Introduction

The noble gases are also well known as the inert gases, reflecting their characteristic lack of chemical interaction with other elements. In the extreme case, a substance whose atoms fail to interact with other substances except by elastic collisions would always be an ideal monatomic gas. In general, the noble gases approach this extreme more closely than other elements. Nevertheless, of course, the noble gases do not fail completely to undergo interactions, and such interactions as do occur are responsible for governing their geochemical distributions.

A number of the basic parameters characterizing the noble gases as elements are presented in Table 2.1. This chapter will treat those aspects of noble gas interactions with other substances that are important geochemically. A much broader and more extensive treatment of the fundamental physical and chemical characteristics of the noble gases can be found in Cook (1961).

It is now well known that despite their name the noble gases (at least Rn, Xe, and Kr) do, in fact, participate in interactions normally considered chemical, notably with F but also with other elements, and the Xe-F bond strength is a substantial 30kcal/mole. Noble gas chemistry is accordingly a subject of considerable theoretical interest. Nevertheless, it is extremely unlikely that conditions resulting in the formation of noble gas compounds would be encountered outside the laboratory, so noble gas chemistry will not be important in geochemistry and will not be discussed here.

In addition to being the collective name for the elements in the rightmost column of the periodic table of the elements, the term “noble gases,” also “rare gases” or occasionally “inert gases,” is a convenient label for the branch of the scientific enterprise concerned with studying the occurrence and distribution of these elements in nature, particularly in the earth and the terrestrial planets. This research area is usually considered part of geochemistry, although other labels would serve as well.

The most familiar and most widely practiced area of geological research involving noble gases is, of course, geochronology, especially K–Ar dating. There are many good books about geochronology and it is not our intention to try to add another. Noble gas geochemistry, the subject of this book, will mean here what it usually suggests in the geological and planetary science community: the study of the natural occurrence of noble gases and what may be learned thereby, other than determination of the ages of rocks.

In the last two decades the discipline of noble gas geochemistry has prospered, at least by the measure of getting its own sessions at scientific conferences and attracting practitioners in sufficient numbers that, regrettably, they no longer all know each other or are even familiar with each other's work. In spite of its fruits, however, noble gas geochemistry often seems to non-practitioners to have much the air of the secret society and its dark art.

Introduction

Their chemical inertness and low abundance make noble gases a unique geochemical tracer, and their application to the study of mantle geochemistry, differentiation, and volatile separation is one of the major successful developments in recent earth science research. Some noble gas isotopic compositions are quite different between the crust and the mantle, and some of these, such as 40Ar/36Ar and 129Xe/130Xe, involve radiogenic isotopes and thus undergo predictable variations in time. Noble gases thus not only provide information on mantle processes and their spatial variations but also provide chronological constraints. In applying noble gases to the study of mantle geochemistry and dynamics, the subject of this chapter, we must first appraise the noble gas state of the mantle and how it differs from the atmosphere. Despite much recent progress, this issue is not yet settled, and some difficulties should be kept in mind during the following discussion. One difficulty is evaluating how representative of the mantle as a whole the various mantle-derived samples actually are. A second difficulty is that noble gases in mantle samples frequently occur in such low concentrations that there can be technical problems in their analysis. A problem corollary to low abundances is that it is not always easy to distinguish true mantle gases from potential atmospheric contamination.

To obtain information on the noble gas state in the mantle, it is necessary to analyze mantle-derived materials that have trapped mantle noble gases.

When the first edition of Noble Gas Geochemistry was published in 1983, this discipline was still comparatively underdeveloped, and few people seemed to expect that this apparently arcane subject would become one of the major tools of geochemistry. But noble gases have become mainstream, spoken of in the same breath as Pb, Sr, and Nd. Due to unique properties such as extreme scarcity in nature and (almost) perfect lack of chemical interaction, noble gases are now being used as a geochemical tracer to address a variety of problems in the earth and planetary sciences in ways that other tracers cannot. In this light, we thought that the time was ripe to revise the first edition in accordance with recent developments.

Current noble gas geochemistry deals with very broad subjects ranging from the origin and evolution of the earth and the solar system to local geological problems. A single-volume monograph cannot deal comprehensively with all these issues. In this revised edition, we, therefore, decided to concentrate on the more fundamental aspects of noble gas geochemistry, necessarily forcing us to give short shrift to many specific geological applications. Considerable space is devoted to a general discussion of the physics and chemistry of noble gases. In the last decade, much laboratory work has led to progress in understanding adsorption, absorption, and diffusion of noble gases in melts and in solids.

Retrospect and Prospect

In view of their scarcity and failure to form chemical compounds, it is not surprising that noble gases remained unknown until relatively late in the history of chemistry. The first known experimental indication of their existence was a persistent gaseous residue after chemical removal of nitrogen and oxygen from air, as noted by Cavendish in 1784; the residue was small, however, “not more than 1/120th part of the whole,” presumably attributed to experimental error, and in any case subsequently ignored. The first definitive identification came when several observers found a previously unknown line in the spectrum of the solar chromosphere during the 1868 eclipse; this was quickly recognized to belong to a new element, not yet known on earth, which was named helium (ηλιov: sun); of course, no chemical characterization was possible.

The actual “discovery” of the noble gases came principally from the work of Rayleigh and Ramsay in the late nineteenth century. In 1892 Rayleigh reported that nitrogen prepared from ammonia was consistently less dense (by 0.5%) than “nitrogen” prepared from air (by removal of oxygen, carbon dioxide, and water). Both Rayleigh and Ramsay, working in collaboration, followed up this experimental clue; pursuing the possibility that the density difference reflected admixture of a heavier gas in air, they, like Cavendish, found a residue when chemically reactive species were removed from air.

Astronomical spectropolarimetry is performed from the X-ray to the radio regimes of the electromagnetic spectrum. The following chapter deals with instruments and their components that are used in the wavelength range from 300 nm to 20 µm. After introducing the terminology and formalisms that are used in the context of astronomical spectropolarimeters, I discuss the most widely used optical components. These include crystal and sheet polarizers, fixed monochromatic and achromatic retarders, and variable retarders such as liquid crystals and photoelastic modulators. Since polarimetric measurements are often limited by systematic errors rather than statistical errors due to photon noise, I deal with these instrumentally induced errors in detail. Among these errors, I discuss instrumental polarization of various kinds and chromatic and angle of incidence errors of optical components. I close with a few examples of successful, modern night-time and solar spectropolarimeters.

Introduction

Scope of chapter

Astronomical polarimetry is performed over a large fraction of the electromagnetic spectrum, from X-rays to radio waves. The following chapter is restricted to the optical range that can be observed from the ground, i.e. 300 nm to 20 µm. Far-infrared polarimetry is described by Hildebrand in this volume. Information on polarimetry in the X-ray and radio regimes can be found in Tinbergen (1996).

Furthermore, the following text focuses on instruments for spectropolarimetry, i.e. the instrumental aspects of polarimetry with a spectral resolution that resolves spectral lines, either with a spectrograph or a filter, i.e. a spectral resolution of λ/δλ = R > 10,000.

The Sun is unique as an astrophysics laboratory because we can spatially resolve its structures in great detail and apply sophisticated diagnostic techniques that require high spectral resolution. The magnetic flux in the solar atmosphere occurs in extremely fragmented, nearly fractal form, with a range of spatial scales that extend well beyond the angular resolution limit of current telescopes and into the optically thin regime. The magnetic field leaves various kinds of “fingerprints” in the polarized spectrum. In the past only the fingerprints of the Zeeman effect have been used, but more recently new, highly sensitive imaging polarimeters have given us access to other physical effects. In particular a wealth of previously unknown spectral structures due to coherent scattering processes have been uncovered. These phenomena show up in linear polarization as a new kind of spectrum (the so-called “second solar spectrum”), which bear little resemblance to the ordinary intensity spectrum. Magnetic fields modify the coherent scattering processes and produce polarized spectral signatures that greatly extend the diagnostic range of the Zeeman effect. This diagnostic window has just been opened, and we are only now beginning to develop the needed diagnostic tools and apply them to learn about previously “invisible” aspects of solar magnetic fields.

The Sun's magnetic field — An introductory overview

Role of magnetic fields in astrophysics

Most of the matter in the universe, like stars, nebulae, and interstellar matter, consists of plasma, partially ionized gas with high electrical conductivity.

The main techniques used to diagnose magnetic fields in stars from polarimetric observations are presented. First, a summary of the physics of spectral line formation in the presence of a magnetic field is given. Departures from the simple case of linear Zeeman effect are briefly considered: partial Paschen-Back effect, contribution of hyperfine structure, and combined Stark and Zeeman effects. Important approximate solutions of the equation of transfer of polarized light in spectral lines are introduced. The procedure for disk-integration of emergent Stokes profiles, which is central to stellar magnetic field studies, is described, with special attention to the treatment of stellar rotation. This formalism is used to discuss the determination of the mean longitudinal magnetic field (through the photographic technique and through Balmer line photopolarimetry). This is done within the specific framework of Ap stars, which, with their unique large-scale organized magnetic fields, are an ideal laboratory for studies of stellar magnetism. Special attention is paid to those Ap stars whose magnetically split line components are resolved in high-dispersion Stokes I spectra, and to the determination of their mean magnetic field modulus. Various techniques of exploitation of the information contained in polarized spectral line profiles are reviewed: the moment technique (in particular, the determination of the crossover and of the mean quadratic field), Zeeman-Doppler imaging, and least-squares deconvolution. The prospects that these methods open for linear polarization studies are sketched.

Most observational work in astrophysics has so far been carried out mainly on the basis of the intensity of the radiation received from the object observed as a function of wavelength. However, an important and frequently overlooked aspect of electromagnetic radiation is its state of polarization, which is related to the orientation of the electric field of the wave. The state of polarization can be conveniently characterized in terms of four quantities that can be measured by furnishing our telescopes with a polarimeter. These observables are the four Stokes parameters (I, Q, U, V) which were formulated by Sir George Stokes in 1852 and introduced into astrophysics by the Nobel laureate Subrahmanyan Chandrasekhar in 1946. A quick, intuitive definition of the meaning of these four parameters can be obtained from Figure 1 of the chapter by Prof. Landi Degl'Innocenti in this book, which we borrowed for the poster announcing the Twelfth Canary Islands Winter School on Astrophysical Spectropolarimetry.

In physics laboratory experiments, where the magnetic field is known beforehand, the observed polarization signals are used to obtain information on the atomic and molecular structure of the system under study. In astrophysics we have the inverse problem, the magnetic field being the unknown quantity. To obtain information about cosmic magnetic fields, therefore, we have to learn how to interpret spectropolarimetric observations correctly by resorting to our knowledge of atomic and molecular physics.

This course is intended to give a description of the basic physical concepts which underlie the study and the interpretation of polarization phenomena. Apart from a brief historical introduction (Sect. 1), the course is organized in three parts. A first part (Sects. 2-6) covers the most relevant facts about the polarization phenomena that are typically encountered in laboratory applications and in everyday life. In Sect. 2, the modern description of polarization in terms of the Stokes parameters is recalled, whereas Sect. 3 is devoted to introduce the basic tools of laboratory polarimetry, such as the Jones calculus and the Mueller matrices. The polarization phenomena which are met in the reflection and refraction of a beam of radiation at the separation surface between two dielectrics, or between a dielectric and a metal, are recalled in Sect. 4. Finally, Sect. 5 gives an introduction to the phenomena of dichroism and of anomalous dispersion and Sect. 6 summarizes the polarization phenomena that are commonly encountered in everyday life. The second part of this course (Sects. 7-14) deals with the description, within the formalism of classical physics, of the spectro-polarimetric properties of the radiation emitted by accelerated charges. Such properties are derived by taking as starting point the Liénard and Wiechert equations that are recalled and discussed in Sect. 7 both in the general case and in the non-relativistic approximation. The results are developed to find the percentage polarization, the radiation diagram, the cross-section and the spectral characteristics of the radiation emitted in different phenomena particularly relevant from the astrophysical point of view.

Maser radiation occurs naturally in interstellar space. Masers provide extremely bright beacons that trace small scale structure in the host environments, which range from comets all the way to external galaxies. The radiation is sometimes, though not always, polarized. When it is, the polarization can reach much higher levels than in thermal sources—the radiation from some masers is fully polarized. This chapter provides an overview of astronomical masers, discusses the differences between maser and non-maser radiation and covers the fundamental theory of maser radiation and its polarization.

In 1963, the first radio emission from an interstellar molecule, the hydroxyl radical OH, was discovered. The ground state of this molecule produces four radio lines at wavelengths of approximately 18 cm (figure 1). When an atomic or molecular system radiates in several lines, certain ratios are expected between the line intensities. However, almost from the start the emission patterns displayed by the four OH lines in most astronomical sources were peculiar, deviating considerably from expectations. In 1965 these peculiarities culminated with the discovery of radio line emission with such exceptional properties, the emitting substance was dubbed ‘mysterium’ for lack of an obvious explanation. The exceptional properties included extremely high brightness, line widths much narrower than in all previous cases and substantial polarization. It did not take too long, though, to realize that ‘mysterium’ radiation was simply maser emission from interstellar OH.

Optical spectropolarimetry and broadband polarimetry in other wavebands has been a key to understanding many diverse aspects of AGN. In some cases polarization is due to synchrotron radiation, and in other cases it's due to scattering. Recognition of relativistically beamed optical synchrotron emission by polarization was vital for understanding blazars (BL Lacs and Optically Violently Variable quasars), both physically and geometrically. Radio polarimetry of quiescent AGN is equally important, again for both purposes. Scattering polarization was central to the Unified Model for Seyferts, Radio Galaxies and (high ionization) Ultraluminous Infrared Galaxies. It provides a periscope for viewing AGN from other directions. Finally, if we could understand its message, polarization would also provide major insights regarding the nature of the AGN “Featureless Continuum” and Broad (emission) Line Region.

I point out that high ionization ULIRGs have all the exact right properties to be called Quasar 2s. Mid-IR observations generally don't penetrate to the nucleus, greatly reducing their ability to diagnose the energy source. In particular, LINER ULIRGs aren't necessarily starburst-dominated, as has been claimed.

Seyfert Galaxies

Type 2 Seyferts

Polarization alignments and hidden Type 1 Seyfert nuclei

In the 1970s the continua of Seyfert 2s were decomposed into two parts: relatively red light from the old stellar population, and a bluer component modeled satisfactorily with a power law. The latter was called the “Featureless Continuum,” in a commendable attempt to avoid prejudice as to its nature.

After twelve years, the Canary Islands Winter School continues to provide a unique opportunity for the participants to broaden their knowledge in a key field of astrophysics. The idea works because promising young scientists and invited lecturers interact, learn and enjoy science in the pleasant environment of the Canary Islands.

The XII edition of the Canary Islands Winter School looked at the Universe from a relatively unexploited viewpoint, namely that fostered by a multidisciplinary branch of science which has a great future in store: spectropolarimetry. Thanks to theoretical and observational spectropolarimetry we will be able to explore new facets of the Universe while unveiling new discoveries still hidden in the electromagnetic radiation we receive. The large telescopes of the future – among them the 10.4 m Gran Telescopio Canarias – and advanced postfocus instrumentation should be designed with a view to rendering feasible high precision spectropolarimetric observations. The theoretical interpretation of observed polarization signals will allow new fundamental advances in our knowledge of cosmic magnetic fields. Spectropolarimetry could well be a revolutionary technique in the astrophysics of the XXI century. That is why the XII Canary Islands Winter School of Astrophysics has been devoted to this promising and exciting field.