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Upper limits on the Stochastic g.w. background

We recall here that upper limits for the stochastic background, in the frequency range of $\simeq 1$ kHz, have been set using bar detectors at room temperature in Glasgow[2,3] ( $\Omega_{gw} \le 10^4$), interferometers[4] ( $\Omega_{gw} \le 3~10^5$) (Garching-Glasgow), the small antenna Altair[5], and the two resonant g.w. detectors Explorer and Nautilus[6].

The result obtained with Explorer and Nautilus is very interesting as it is the first time that two cryogenic resonant detectors have been used to do this measurement. As this is presently the best upper limit in the frequency range of 1 kHz, we recall here briefly the result. The detector noise spectral densities have minima at the two resonances, around 904 and 921 Hz, and are shown in Fig.[*]. The analysis has been done over a bandwidth of order of 0.05 Hz , $907.1508-907.257 ~Hz$. In this bandwidth the averaged Nautilus spectrum is constant at the level $1.5 \cdot 10^{-42}~/\mbox{Hz}$, and the Explorer spectrum varies by a factor 2, in the range $3\cdot 10^{-43}~/\mbox{Hz}-6 \cdot 10^{-43}~/\mbox{Hz}$

The overlapped data cover a period of $12.57~hours$ from February, 7th, 1997, 22 h, 18 m (day=35466.9298) to the 8th, 12 h, 11 m (day=35467.5916).

\begin{figure}%%ORIGINAL SIZE: width=1.4TRUEIN; height=1.5TRUEIN
...riment. The minima correspond to the resonances
of the detectors.} \end{figure}

The result of the cross-correlation analysis of the data of the two detectors is shown in Fig.2: the lower curve shows the modulus of the cross spectrum $S_{12}(f)$, compared to the square root of the product of the two spectra $\sqrt{S_{1h}(f)S_{2h}(f)}$. In the case of total correlation the two curves should coincide a.

In case of null correlation we expect the standard deviation to be smaller than that obtained with only one detector by a factor $(t_m~\Delta \! f)^{1/2} \simeq 70$, when integrating over the bandwidth $\Delta \! f=0.1~Hz$. This factor represents the sensitivity improvement of the cross-correlation experiment with respect to the use of only one detector, if they were ``near" and had the same sensitivity.

The result obtained by averaging over a 0.1 Hz bandwidth is:

\begin{displaymath}{S_{12}(907.20;0.1)}= (1.0 \pm 0.6) 10^{-44}~Hz^{-1}\end{displaymath}

\begin{figure}%%ORIGINAL SIZE: width=1.4TRUEIN; height=1.5TRUEIN
$(t_m~\delta \! f)^{1/2}$\ is $\simeq 6$\ at each frequency.}\end{figure}

By expressing the above in terms of $\Omega_{gw}(f)$, that is using Eq.[*] (with $S_{12}(f)$ in place of $S_{h}(f)$) and taking into account the factor $6$, that is the worsening due to the distance between Explorer and Nautilus, we get

\begin{displaymath}\Omega_{gw}(907.20; 0.1) \leq 6 \cdot 10

We note that by extending the period of correlation to one year, we can obtain, with the detectors in operation now, an upper limit less than unity. This would be already very interesting for the various theoretical scenarios of the gravitational wave background.

next up previous
Next: Stochastic Background of Gravitational Up: info2 Previous: GW Experiments and Early
pia astone 2001-08-23