomial fit, which allows us to convert the strength of an observed event into the equivalent $h_{\mathrm{RSS}}$ value and determine the associated $90\%$ C.L. error bars. The markers with error bars represent the $90\%$ C.L. regions for subsets of the data. For each marker, $90\%$ of the measurements used were within the horizontal error bars and $90\%$ of the detected event strengths values fell within the vertical error bars. The vertical dash-dotted line represents the $50\%$ detection efficiency associated with the waveform type and the chosen detection threshold (horizontal dotted line). As expected, the crossing of the threshold and the $50\%$ efficiency lines agree well with the fit and the center of the corresponding marker. The vertical dashed line represents the boundary of the region where we have better than $90\%$ detection efficiency. The “corner” defined by the event strength threshold and the $90\%$ detection efficiency boundary (dashed lines) agrees well with the curve outlined by the lower end of the vertical error bars of the markers. All events in the upper right corner of the plot (above and beyond the dashed lines) are detectable with high confidence. This plot is typical for different waveforms considered in the analysis.

Figure 8

Sensitivity of the detection algorithm for detecting sine-Gaussian waveforms versus characteristic frequency. The plot shows the strength necessary for $90\%$ detection efficiency. The gray spectra illustrate the sensitivity of the 2K and 4K Hanford detectors during the time surrounding the GRB030329 trigger. The error bars reflect a total $15\%$ error.

Figure 9

Number of events versus event strength in the signal region (circle). The diamonds show the expected distribution based on the background region. The squares mark the expected distribution based on nonphysical time shifts (ranging from 2 to 9 sec) between the H1 and H2 data streams in the background region. The error bars reflect $90\%$ C.L. Poisson errors. The position of the symbols correspond to the center of the bins.