Antenna Sensitivity

A gravitational wave produces a spatially varying force, or stress, that will stretch and compress a bar antenna. This stress does work, thus energy can be added to or subtracted from the antenna. The more massive the antenna, the greater the amount of energy change. In other words, the gravitational force causes changes in the vibrational amplitude or phase of the antenna. It is this change in state that we try to detect.

By making the antenna's quadrupole modes resonant at the wave's frequency, the detector keeps a "memory" of the excitation, allowing extra time to detect the signal. Instead of looking at an instant of data, we can integrate over longer periods of time to look for changes in the amplitude or phase of the detector.

The sensitivity of an antenna can be improved by a number of ways. First, we can increase the force a gravitational wave will exert on the antenna by increasing its mass. Second, we can make the antenna equally sensitive to all directions and polarizations. Third, we can lower the noise temperature (level of excitation from non-gravitational sources) of the antenna. We briefly describe here the physical mechanisms that determine the noise of the antenna.

There are many non-gravitational sources that can excite the resonances of the detector. The largest of these sources can be external vibrations, such as ground noise. A sophisticated vibration isolation system is necessary to keep these forces from exciting the antenna.

Figure 1: A typical strain noise spectrum for the 1991 run of the LSU ALLEGRO detector.

Thermal noise will also contribute to the noise of the system. The thermal energy is proportional to the temperature of the detector, so cooling the antenna to very low temperatures will lower the noise of the system. The thermal energy is also proportional to the relaxation time of the resonant mass. By using high-Q material, such as Aluminum alloy 5056, the transfer of energy to and from the heat bath will be much slower. If we keep the integration time of our observations short, the effect of the thermal noise can be minimized. By increasing the Q of the system we not only lower the size of the noise spectrum of the detector, but give ourselves the possibility of using a longer integration time before the thermal noise dominates.

Another source of noise comes from the motion sensors. This type of noise can be referred to as "series" noise. This is an additive noise that usually comes from the first electronic amplifier. It is wide band and does not indicate excitation of the detector. A longer integration time reduces the effect of broad band noise, so it behaves in an opposite manner to thermal noise. This is another reason to require a high-Q system: it reduces the effect of "force noise" on the system allowing you to use a longer integration time. The series noise can also be reduced in the obvious way by reducing the amplifier noise.

Another way to improve the signal to noise ratio is to increase the coupling of the transducer to the antenna. Increased coupling will boost the amount of signal energy transferred to the motion sensor without increasing the series noise, so there will be a net gain in signal to noise.

The motion sensors can also generate a force noise that can excite the resonant mass. This type of noise is referred to as back-action noise. Just as the transducer can see what the large mass is doing, the large mass can also see what the transducer is doing. Increasing the coupling will cause more back-action noise to be transferred to the antenna.

This page is a modified excerpt of Stephen Merkowitz's Dissertation.