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.

Introduction

As we have seen in the preceding chapter, observations made in cool visible and EUV lines have provided extensive information on the large-scale systems of loops which dominate the structure of the lower corona above active regions. The loops are believed to trace out closed lines of force of the magnetic field which protrude up from beneath the photosphere and expand to fill the whole of the coronal volume above an active region. Hence a picture of the loop systems gives us some insight into the three-dimensional configuration of the magnetic field. But the picture obtained from observations of cool loops is far from complete. For more detail we have to turn to observations of hot loops, filled with material at coronal temperatures of a million degrees or more; these form the subject of the present chapter.

Emission from material at coronal temperatures dominates the EUV and soft X-ray regions of the solar spectrum. The lack of any appreciable photospheric or chromospheric emission at these wavelengths enables the corona to be viewed directly against the disk and, in fact, most of the available information on hot loops has been obtained from such (space) observations. In addition, other important contributions to our knowledge have come from the visible and radio regions of the spectrum. The line and continuum radiation emitted by the corona in the visible region is many orders of magnitude too faint to be detected on the disk against the glare of the underlying photosphere.

Introduction

Solar flares are remarkably diverse and complicated phenomena involving the transient heating of localized regions of the corona and underlying chromosphere within an active region. The sudden release of energy is accompanied by the emission of electromagnetic radiation over a very wide span of the spectrum, ranging – in extreme cases – from γ-rays to kilometric radio waves. In almost all cases flares seen in the chromospheric Hα line also produce an increase in the flux of soft X-rays. Moreover, the variation in the soft X-ray flux with time roughly follows that of the Hα intensity at the brightest point of the flare (Svestka, 1981, p. 74). Both curves are characterized by a rapid rise to a comparatively short-lived maximum, followed by a much slower decay. The intensity of the soft Xray emission generally increases with the optical importance of the flare, although individual flares may show marked deviations from this rule. For this reason it has become customary to assign both an optical (Hα) and an X-ray importance to each flare. Both the Hα and soft X-ray emission pertain to what is conventionally called the ‘thermaly’ or ‘quasi-thermal’ component of the flare, i.e. they originate in plasmas where the distribution of electron velocities is believed to be Maxwellian.

Flares are classified optically according to their area at the time of maximum Hα brightness into the four categories listed in Table 4.1, adapted from Svestka (1981).

The discovery that a significant part of the energy emission from the solar corona is concentrated along well-defined curved paths – called loops – represents a major advance in our understanding of the Sun. Such plasma loops are the basic structural elements of the corona, particularly in and over active regions. Moreover, they play a decisive role in the origin and physics of solar flares. Our new insight is due largely to the wealth of space observations of the Sun obtained, in particular, from the manned satellite Skylab (1973–4) and the unmanned satellites Solar Maximum Mission and Hinotori which followed. Ground-based observations in the visible and microwave regions of the electromagnetic spectrum have also played a vital role. The literature on coronal plasma loops is vast and includes not only hundreds of research papers but also the proceedings of numerous symposia and workshops. This book presents for the first time a comprehensive, unified and well-illustrated account of the properties of coronal loops based on the best space and ground-based observations currently available (Chapters 2–4). A magnetohydrodynamic analysis of the stability and dynamics of loops is presented in Chapter 5, while the final chapter (Chapter 6) explores the wider implications of the loop regime on our understanding of both the solar corona and stellar coronae.