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.

The large-scale features of the magnetic field in the arms of the Galaxy have been traced by observations of polarized starlight, synchrotron emission, Zeeman splitting, and Faraday rotation. More recently, it has become possible to map fields in dense clouds by observations of polarized thermal emission from magnetically aligned dust grains. Observations at far-infrared and submillimeter wavelengths provide measurements of the field as projected on the sky at hundreds of points in individual clouds. In the polarization maps, especially when compared at several wavelengths, one finds examples of fields shaped by gravitational contraction, differential rotation, and compression. One also finds evidence for unresolved thermal structure and turbulence. To interpret the results one must understand the physical principles that relate emission, absorption, and scattering; and that relate polarization to the shapes and materials of the emitting dust grains. When these principles are applied to emission one finds that the degree of polarization in homogeneous clouds should be nearly independent of wavelength in the far-infrared and submillimeter portions of the spectrum. The steep polarization spectra actually observed can tentatively be understood if one assumes a heterogeneous temperature and radiation structure in which there is a correlation between temperature and grain alignment. The potential sources of systematic errors in polarization measurements are such that anyone entering the field must carefully review the appropriate observing and analysis techniques. With attention to the required techniques and with new instruments to be commissioned in the next few years it should become feasible to pursue scientific goals that have thus far been largely inaccessible.

Recent developments in the spectropolarimetric study of compact objects, specifically black holes (stellar and massive) and neutron stars are reviewed. The lectures are organized around five topics: disks, jets, outflows, neutron stars and black holes. They emphasize physical mechanisms and are intended to bridge the gap between the fundamentals of polarimetry and the phenomenology of observed cosmic sources of polarized radiation, as covered by the other lecturers. There has been considerable recent progress in spectropolarimetry from radio through optical frequencies and this is producing some unique diagnostics of the physical conditions around compact objects. It is argued that there is a great need to develop a correspondingly sensitive polarimetric capability at ultraviolet through γ-ray energies.

Spectropolarimetric observations, particularly those at radio and optical wavelengths, have played an important role in high energy astrophysics. From the discovery of synchrotron radiation to the first good evidence for AGN unification, from the polarization patterns in the coherent emission of radio pulsars to the discovery of variable, linear polarization in the absorption troughs of broad absorption line quasars, polarization studies often provide the best and sometimes the only clue we have as to the geometric disposition of the emitting elements in these diverse sources when we cannot resolve them directly.

These notes summarize lectures delivered by Roger Blandford at the XII Canary Islands Winter School on Astrophysical Spectropolarimetry.

Introduction

Rapid expansion in nova, stellar atmospheres of supernovae and similar objects is established through several spectroscopic observations. In spectra of these objects, the absorption lines shift towards the violet side from the rest position indicating matter outflow in their atmospheres. These lines are accompanied by red shifted emission characteristics of P Cygni type as seen in figure 7.1 (see Beals (1950), Kuan and Kuhi (1975)). Beals (1929, 1931) interpreted the large widths in the lines of WR spectra to be due to the velocities of expansion of the order of 3000 km s-1 indicative of a rapid outflow of the matter in the outer layers of these stars. He suggested that this outflow of matter is influenced by the radiation pressure in the medium.

It is difficult to obtain the solution of the transfer equation in such spherical media. Beals (1929, 1930, 1931, 1934), Chandrasekhar (1934), Gerasimovič (1934) and Wilson (1934) investigated this problem assuming the medium to be optically thin, neglecting the transfer effects. Struve and Elvey (1934) found that the Doppler widths derived from the flat part of the growth curve were much larger than the thermal value, which they attributed to the ‘turbulent’ motion in the atmosphere which is non-thermal. Struve's observations (1946) showed large scale velocities through the fact that the line profile widths in certain stars were larger than the Doppler widths obtained from curve of growth analysis of their spectra.