The importance of EUV spectra of white dwarfs

It is clear, from chapters 3 and 4 (sections 3.6, 3.7, 4.3.2), that the ROSAT and EUVE sky surveys have made significant contributions to our understanding of the physical structure and evolution of white dwarfs. Among the most important discoveries are the ubiquitous presence of heavy elements in the very hottest DA stars (above 40 000–50 000 K), the existence of many unsuspected binary systems containing a white dwarf component and a population of white dwarfs with masses too high to be the product of single star evolution. In each case, however, the detailed information that could be extracted from the broadband photometric data was often rather limited. For example, although simple photospheric models (e.g. H+He) could often be ruled out, it was not possible to distinguish between more complex compositions with varying fractions of He and heavier elements. Furthermore, rather simplistic assumptions needed to be made about the relative fractions of the H and He in the interstellar medium besides the degree of ionisation of each element, to restrict the number of free parameters to a tractable level in any analysis. Direct spectroscopic observations of gas in the LISM (see sections 7.3 and 7.6) indicate that the convenient assumption of a cosmic He/H ratio (0.1) and minimal ionisation is unlikely to be reasonable.

Spectroscopic observations of white dwarfs in the EUV can address a number of important questions.

Active galaxies

While extragalactic objects such as normal and active galaxies are certainly the most EUV luminous sources discovered, they are also among the most difficult to observe. Their great distance, coupled with the absorbing effect of the intergalactic medium and the interstellar gas in our own galaxy, yields fluxes fainter than most of the more local EUV sources. Hence, the acquisition of EUV spectra requires comparatively long exposure times. With the capability of EUVE, typical minimum exposure times were a few hundred thousand seconds, approaching the practical limit imposed by the instrument background, beyond which no further improvement in signal-to-noise could be achieved. Consequently, the number of extragalactic objects for which spectroscopic observations have been feasible is small. Furthermore, these sources are only visible in the short wavelength region of the EUVE short wavelength spectrometer. Table 10.1 lists those objects which have published EUV spectra, noting their exposure times and classification. Two BL Lac objects and 5 Seyfert galaxies, probably all type I, are listed.

The now commonly accepted explanation of the various different types of AGN is the so-called ‘Unified Model’, which adopts a common physical mechanism for the source, the AGN types representing different viewing angles. In this model, the central energy source is a massive black hole accreting matter from its host galaxy via a disc. This disc is surrounded by a thick torus of material as shown in figure 10.1.

The limitations of photometric techniques

The photometric all-sky surveys conducted in the EUV by the ROSAT WFC and EUVE have been sources of important information concerning the general properties of groups of objects contained in the EUV source population, including late-type stars, white dwarfs, cataclysmic variables and active galactic nuclei. However, when considering individual objects in detail, the amount of information that can be extracted from three or four such data points is limited. For example, if heavy elements are present in the atmosphere of a hot white dwarf, the survey data can only give an indication of the level of opacity and are unable to distinguish between the possible species responsible and especially whether or not helium is present. Similarly, in studying the emission from stellar coronae, only crude estimates of conditions in the plasma can be made and usually only when simplifying assumptions such as the existence of a single temperature component are incorporated into the analysis. The overwhelming advantage of spectroscopic observations lies in the ability to study individual spectral features or blends of features, giving a more detailed picture of the underlying physical processes responsible for the EUV emission.

The Extreme Ultraviolet Explorer spectrometer

The main components of EUVE have been described in detail in chapter 4 with the exception of the spectrometer. This instrument made use of part of the converging beam of the Wolter type II deep survey telescope, intercepting this with three variable line space reflection gratings (Hettrick et al. 1985).

The Extreme Ultraviolet Explorer

S. Bowyer and his team at the University of California, Berkeley, the pioneers of EUV astronomy, originally proposed the Extreme Ultraviolet Explorer (EUVE) mission to NASA in 1975. Selected for development in 1976, it was eventually launched in June 1992, almost exactly two years after ROSAT. The science payload was developed and built by the Space Sciences Laboratory and Center for EUV Astrophysics of the University of California at Berkeley. Like the WFC, a principal aim of EUVE was to survey the sky at EUV wavelengths and to produce a catalogue of sources. However, the two missions differed in several respects. While the WFC had a filter complement allowing it to observe at the longer wavelengths of the EUV band (P1 and P2 filters), the survey was only conducted at the shorter wavelengths from 60 Å to ≈200 Å. By contrast, the EUVE survey was carried out in four separate wavelength ranges, extending out to ≈800 Å. In addition, EUVE carried on board a spectrometer for pointed observations following the survey phase of the mission. The spectrometer will be discussed in detail in chapter 6, but half the effective area of its telescope was utilised for a deep survey imager, giving exposure times significantly larger than either the WFC or EUVE all-sky surveys but over a restricted region of sky. The following sections include a detailed description of the payload components drawn from several papers in the scientific literature (see e.g. Bowyer and Malina 1991a,b).

A view of local interstellar space

It is generally accepted that the solar system resides inside a relatively dense local interstellar cloud a few parsecs across with a mean neutral hydrogen density of ≈0.1 cm−3 (e.g. Frisch 1994; Gry et al. 1995). This cloud, the so-called local interstellar cloud (LIC) or surrounding interstellar cloud (SIC), lies inside a region of much lower density, often referred to as the local bubble (figure 7.1). The general picture built up is one where this bubble has been created by the shock wave from a past supernova explosion, which would also have ionised the local cloud. The current ionisation state of the local cloud is then expected to depend on the recombination history of the ionised material, i.e. the length of time since the shock wave passed through. However, if the flux of ionising photons from hot stellar sources is significant, the net recombination rate may be reduced (Cheng and Bruhweiler 1990; Lyuand Bruhweiler 1996). The photometric data from the ROSAT WFC survey have been used to map out the general dimensions of the cavity by Warwick et al. (1993) and Diamond et al. (1995), as already discussed in section 3.9.2. However, this relatively crude interpretation of the observations probably hides greater complexity. For example, several studies of the lines-of-sight towards β and ∊ CMa had already demonstrated the existence of a low density tunnel some 200–300 pc in extent, even before any EUV observations were carried out (e.g. Welsh 1991).

The main problem in astrophysics is that of inferring the physical properties of the medium from the observables: the Stokes spectrum. Unfortunately, no in situ measurements can be made of the temperatures, densities, velocities, magnetic fields, and other physical quantities to probe the astronomical object, or at least that portion of the astronomical object where photons come from. Astrophysical measurements are of the physical properties of the (polarized) radiation, not of the celestial object itself. From these measurements, and with the help of some known physics, the astronomer is challenged to infer the properties of the medium that light has passed through. Certainly, we speak loosely when we use the same word measurement for both the process of characterizing light and that of interpreting the observed Stokes spectrum in terms of the medium properties: calibration is neither as easy nor as accurate as in laboratory measurements. The only available “meter” is the RTE, which contains the relationship between the observable (the Stokes spectrum) and the unknowns (the medium physical quantities). More specifically, the link between the medium and the observable lies in the coefficients of the RTE, namely, the propagation matrix and the source function vector.

Now that we have formulated the general RTE for a stratified anisotropic medium in LTE, let us particularize our study to the case of an atomic vapor permeated by a magnetic field, B. For convenience, we shall consider the medium to be isotropic in the absence of an “external” magnetic field. It is thus B that establishes the optical anisotropy by introducing a “preferential” direction.

In order to understand the basic concepts, we start again with the simple Lorentz model of the electron as in Chapter 6 (this time introducing the Lorentz force in the dynamical balance). In this way, the so-called “normal” Zeeman effect gets fully explained. The “anomalous” Zeeman effect, however, needs further results from quantum mechanics that will be summarized later. As the reader may already have realized from the historical introduction, this procedure conforms with historical developments. As in many other branches of physics, a chronological treatment helps in comprehension, although it is not strictly necessary.

In this chapter, we shall see that a single (unpolarized) spectral line in the absence of a magnetic field splits into various Zeeman components, each with a distinct state of polarization that may, of course, vary along the profile.

The Lorentz model of the electron

Let us resume our discussion of Section 6.2 on the Lorentz model.

Once one has a solution of the RTE, the most simple procedure of inference can be devised such that a comparison between calculated and observed Stokes spectra suggests modifications in prescribed models of the medium. Iteratively improved models refine the match between observations and theoretical calculations. When the match is good enough, the last model in the iteration is taken as a model of the medium and its characteristic parameters are the inferred parameters of the medium. This trial-and-error method may be useful when the model medium is very simple and contains just a few free parameters. Note that every change of a given free parameter implies an integration of the RTE which is a process requiring a great deal of computer time. If the number of free parameters is large, the manual trial-and-error method can become impracticable, but even automated trialand-error procedures that modify the various parameters randomly (blindly) may not converge to a physically reasonable final model of the medium. The results may even seem reasonable but be greatly in error.

Were one asked for a concise description of most astrophysical tasks, one possible answer might be ‘understanding the message of light from heavenly bodies’. Light – or electromagnetic radiation – is the astronomer's main (almost his sole) source of information. The statement that nobody can measure the physical parameters of the solar atmosphere, although at first sight shocking, merely calls attention to the fact that astrophysics is an observational rather than an experimental science. This characteristic is often forgotten. We do not measure solar or stellar temperatures, velocities, magnetic fields, etc., simply because we do not have thermometers, tachometers, magnetometers, etc., that would permit in situ measurements of these parameters. Rather, we are only able to measure light. The astronomical parameters are inferred from these measurements, often with the help of some laboratory physics. Thus, the reliability of such astronomical inferences hinges on the accuracy of measurements of light.

This chapter is aimed at understanding how nature and laboratory devices may change the polarization state of light. The transformations of the Stokes parameters are assumed to be linear, i.e., in terms of addition and multiplication by scalars. This is why we are restricted to linear optical systems. The qualifiers quasi-monochromatic and plane will be omitted from now on under the assumption that we are in fact dealing with this type of electromagnetic wave.

Propagation of light through anisotropic media

Changing the polarization state of light means modifying the coherency matrix elements, which in turn require that different components of the electric field vector are acted on differently by the medium. If Ex and Ey suffer the same alteration, a scaling of C is effected, so that the polarization state is unchanged. As a matter of fact, we have seen in the previous chapter how both the linear analyzer and the linear retarder act differently on given components of E. The wave equation (2.1), however, predicts no different behavior for the orthogonal components.

So far we have avoided detailed discussion about two physical phenomena that are crucial in the context of this book and for any understanding of the interaction between matter and radiation in general. These two phenomena are absorption and dispersion, that is, the removal of energy from the electromagnetic field by matter and the dephasing of the electric field components as light streams through the medium. Although we have barely mentioned the existence of these effects, we shall need a deeper insight into both of them. We shall see that retardance, birefringence, and absorption properties of polarization systems, assumed in the preceding sections, are based on these phenomena, whose wavelength dependence is understood in terms of the wavelength dependence of the dielectric permittivity and, hence, of the refractive index of the medium. By studying absorption and dispersion we are producing the necessary bricks with which to build a theory of radiative energy transfer which will be discussed in following chapters. We shall continue to assume unit isotropic magnetic permeability of μ = 1 for the medium.

Certainly, a full account of absorption and dispersion processes can be carried out only within the framework of quantum mechanics.

Spectropolarimetry, as the name suggests, is the measurement of light that has been analyzed both spectroscopically and polarimetrically. In other words, both the wavelength distribution of energy and the vector properties of electromagnetic radiation are measured with the highest possible resolution and accuracy. Thus, spectropolarimetry embraces a number of techniques used in order to characterize light in the most exhaustive way. Such techniques are ultimately based on a theory that, from its beginnings in the closing years of the nineteenth century, finally grew to maturity in the 1990s. Therefore, under the heading of spectropolarimetry we will find several disciplines, which, despite being interrelated or rather, although our aim is to stress their interrelatedness, may be considered independent.

A historical perspective is always helpful for grasping the importance of physical phenomena and their corresponding explanations. The main objective of this chapter is to give a brief description of the salient events and findings in history related to some of the independent disciplines covered in this book.

So far, the polarization properties of the simplest conceivable electromagnetic radiation have been described. However, building a polarization theory that is useful in the real world necessarily requires the consideration of light whose spectrum contains a continuous distribution of monochromatic plane waves within a finite width of frequencies. Heisenberg's uncertainty principle implies infinite time intervals for detecting purely monochromatic light (in other words, we can simply say that monochromatic light does not exist in reality). In this section we shall see that the concept of polarization is also applicable to polychromatic light. As a matter of fact, polychromatic light may share the properties of totally polarized radiation and hence be indistinguishable from monochromatic light in so far as polarimetric measurements are concerned. The coherency matrix and the Stokes parameters can also be defined for a polychromatic light beam, although the binding conditions (2.18) for C and (2.22) for I, Q, U, and V will be slightly modified and the new concepts of partial polarization and degree of polarization will naturally come into play.

Polychromatic light as a statistical superposition of monochromatic light

Under the hypotheses of linearity, stationarity, and continuity, one can assume any polychromatic light beam to be the superposition of monochromatic, time-harmonic plane waves of different frequencies within an interval of width Δv around a central frequency v0.