Analysis of 3 years of data from the gravitational wave detectors EXPLORER and NAUTILUS

We performed a search for short gravitational wave bursts using about 3 years of data of the resonant bar detectors Nautilus and Explorer. Two types of analysis were performed: a search for coincidences with a low background of accidentals (0.1 over the entire period), and the calculation of upper limits on the rate of gravitational wave bursts. Here we give a detailed account of the methodology and we report the results: a null search for coincident events and an upper limit that improves over all previous limits from resonant antennas, and is competitive, in the range $h_{\mathrm{rss}}\sim {10}^{-19}$, with limits from interferometric detectors. Some new methodological features are introduced that have proven successful in the upper limits evaluation.

Figure 1

Spectral sensitivity curves of EXPLORER and NAUTILUS. The two bandwidths overlap for a large fraction of the total sensitive region.

Figure 2

Excitation of the detectors, as seen in the filtered data, due to two large cosmic-ray showers: an event of Explorer 2008 and an event of Nautilus 2007. Only the maximum value of these signals can be interpreted in terms of the assumed $h_{\mathrm{rss}}$ excitation; the shape of the pulse is due to the antenna response. The two plots are so dissimilar because of the differences in the bandwidths (see Fig. 1): while Nautilus has its sensitivity around one main frequency, Explorer is most sensitive on two frequencies and therefore its time-domain response exhibits beats.

Figure 3

Efficiencies of Explorer and Nautilus in 2009. The four lines refer to injections with $h_{\mathrm{rss}}=(7.97,9.76,11.27,12.6)\times {10}^{-20}{\mathrm{s}}^{1/2}$.

Figure 4

ROCs for Explorer and Nautilus in year 2010.

Figure 5

ROCs for Explorer and Nautilus, at an injected amplitude $h_{\mathrm{rss}}=9.76\times {10}^{-20}{\mathrm{s}}^{1/2}$ in the five subperiods.

Figure 6

ROCs for the combined observatory ($\mathrm{\text{Explorer}}+\mathrm{\text{Nautilus}}$). Left: in 2010, at the four injection amplitudes considered in Fig. 4; right: at an injected amplitude $h_{\mathrm{rss}}=9.76\times {10}^{-20}{\mathrm{s}}^{1/2}$ in the five subperiods.

Figure 7

Maximum efficiency $\overline{\epsilon }$ achievable with a background set at 0.1 accidentals in the entire observation time. The top line shows the efficiency with thresholds optimized at each abscissa point (injected amplitude), while the other curves are produced with different choices of a unique set of thresholds.

Figure 8

Thresholds of Explorer and Nautilus resulting from the UL optimization.

Figure 9

$\mathit{R}$-curves at $h_{\mathrm{rss}}=5.63\times {10}^{-20}$ (a) and $7.97\times {10}^{-20}$ (b) ${\mathrm{s}}^{1/2}$ in the five subperiods of data taking.

Figure 10

Total $\mathit{R}$-curves at different values of injected $h_{\mathrm{rss}}$.

Figure 11

Comparison between the upper limit computed with the optimized procedure described in the text (opt) and with a procedure with fixed thresholds, those defined by the coincidence search (fix). There is an evident large gain at low amplitude.

Figure 12

Comparison between our 95% upper limit and previously published results. All LIGO and Virgo results, and in particular the solid curve (LV2), refer to 90% ULs.