In this chapter we cover those solutions containing a perfect fluid, and admitting at least an H1 and at most an H3, which are not discussed elsewhere. Most of the known solutions admit a G2I acting on spacelike orbits, and can be considered to be cosmologies. Vacuum and Einstein–Maxwell solutions with a G2 on S2 in which the gradient of the W of (17.4) is timelike may also ipso facto be called cosmological. In this book, they and vacua with a G1 are covered by Chapters 17–22, 25 and 34.

Solutions with a Gr, r ≥ 3, are discussed in Chapters 13–16: see the tables in §13.5. Relations between them, in vacuum, Einstein–Maxwell and stiff fluid cases, arise from applying generating techniques when the G3 contains a G2I (see §10.11, Chapter 34 and, e.g., Kitchingham (1986)). Stationary axisymmetric fluid solutions appear in Chapter 21.

Theorem 10.2 enables one to generate an infinity of solutions with a G2I on S2 and equation of state p = μ from vacuum solutions. Vacua and stiff fluids with a G2I on S2 obtainable using the methods of Chapters 10 and 34 have been surveyed by e.g. Carmeli et al. (1981), Krasiński (1997) and Belinski and Verdaguer (2001).

When, in 1975, two of the authors (D.K. and H.S.) proposed to change their field of research back to the subject of exact solutions of Einstein's field equations, they of course felt it necessary to make a careful study of the papers published in the meantime, so as to avoid duplication of known results. A fairly comprehensive review or book on the exact solutions would have been a great help, but no such book was available. This prompted them to ask ‘Why not use the preparatory work we have to do in any case to write such a book?’ After some discussion, they agreed to go ahead with this idea, and then they looked for coauthors. They succeeded in finding two.

The first was E.H., a member of the Jena relativity group, who had been engaged before in exact solutions and was also inclined to return to them. The second, M.M., became involved by responding to the existing authors' appeal for information and then (during a visit by H.S. to London) agreeing to look over the English text. Eventually he agreed to write some parts of the book.

The quartet's original optimism somewhat diminished when references to over 2000 papers had been collected and the magnitude of the task became all too clear.

When discussing solutions, we should often like to be able to decide, in an invariant manner, whether two metrics, each given in some specific coordinate system, are identical or not, or whether a given metric is new or not. For such purposes it is useful to have an invariantly-defined and unique complete characterization of each metric. Such a characterization can be attempted using scalar polynomial invariants, whose definition and construction are discussed in §9.1. However, it turns out that those invariants do not characterize space-times uniquely.

A method which does provide a unique coordinate-independent characterization, using Cartan invariants, is described in §9.2. This enables one to compare metrics given in differing coordinate systems, which distinguishes the results from those on uniqueness of the metric given the coordinate components for curvature and its derivatives (for which see e.g. Ihrig (1975), Hall and Kay (1988)). That uniqueness is related to the structure of the holonomy group, defined for each point p as the group of linear transformations of the tangent space at p generated by the holonomy (see §2.10) for different closed curves, or of the infinitesimal holonomy group, which is generated by the curvature and its derivatives but is equal to the holonomy group at almost all points in simply-connected smooth manifolds. These groups are subgroups of the Lorentz group and their properties can also be related to classification of curvature and the existence of constant tensor fields (Goldberg and Kerr 1961, Beiglböck 1964, Ihrig 1975, Hall 1991).

Looking back

The astrophysical research discipline we now know as Extreme Ultraviolet astronomy is approximately 30 years old. An observational technique once dismissed as impossible has become established as a significant branch of space astronomy and a major contributor to our knowledge of the Universe. In several areas, the science obtained from EUV observations is unique. For example, the presence of the He II Lyman series in this spectral range provides a diagnostic tool for the study of the second most abundant element in the Universe in the atmospheres of hot stars and in interstellar space. The determination of the ionisation fraction of helium in the local ISM could not have been carried out in any other spectral range.

EUV astronomy has passed through the development phases that might be deemed typical of a discipline depending on access to space. Beginning with the sounding rocket borne experiments of the early 1970s, the longer duration Apollo–Soyuz Test Project highlighted the potential of the field, with the first reported source detections in 1975. However, it was a further 15 years before the next major advance with the first EUV all-sky survey of the ROSAT WFC (in 1990) followed by the wider spectral coverage of the EUVE survey in 1992. The underlying reasons for this hiatus had more to do with national and international politics, together with the economics of funding opportunities and even the launch delays following the Challenger disaster, than technological limitations.

Compared to the large numbers of coronal sources and white dwarf stars found in the EUV all-sky survey catalogues, the number of cataclysmic variable detections is small, numbering only ≈25 objects. Nevertheless, many of these systems were bright enough to have been suitable targets for spectroscopic observations with EUVE, but these studies were complicated by the fact that the sources are highly variable and the exposure times needed to produce good signal-to-noise were at least 50 ks for the brightest sources, much longer than the binary and rotation periods. Hence, with EUVE it was only possible to obtain observations of the time averaged spectrum, except in periods of outburst, which lasted for several days.

Cataclysmic variables can be conveniently divided into two groups: (i) those where the white dwarf does not have a significant magnetic field (<0.1–1 MG) and accretion onto its surface occurs via an accretion disc (e.g. figure 9.1); (ii) the polars–systems in which the white dwarf does have a strong magnetic field (≈10–100 MG) which prevents the formation of an accretion disc and channels accrete material onto the magnetic poles of the white dwarf along the field lines (figure 9.2). A small number of magnetic systems, the intermediate polars, have weaker fields (B ≈ 1–10 MG) allowing a partial disc to accumulate which is disrupted by the field in its inner regions. As in the polars, accretion onto the white dwarf follows the field lines onto the magnetic poles (figure 9.2).

Astrophysical significance of the EUV

The Extreme Ultraviolet (EUV) nominally spans the wavelength range from 100 to 1000 Å, although for practical purposes the edges are often somewhat indistinct as instrument band-passes extend shortward into the soft X-ray or longward into the far ultraviolet (far UV). Like X-ray emission, the production of EUV photons is primarily associated with the existence of hot gas in the Universe. Indeed, X-ray astronomy has long been established as a primary tool for studying a diverse range of astronomical objects from stars through to clusters of galaxies. An important question is what information can EUV observations provide that cannot be obtained from other wavebands? In broad terms, studying photons with energies between ultraviolet (UV) and X-ray ranges means examining gas with intermediate temperature. However, the situation is really more complex. For example, EUV studies of hot thin plasma in stars deal mainly with temperatures between a few times 105 and a few times 106 K, while hot blackbody-like objects such as white dwarfs are bright EUV sources at temperatures a factor of 10 below these. Perhaps the most significant contribution EUV observations can make to astrophysics in general is by providing access to the most important spectroscopic features of helium – the He I and He II ground state continua together with the He I and He II resonance lines.

This book is the first comprehensive description of the development of the discipline of astronomy in the Extreme Ultraviolet (EUV) wavelength range (≈ 100–1000 Å), from its beginnings in the late 1960s through to the results of the latest satellite missions flown during the 1990s. It is particularly timely to publish this work now as the Extreme Ultraviolet Explorer, the last operational cosmic EUV observatory, was shut down in 2001 and re-entered the Earth's atmosphere in early 2002. Although new EUV telescopes are being designed, it will be several years before a new orbital observatory can come to fruition. Hence, for a while, progress beyond that reported in this book will be slow.

We intended this book to be for astrophysicists and space scientists wanting a general introduction to both the observational techniques and the scientific results from EUV astronomy. Consequently, our goal has been to collect together in a single volume material on the early history, the instrumentation and the detailed study of particular groups of astronomical objects. EUV observations of the Sun are not within the scope of this current work, since the Sun can be observed in far more detail than most sources of EUV emission, providing material for a book on its own. We have found it useful to deal with the subject in its historical context. Therefore, we do not have specific chapters on instrumentation but integrate such material into the development of the scientific results on a mission-by-mission basis.

Introduction

The first true space observatories incorporating imaging telescopes and providing access to the soft X-ray band, but providing some overlapping response into the EUV were flown in the late 1970s and early 1980s. With the Einstein and European X-ray Astronomy Satellite (EXOSAT) satellites, launched in 1978 and 1983 respectively, long exposure times coupled with high point source sensitivity became available to high-energy astronomers for the first time. This progress depended mainly on developments in optics and detector technology but also coincided with a more sophisticated understanding of the physical processes involved in soft X-ray and EUV emission and a better appreciation of the potential significance of observations in these wavebands. This chapter describes the Einstein and EXOSAT missions detailing both the telescope and detector technology. Developments in the understanding of the physical emission processes are outlined to set the context for discussion of the most significant results from these observatories, relevant to the broad field of EUV astronomy.

Parallel developments in far-UV astronomy, arising mainly from the International Ultraviolet Explorer (IUE) observatory, provide an important complement to the work of Einstein and EXOSAT. However, since the technology of IUE is quite different to that used at shorter wavelengths we concentrate solely on the appropriate scientific results. Finally, the Voyager ultraviolet spectrometer (UVS), while mainly designed for planetary studies, was used during cruise phases of the mission, providing the first stellar EUV spectra in the region just below the Lyman limit at 912 Å.

Emission from B stars

Prior to the EUV sky surveys, O and B stars exhibiting strong mass-loss were expected to be a minor, but nevertheless important, group of EUV sources, the emission arising from hot, shocked gas in the stellar winds. Little thought was given to the likelihood of detecting photospheric EUV flux since photospheric helium was expected to restrict emission to the longest EUV wavelengths, most affected by interstellar attenuation. Nevertheless, the existence of the so-called β CMa tunnel of low column density, extending over distances of 200–300 pc (e.g. Welsh 1991) promoted the hope that a few such objects might be detected in this direction at wavelengths longward of 504 Å. The subsequent detection of the B2 II star ∊ CMa (Adhara, d = 188 pc) in the 500–740 Å (tin) filter during the EUVE sky search was not, therefore, particularly remarkable. However, the intensity of the flux recorded outshone all other non-solar sources of EUV radiation, including the well-known hot white dwarf HZ 43, previously believed to be the brightest EUV source, although this star remains the brightest object at the shortest EUV wavelengths (Vallerga et al. 1993).

The magnitude of the detected EUVE tin count rate (98 ± 10 counts s−1) was a strong indication that the line-of-sight column density was even lower than the upper limit of 3 × 1018 cm−2 estimated indirectly by Welsh (1991) from NaI absorption line studies.

Introduction

Even before the launches of the Einstein and EXOSAT observatories, it was clear that the next major step forward in EUV astronomy should be a survey of the entire sky, along the lines of the X-ray sky surveys of the 1970s. Such a survey was necessary to map out the positions of all sources of EUV radiation and determine the best directions in which to observe. Indeed, the groups at University of California, Berkeley had been selected by NASA to fly such an experiment on the Orbiting Solar Observatory (OSO) J satellite but, unfortunately, the OSO series was cancelled after the flight of OSO-I. Following the success of the Apollo–Soyuz mission in 1975, scientific interest was revived in the survey concept and the Extreme Ultraviolet Explorer (EUVE) mission was subsequently approved in 1976. Interest in the EUV waveband was also growing in Europe. Having successfully flown a series of imaging X-ray astronomy experiments between 1976 and 1978, the Massachussetts Institute of Technology (MIT)/University of Leicester collaboration sought a new direction of research, with the imminent launch of Einstein, and began development of a new imaging telescope operating in the EUV. This was seen as a direct extension of the mirror technology already refined in the soft X-ray and was combined with the MCP detector expertise acquired from work on the Einstein HRI.

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.