Spherical Antennae

There are ways to improve resonant-mass antennas that are independent of the noise temperature. One way is to increase the cross-section of the antenna. Another is to construct many antennas, each aimed in a different direction, so every source direction and polarization will be in the most sensitive part of at least one antenna pattern. This method adds the ability to determine source direction and polarization. A "spherical" antenna will provide all three advantages in a single instrument. We use the word "spherical" for any shape that approximates a true sphere and has equivalent quadrupole vibrational modes.

The important question becomes: what quantitative improvement can a sphere actually deliver? We have invented a design for a nearly spherical antenna, which we call a Truncated Icosahedral Gravitational Wave Antenna, or TIGA, that provides a straightforward solution to certain complications of a spherical antenna, and lets us calculate the quantitative improvement. We conclude that a TIGA will be about 56 times more sensitive in energy than the typical equivalent bar-type antenna with the same noise temperature. Combined with a quantum limited noise temperature, this is a sufficient factor to increase our range by more than the desired factor. If we further assume construction of a set of detectors for different frequencies, (a "xylophone"), the sensitivity is further improved and wave form information can be obtained.

Figure 1: The truncated icosahedral gravitational wave antenna (TIGA) with secondary resonator locations indicated.

Figure 2: The LSU prototype TIGA suspended by its center of mass.

It was recognized long ago that a sphere is a very natural shape for a resonant mass detector of gravitational waves. A free sphere has five degenerate quadrupole modes of vibration that will interact strongly with a gravitational wave. Each free mode can act as a separate antenna, oriented towards a different polarization or direction. Wagoner and Paik found a set of equations to determine the source direction in the celestial hemisphere from the free mode amplitudes. Compared to a bar with the same quadrupole mode frequency and a typical length to diameter ratio of 4.2, the improvement in cross-section is about a factor of 60.

That result was ignored, perhaps because a simple spherical resonator is not a practical detector. One requirement for practicality is a set of secondary mechanical resonators. All successful cryogenic bar-type detectors have such resonators; they act as mechanical-impedance transformers between the primary vibrational modes of the antenna and the actual motion sensors, producing an essential increase in the electro-mechanical coupling. We expect that a sphere with five primary modes will require at least five secondary resonators. Another requirement for practicality is a clear method for spatial deconvolution of the signal, so we can determine its direction and polarization. A third requirement is a way to quantify the noise when multiple motion sensors are used.

In recent publications we have shown that it is possible to deconvolve the complexities of a sphere coupled to a set of mechanical resonators. We have developed a theory that enables us to reconstruct all the information about an incident gravitational wave from the motion of the mechanical resonators. We have also constructed a room-temperature prototype antenna, and have shown that the problems associated with the breaking of perfect symmetry assumed in the theory can be solved in practice.

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