THE STATIC UNIVERSE IN NEWTON'S THEORY

Back in the 1690s, Isaac Newton attempted an ambitious application of his law of gravitation. Newton wanted to describe, with the help of his theory of gravity, the largest physical system that can be imagined – the Universe. How did Newton fare in this attempt?

In a letter to Richard Bentley dated 10 December 1692, Newton expressed his difficulties in the following words:

Figure 9–1, which illustrates a finite and uniform distribution of matter in the form of a sphere initially at rest, helps explain Newton's difficulty. Will the sphere stay at rest forever? The matter in the sphere has its own force of gravity, which tends to pull the different parts of the sphere toward one another, with the result that the sphere as a whole contracts. We have encountered this force of selfgravity in stars (Chapter 4) and in the phenomenon of black-hole formation (Chapter 7).

In this chapter, instrumental principles will be discussed, with emphasis on system behaviour and without any preconceptions about the wavelength at which one observes. Practical illustrations will inevitably relate to a particular wavelength region (optical and radio, which is where the experience resides). It may therefore be necessary to scan chapter 6 before attempting to understand the present chapter in detail.

Telescopes

The first optical element of an astronomical observing system is always a telescope (disregarding the atmosphere for the present discussion). It is important to realize that, in general, a telescope will modify the polarization of the radiation before the polarimeter measures it. It is equally important to have some general feeling for the conditions under which such modification is likely to be appreciable and how it can be minimized.

The guiding principle is symmetry; any departures from full symmetry will modify the polarization. The considerations below illustrate this, but full understanding will require mathematical treatment by Mueller or Jones calculus, with optical constants applicable to the wavelength of interest.

Oblique incidence on a mirror produces both diattenuation (polarizing action) and retardation (wave plate action). These effects are minimal at near-normal and, somewhat surprisingly, at grazing incidence; the largest effects occur at intermediate angles of incidence, the details depending on the values of the real and imaginary parts of the refractive index (which in their turn depend on the wavelength).

In this final chapter, several original papers from the literature are introduced, primarily as illustrations of modern instrumentation. The focus of this book being the measurement of polarization, the astronomy involved was a secondary consideration in selecting these particular papers from the wide range available. Readers are urged to test their grasp of polarimetric fundamentals by selecting a dozen or so further papers from those listed in the subject index of the more recent volumes of Astronomy and Astrophysics Abstracts under ‘polarimeters’, ‘polarimetry’ or ‘polarization’.

Multi-channel optical polarimetry using photomultipliers

A suitable example of optical polarimetry by the ‘classical’ technique of 100 Hz modulation and photomultiplier detectors is given in Können and Tinbergen (1991) and Können et al. (1993). It concerns an attempt to detect ice crystals in the upper parts of the Venus atmosphere by using the polarization peak at the 22° halo angle as a diagnostic. A large body of earlier Venus polarimetry exists, and scientific results derived from it are reviewed in Van de Hulst (1980, section 18.1.5 and references therein).

The terrestrial 22° halo and related phenomena owe their polarization to birefringence of the ice crystals that produce the halo. These crystals operate as 60° prisms, deviating the light from the Sun by an amount depending on the refractive index of the ice, hence by an amount which depends on the polarization of the light.

Almost every issue of the leading astronomical journals includes some polarimetry, either directly or indirectly. Polarimetry as a working tool has clearly come of age. Optical and radio techniques are most advanced, but infrared, sub-millimetre and ultraviolet are following on rapidly, while X-ray techniques are being developed also. There is no technical reason why astronomers should not use polarimetry when it suits their astronomical purposes; polarimetry often yields information that other methods of observation cannot give, and this is the main reason why all astronomers, and today's students in particular, should understand the basic ideas behind polarimetry.

Within the astronomical context, the degree of polarization is often low; a few per cent is typical, though both higher and (much) lower values occur. A polarimetric measurement is basically that of the ratio of the small difference between two signals to their sum. Difference and ratio methods have been devised to measure this small difference without systematic bias or drift errors, but photometric noise (detector noise or photon noise of the signal itself) is always present. To reduce this noise to the low level required for sufficiently accurate polarimetry, considerable observing time on a large telescope is generally needed. Polarimetry should therefore not be used indiscriminately, but only when it provides insight which other methods cannot give. Such judgment also requires a grasp of polarimetric basics.

This book aims to create an awareness of what polarimetry can do and at what price (in observing time, in complexity of equipment and of procedures).

In het land der blinden is Eénoog koning. This saying in my mother tongue contains a sufficient number of Germanic roots for English speakers to guess that the situation depicted is only marginally better than ‘the blind leading the blind’. It aptly describes the current situation in astronomical polarimetry and provides the justification for my attempt to write a primer for students and other polarimetric novices. If we can take today's students straight from polarimetric fundamentals to what is best in modern research practice, then five years from now we shall have a polarization community with both eyes wide open and firmly fixed beyond present-day horizons. That is what this book is about.

Polarimetry, performed mainly by optical or radio specialists, has already made a considerable impact on astronomy, and it deserves to be a standard observational technique, to be used whenever it is best for the job in hand. Accordingly, all astronomers should acquire polarimetric basics. My aim is to allow the reader, starting at first principles, to make use of the very latest literature. To preserve readibility, I have omitted most of the historical development. The References section at the end of the book reflects this attitude; interested readers can always trace the history backwards from modern papers.

I have tried to resist any tendency to write a comprehensive monograph.

In this chapter, the main concepts of polarized radiation will be introduced and discussed. These concepts apply at all wavelengths. Electromagnetic radiation will be treated as a continuous travelling-wave phenomenon. Quantum considerations can be postponed until the moment the radiation strikes a detector and is converted into an electrical signal. Ideal detectors are not sensitive to polarization, and, to the extent that a real-life detector can be seen as an ideal one preceded by polarization optics, quantum and polarization considerations can live side by side without the one influencing the arguments concerning the other. Of the electromagnetic wave, only the electric vector will be considered; the corresponding magnetic vector follows from Maxwell's equations.

Astronomical signals are noise-like. These noise-like variations of electric field strength (of the electromagnetic wave) may be passed through a narrow-band filter, so that a ‘quasi-monochromatic’ wave remains. Such a wave contains a very narrow band of frequencies and may be seen as a sinusoidal carrier wave at signal frequency, modulated both in amplitude and phase by noise-like variations. The highest frequencies (the fastest variations) in the modulating noise determine the width of the sidebands around the carrier wave in the frequency spectrum. Any wide-band (‘polychromatic’) signal may be seen as the sum of many quasi-monochromatic signals, all with different carrier frequencies and generally each with its own amplitude and phase modulation.

In this chapter I shall discuss the scientific reasons for measuring the polarization of astronomical signals. The central question is: ‘What does nature express as polarization rather than as some other property of the signal?’. This, of course, is the scientific point of departure for all astronomical polarimetry, but the basic concepts of polarization and (un)polarized radiation needed clarification before scientific necessity could be discussed properly. This chapter will be only a brief overview of the relevant astronomy; a number of recent reviews are available to help the reader become familiar with the astronomical applications. The subject of this book is polarimetry, the desirability of measuring the polarization will be taken for granted.

The light of most stars is itself unpolarized. In fact, whenever one needs an optical ‘zero-polarization’ reference source, one is generally pushed to use stars rather than lamps. The reason for the low polarization is the great distance (point source) and the spherical symmetry of most stars: any linear polarization there might be is averaged out over the star's visible disc. In the radio domain, antenna properties are highly polarization-dependent, and without specialized techniques large spurious apparent polarization is generated within the instrument. Thus, circumstances conspired to make astronomical polarimetry a late arrival. Even in the spectral regions of greatest instrumental sophistication, polarimetry remained a specialist technique; solar physics has been the notable exception. As a corollary of this lack of attention to polarimetry, awareness of polarization-induced photometric errors within telescopes and instruments has been minimal.

This chapter will focus on those aspects of polarimetric instruments that are peculiar to certain wavelength regions. The concepts discussed in previous chapters will be used freely. Non-polarimetric wavelength-peculiar concepts will generally be taken for granted, but a few are essential and must be recapitulated briefly.

Optical/infrared systems

Optical polarimetric instrumentation has a long history of development. Early polarimeters had errors at the level of a few tenths of a per cent at best, and polarization signals were small, so that polarimetry was very much a specialist craft. B. Lyot was the first to obtain very high accuracy by devising a modulator and using it on the Sun. For stars, the signals were generally so small that photon shot noise was appreciable, and there was little incentive to design sophisticated systems of unavoidably smaller throughput.

The situation has changed drastically within the last decade or two. Larger telescopes are available, CCD detectors now offer thousands of parallel channels of potentially very good accuracy, and improved modulators of high transmission have been devised. The higher signal levels have meant that greater resolution (spectral, temporal, spatial) can be used, and this has had the effect of increasing the degree of polarization provided by nature (less smearing of polarizations from neighbouring resolution elements); the end result is that (i) many more situations within astronomy can usefully be tackled by polarimetry without exceptional cost in telescope time and (ii) ‘common-user’ polarimetry is becoming available in the optical/near-infrared wavelength region (the ‘CCD domain’).

This chapter introduces the tools used by astronomers and instrument designers in describing the action of a medium on the polarization of the radiation passing through it. In the majority of situations encountered in astronomy, the phase of the wave is unimportant, and we need a way to describe the transformation of Stokes parameters, i.e. the changing polarization forms which support the flow of radiant energy. For cases where the phase of the polarized radiation is important (e.g. polarization effects within an optical interferometer, the focusing of a plane wave by a radio telescope, or the amplification of polarized radiation within an astronomical maser), an alternative formulation will be introduced (in section 4.2) that describes the transformation (including phase) of the electric field vibrations of two orthogonal 100% polarized waves (usually linear polarization). In this formulation, partial polarization cannot be handled, and we must make separate calculations for two orthogonal polarizations of the incident radiation, constructing the incoherent sum at the end. Shurcliff (1962, sections 8.6, 8.7, 8.9) details the early history of these two calculi and compares their fields of use; a concise statement of the relationship between the two calculi may be found in Stenflo (1994, section 2.6).

Mueller matrices

As discussed in chapter 2, the four Stokes parameters denote the flow of radiant energy in specific vibrations of the electromagnetic field, and all four are expressed in the same units.

Today, the study of The Structure of the Sun is one of the most exciting and rapidly evolving fields in physics. Helioseismology has provided us with a new tool to measure the physical state of the interior of a star, our Sun. This technique is successful to a depth of 0.7 R⊙ (i.e. 0.3 R⊙ from the centre). Deeper than this, observational data has been scarce. However, data are now becoming available from Earth-bound helioseismic networks (GONG, TON, IRIS, BISON,…) and from experiments on board SOHO (GOLF, MDI, VIRGO). These should allow the spectrum of gravity modes for the Sun to be determined, and thus the physical state of the solar core.

This book provides an up-to-date and comprehensive review of our current understanding of the Sun. Each chapter is written by a world expert. They are based on lectures given at the VIth Canary Islands Winter School on Astrophysics. This timely conference brought together leading scientists in the field, postgraduates and recent postdocs students. The aim was to take stock of the new understanding of the Sun and to focus on avenues for fruitful future research. Eight lecturers, around 60 students, and staff from the IAC met in the Hotel Gran Tinerfe in Playa de las Américas (Adeje, Tenerife) from the 5th to the 16th of December, 1994. It was a fortnight of intense and enjoyable scientific work.