Upper limits from the LIGO and TAMA detectors on the rate of gravitational-wave bursts

We report on the first joint search for gravitational waves by the TAMA and LIGO collaborations. We looked for millisecond-duration unmodeled gravitational-wave bursts in 473 hr of coincident data collected during early 2003. No candidate signals were found. We set an upper limit of 0.12 events per day on the rate of detectable gravitational-wave bursts, at 90% confidence level. From software simulations, we estimate that our detector network was sensitive to bursts with root-sum-square strain amplitude above approximately $1–3\times {10}^{-19}{\mathrm{Hz}}^{-1/2}$ in the frequency band 700-2000 Hz. We describe the details of this collaborative search, with particular emphasis on its advantages and disadvantages compared to searches by LIGO and TAMA separately using the same data. Benefits include a lower background and longer observation time, at some cost in sensitivity and bandwidth. We also demonstrate techniques for performing coincidence searches with a heterogeneous network of detectors with different noise spectra and orientations. These techniques include using coordinated software signal injections to estimate the network sensitivity, and tuning the analysis to maximize the sensitivity and the livetime, subject to constraints on the background.

Figure 1

Polarization-averaged antenna amplitude responses $(F_{+}^2+F_{\times }^2{)}^{1/2}\in [0,1]$, in Earth-based coordinates. [See Eq. (4.3) and [19] for definitions of these functions and of Earth-based coordinates.] The top plot is for the LIGO Hanford detectors (H1, H2). The middle plot is for LIGO Livingston (L1). The bottom plot is for TAMA (T1). High contour values indicate sky directions of high sensitivity. The directions of maximum (null) sensitivity for each detector are indicated by the * (.) symbols. The directions of LIGO’s maximum sensitivity lie close to areas of TAMA’s worst sensitivity and vice versa.

Figure 2

S2-averaged amplitude noise spectra for the LIGO detectors, and a representative DT8 spectrum for the TAMA detector. We focus on GWBs which have significant energy in the frequency range 700-2000 Hz (indicated by the vertical dashed lines), where each interferometer has approximately the same noise level.

Figure 3

The same amplitude noise spectra as in Fig. 2, focusing on the frequency range 700-2000 Hz. The peaks at multiples of 400/3 Hz in the TAMA spectrum are due to a coupling between the radio-frequency modulation signal and the laser source; these frequencies are removed by the data conditioning discussed in Sec. 3a2.

Figure 4

Schematic of our analysis pipeline. Data from each detector is analyzed for bursts using the tfclusters (TFC) or excess power (POW) algorithm. Optionally, a time shift of 5–115 s is added to the event triggers from some sites. We look for simultaneous events from each operating detector, then apply the $r$-statistic waveform consistency test to the data from the LIGO detectors. Surviving coincidences are possible GWBs if no time shifts were used; otherwise they are accidental coincidences (background). The detection efficiency of the network is estimated by adding simulated GWBs to the data from each detector and repeating the analysis. Note that one of the L1 or T1 detectors may not be operating at any given time.

Figure 5

Autocorrelogram of trigger peak times from each detector. These are histograms of the difference in peak time between each pair of triggers from a given detector, binned in 0.2 s intervals. The horizontal axis is the time difference (units of s); the vertical axis is the number of trigger pairs per bin divided by the observation time and the bin width (units of ${\mathrm{s}}^{-2}$). With this normalization, the mean value is the square of the trigger rate. An autocorrelogram value significantly above the mean indicates a correlation in the time of event triggers. Each detector shows some excess above Poisson rates at delays of up to a few seconds. The sharp dip in the T1 curve near zero time is due to the clustering of the T1 triggers. The smaller relative fluctuations in the L1 and T1 curves are due to the much higher trigger rates from these detectors, which results in more triggers per bin.

Figure 6

Amplitude $h_{\mathrm{rss}}^{50\%}$ for 50% detection efficiency versus background rate for each of the individual detectors, and for the three coincidence combinations. The circles on the single-detector curves indicate the tuning selected for trigger generation. The circle, square, and triangle denote the resulting amplitude at 50% efficiency and an upper limit on the background rate for the H1-H2-L1-T1, H1-H2-nL1-T1, and H1-H2-L1-nT1 networks after the $r$-statistic with these tuning choices. (We can only compute upper limits on the background rates for coincidence because no time-shifted coincidences survive the waveform consistency test.) The efficiency is averaged over all of the sine-Gaussian signals in our analysis band.

Figure 7

Detection efficiency over the various data sets individually, and combined, using the final tuning. The combined efficiency curve is the average of the curves for the three data sets, weighted by their observation times. These efficiencies are averaged over all of the sine-Gaussian signals in our analysis band. There is a statistical uncertainty at each point in these curves of approximately 1%–3% due to the finite number of simulations performed.

Figure 8

Detection efficiency for the combined data set, by central frequency $f_0$ of the sine-Gaussian signal in Eq. (4.1). There is a statistical uncertainty at each point in these curves of approximately 2%–4% due to the finite number of simulations performed.

Figure 9

Detection efficiency for the H1-H2-L1-nT1 data set (i.e., with only the LIGO detectors operating), by central frequency $f_0$ of the sine-Gaussian signal in Eq. (4.1). There is a statistical uncertainty at each point in these curves of approximately 2%–6% due to the finite number of simulations performed. The improved efficiency for lower-frequency signals indicates that sensitivity at these frequencies is limited by the TAMA detector. This behavior is consistent with the noise spectra shown in Fig. 3.

Figure 10

Rate-versus-strength upper limits from each LIGO-TAMA data set, and combined, for the isotropic distribution of sources of sine-Gaussian GWBs described in Sec. 4a. The region above any curve is excluded by that experiment with at least 90% confidence. These curves include the allowances for uncertainties in the calibration and in the efficiencies discussed in Sec. 4c.

Figure 11

Comparison of the rate-versus-strength upper limits for $f_0=849\mathrm{Hz}$ sine-Gaussians from the combined LIGO-TAMA data set (including systematic and statistical uncertainties) with those from the LIGO-only S1 and S2 bursts searches [16, 21] and the TAMA-only DT9 search [17]. The combined LIGO-TAMA network has a superior rate upper limit for strong signals due to its larger observation time, while the LIGO-only S2 network has better sensitivity to weak signals. The TAMA-only DT9 amplitude sensitivity is limited by the high SNR threshold needed achieve a background rate of order one event over the observation time. Note that the LIGO-only S2 search had a nominal frequency range of 100-1100 Hz, while the LIGO-TAMA search band is 700-2000 Hz.