The antenna sensitivity to burst signals

• The antenna sensitivity $h$ to burst signals is a function of its strain sensitivity $\tilde{h}$ and bandwidth $\delta f$

$$h \simeq \frac{1}{\tau_g} \sqrt{\frac{2 S_h}{ \pi \delta f}}$$

where:

• $\tau_g$ is the time duration of the burst, [s]
• $\delta f$ is the frequency bandwidth, [Hz]
• $S_h={\tilde{h}}^2$ is the noise spectral density [1/Hz]

This formula is approximated, since it is valid in the approximation of constant strain sensitivity over the frequency bandwidth of the detector. The exact formula is derived in Extract from LNF internal report, 1996

Another useful formula relates $h$ and the noise effective temperature $T_{eff}$, that is the noise after applying to the GW data a filter matched to delta-like signals.

$$h \simeq \frac{L}{\tau_g v^2} \sqrt{\frac{kT_{eff}}{M}}$$

where:

• $v$ is the sound velocity in the bar
• $M$ is the mass of the bar.