Introduction

Resonant-bar detectors are designed to measure the acoustic signal induced in a massive bar due to its coupling to a gravitational wave. The large amplitude of thermal vibration in the bar normally considerably exceeds the amplitudes expected from astrophysical sources, and without methods to suppress this noise the principle of detection by resonant masses would be impossible. Weber's key contribution was the realisation that in a high Q antenna-one with a low acoustic loss – the effective noise energy is reduced by a factor ∽τi/τa where τi is the effective measurement integration time, and τa is the antenna ring down time. The advantage from using a low acoustic loss antenna is a direct result of the fluctuation-dissipation theorem. A high Q antenna approaches an ideal harmonic oscillator, whose motion is exactly predictable at a time in the future from the observed amplitude, frequency and phase at an earlier time.

In this chapter we will examine the key concepts of resonant-bar detectors, and provide the framework for the following chapters on different aspects of resonant-bar technology.

Intrinsic noise in resonant-mass antennas

In 1971, Gibbons and Hawking gave an analysis of resonant-mass antennas which led to improved techniques and better understanding of the noise sources. They noted that Weber had monitored the energy or RMS amplitude of the fundamental mode of his antennas.

Introduction

The detection of gravitational waves with frequencies less than 1 kHz appears to be impossible on earth, due to the magnitude of the earth's seismic noise at these frequencies. These waves, therefore, will only be seen in space-based detectors.

A simple gravitational wave detector in space can be created by setting up two free masses and using an electromagnetic signal passing from one to the other as a probe of the spacetime curvature of the region between them. This is the fundamental idea involved in several gravitational wave detectors in space, including pulsar timing, two-way Doppler tracking of interplanetary spacecraft, and spaceborne interferometers. In this article we will discuss the theory and practice of such detectors.

The outline of this chapter is as follows. In section 17.2, we will briefly discuss the sources for the gravitational waves that are to be the targets of the space-based detectors. Then, in section 17.3, the effect of a plane gravitational wave on the arrival time of electromagnetic signals is derived. Our derivation follows that of Hellings (1983) and gives the same result as that first found by Estabrook and Wahlquist (1975). In sections 17.4 and 17.5, these results are used to discuss existing results from pulsar timing experiments and spacecraft Doppler tracking experiments. Finally, prospects for space interferometers are discussed in section 17.6.

Generally, gravitational radiation (GR) is divided into three classes according to its nature: burst, continuous and stochastic waves. Continuous waves can be described as a sinusoidal stationary train of metric perturbation for a sufficiently long time, in contrast with burst waves, which are characterized by their short duration. The third type of GR, stochastic waves, is characterized by its random nature of statistics of arrival, regardless of wave form.

In searching for continuous waves with resonant antennas, various kinds of detecting methods and signal analyses are employed which are different from those used in the detection of burst waves. For example, a resonant antenna should be tuned precisely to the frequency of the source in order to obtain the best sensitivity. Also, long-time integration of the signal output from the detector is a necessary technique for distinguishing a coherent signal buried in a noise. Under these circumstances, usually, the sensitivity of a detector for continuous waves is determined by the level of Brownian motion of the antenna. These features are not common with the case of burst events.

Continuous sources, such as pulsars and binaries, have rather low frequencies, except for rapid pulsars (Backer et al., 1982) or new-born pulsars. Since the pioneering work of J. Weber (1969) bars have been widely used as resonant antennas in detecting burst waves.

Introduction

All laser interferometers rely on measuring the strain in space caused by a gravitational wave, sensitivities of the order of 10–22 over millisecond timescales being required to allow a good probability of detection.

In principle the strain as monitored by the change in separation of two test masses hung as pendulums can be measured against the wavelength of light from a stable source, but the degree of wavelength or frequency stability required of the source is unreasonably high. It is much more conceivable to measure the distance between test masses along an arm with respect to the distance between similar masses along a perpendicular arm. This is particularly appropriate since the interaction of a gravitational wave is quadrupole in nature and so can cause an opposite sign of length change in the two arms. The measurement of a differential length change of this type when performed by interferometry puts much less demand in principle on the frequency stability of the illuminating laser light – since a Michelson interferometer is insensitive to changes in the wavelength of the light used if the path lengths are equal. However, in practice a fairly high degree of frequency stability is required. In the case of optical delay lines in the arms of a Michelson interferometer this is a result of the difficulty in achieving equal path lengths and of some light being scattered back early without completing the full number of reflections (Billing et al, 1983).

Principle of measurement

Gravitational waves manifest themselves as a variation of the metric of space-time. From an experimental point of view this can be considered as a time-dependent strain in space, which can be observed optically by registering the travel time of light between free test masses. Such experiments were first proposed by Gertsenshtein and Pustovoit (1963) and investigated in more detail by Weiss (1972) and Forward (1978). The corresponding arrangements are broadband in nature, as the effect of a gravitational wave onto the propagation of light between essentially free test masses is to be observed. No frequency is preferred, unless the storage time of the light inside the interferometer becomes comparable to the periods of the signals to be observed. Resonances of the test masses, for instance, are unwanted side-effects in this context. Since the strain in space introduced by gravitational waves has opposite signs in two directions perpendicular to each other, an ideal instrument is a Michelson interferometer (figure 11.1a). The signal at its output is a function of the path difference between the two arms. The beamsplitter and the mirrors serve as test masses. A gravitational wave with optimal polarization and direction of propagation would be incident perpendicularly on to the plane of the interferometer, making one arm shrink and the other one grow during half of a period; for the next half cycle the signs change.

This book is about gravitational radiation detectors. It is about experimental physics: the physics of extremely sensitive instruments designed to detect the infinitesimal time varying strains in spacetime which are gravitational waves.

For half a century most physicists considered the detection of gravitational waves to be an impossibility, but 30 years ago Joseph Weber first outlined possible means of detection, and followed this by a lonely pioneering decade of instrument development. About 20 years ago a range of new technologies appeared on the horizon, and we have now seen two decades of advance in a variety of areas, often driven by the needs of gravitational radiation detection. Looked at as a whole these represent a spectacular advance in technological capability, and now it is possible to look forward to a future when gravitational astronomy will plug a major gap in our knowledge of the universe.

The first area of intense effort was in the development of improved resonant bar antennas. This led to the development and understanding of systems and materials with ultralow acoustic loss, and ultralow electromagnetic loss. The development of low loss microwave cavities led to new technologies for vibration transducers and frequency standards. The need for sensitive amplifiers was met by the development of greatly improved superconducting quantum interference devices (SQUIDs) and cryogenic gallium arsenide field effect transistor amplifiers. The understanding of quantum mechanical limitations to measurement led to the development of techniques called variously squeezing, quantum nondemolition and back action evasion.

Introduction

The gravitational wave detection technique discussed here is a long-baseline nearly-free-mass technique, devised initially with the aim of obtaining high gravity-wave sensitivity with minimum practicable cost. The distinctive part of the technique is the use as sensors of a pair of optical cavities formed between mirrors attached to test masses defining two perpendicular baselines, illuminated by an external laser source. To introduce the basic concept it may be useful to summarize the train of ideas which led up to it.

Experience and analyses in the early 1970s of resonant-bar gravity-wave detectors indicated that, although it is in principle possible to achieve by this technique the high sensitivity likely to be required for detection of expected astronomical sources, the small energy exchange with the gravitational wave leads to increasingly difficult experimental problems as sensitivity is improved. Alternative techniques using free test masses at large separations, monitored by optical or microwave methods, can sample much larger baselines and make relatively less serious any thermal, seismic, and amplifier noise, as well as the uncertaintyprinciple quantum limit for the test masses. Measurement of the small relative displacements involved, which might correspond at 1 kHz to strains of order one part in 1021 or less in a 1 kHz bandwidth, is however a serious challenge for interferometers of any kind. If a simple Michelson interferometer were used the photon shot noise limit would demand an impracticably high light flux. One way of improving sensitivity was proposed by R.

Introduction to recycling

All the long baseline interferometers for the detection of gravitational radiation which are presently being studied are based on the construction of a large, Michelson-like interferometer with an armlength of 1 to 4 km, containing some kind of gravito-optic transducer in each arm. In order to improve the shot-noise limited sensitivity, all these interferometers will use high-power lasers, in conjunction with so-called light recycling techniques. The basic idea of recycling was proposed by R. W. P. Drever (1983): it consists in building a resonant optical cavity which contains the interferometer, so that, if the losses are low and if the cavity is kept on resonance with the incoming monochromatic light, there is a power build-up which results in a reduction of the shot noise. This can be realized in different ways, depending on the geometry of the gravito-optic transducer (delay line or Fabry-Perot).

A general theory of recycling interferometers was recently developed and published (Vinet et al, 1988) and the Garching (Schnupp, 1987) and Orsay (Man, 1987) groups have obtained the first experimental verifications of the efficiency of this technique. In this chapter, we first remind the reader of the main ideas and results of the theory, which is fully expressed in Vinet et al. (1988). We then describe today's experimental achievements, and we end up with a short discussion of possible future improvements.

Introduction

The preceding chapter has discussed the structure and heating of single plasma loops in the solar corona. We turn now to consider systems of loops, exploring the questions of the origin, evolution and global topology of plasma loops and their associated magnetic fields in the corona of the Sun and in the coronae of other stars.

Two major physical processes determine the structure and development of the plasma loops that are so frequently delineated in the solar corona. First, the coronal magnetic field in regions occupied by loops must conform to an elongated or tubular topology compatible with the presence of potential or force-free conditions in the corona (Sections 5.2.2, 5.2.3) and with the existence of spatially isolated sources with complex polarities intermingled in the photosphere. Secondly, the injection, transport and dissipation of matter and energy fluxes in the corona must be localized in and guided by this tubular magnetic topology. The anisotropic character of energy and mass transport coefficients in the presence of a magnetic field helps to explain this behaviour. However, anisotropic transport coefficients by themselves do not explain why only some magnetic tubes are delineated at any time. Spatially localized conversion and concentration of the mass and energy fluxes must also occur and, as we shall see, this aspect of the phenomenon is mediated by processes occurring beneath the visible layers of the Sun.