INTRODUCTION

Those of us who had the privilege of being Dennis Sciama's students during what Hajicek has described as ‘the Golden Age of General Relativity’ can trace many of the current concerns of the subject back to the ideas which he fostered, either directly or indirectly, within his research group in Cambridge. This was the environment in which major contributions to most of the foundational ideas about singularities: from the controversies about the steady state and big bang theories; through the critique of the early Lifshitz-Khalatnikov arguments which at first suggested that the big bang singularity was not generic, leading to definitions of just what constituted a singularity; to the Hawking-Penrose singularity theorems themselves. The issue of cosmic censorship stemmed naturally from this work, and illustrates well the combination of rigorous mathematics with a firm hold on physical relevance which he established at that time. In this talk I shall try to give an outline of the historical work on cosmic censorship, focussing at the end on my own recent work on shell crossing singularities. I shall not be concerned with what George Ellis, in this meeting, has termed the position of the goal posts — the details of exactly what the target is; rather, I shall be arguing that we should in fact be playing a different game.

A fully covariant approach to transfer phenomena by using flux-limiters is presented. Explicit formulas for the radiation flux and radiation stress tensor are given for a wide class of physical situations.

INTRODUCTION

In several areas of cosmology and astrophysics the transfer of radiation through high-speed moving media plays a crucial role (accretion flow into black holes, X-ray bursts on a neutron star, supernova collapse, jets in radio sources, galaxy formation, phase transition in the early universe). If one wants to take into account all the effects associated with these transport processes, the full relativistic transport equation must be used.

Early discussion of radiative viscosity was performed by several authors in a non covariant formulation (Jeans 1925, Rosseland 1926, Vogt 1928, Milne 1929), but the appropriate transfer equation for the case of special relativity was given in a classical paper by Thomas (1930). A manifestly covariant form of the transfer equation was obtained by Hazelhurst and Sargent (1959), by using a geometrical formalism. Finally Lindquist (1966) performed the extension to the general relativistic situation and Mihalas (1983) analyzed in depth the order of magnitude of the various terms which appear in the transport equation.

From a mathematical point of view, the transport equation is an integro—differential equation and the task to solve it is in general very hard.

The Crisium basin (Figure 5.1) was recognized as a multi-ring structure by Baldwin (1949, 1963) and Hartmann and Kuiper (1962), who were struck by its remarkable elliptical appearance. Although similar to other basins in the morphologic elements of ring massifs, ejecta, and secondary craters, Crisium displays several features that suggest it may have undergone a distinctly different style of post-impact modification. I will describe the regional and basin geology of the Crisium area and address the nature and causes of these morphological differences.

Regional geological setting

The Crisium basin (Figure 1.1) is on the eastern edge of the near side of the Moon, north of Mare Fecunditatis and southeast of Mare Serenitatis. The basin appears to have formed within a zone of typical highlands crust and mare volcanism was active in this region prior to the basin impact (Schultz and Spudis, 1979, 1983). The average thickness of the crust here is about 60 km (Bills and Ferrari, 1976). The interior of the Crisium basin is completely mare-flooded, which has obscured the relations of basin materials; this obscuration has resulted in controversy regarding the true topographic rim of the basin (Howard et al., 1974; Wilhelms, 1980b, 1987; Croft, 1981b), as discussed below.

The Crisium basin (Figure 5.1) appears to have had minimal interaction with older basin structures. The nearest pre-Crisium basin is the Fecunditatis basin, whose center is located approximately 700 km to the south of Crisium. This basin is tangential to the outermost Crisium ring of about 1000 km diameter mapped by Wilhelms and McCauley (1971) and Fecunditatis effects on the generation of Crisium topography have probably been relatively minor.

The formation of multi-ring basins is one of the most important geological processes in the early history of the Solar System. These impacts can greatly affect the morphology and observed surface composition of planetary crusts. The formation of basins may influence lithospheric development and growth and thus alter the thermal history of the planet. Basin-forming impacts can catalyze volcanic eruptions and initiate major modifications of crustal structure subsequent to the development of their multi-ring topography.

In this chapter, I will conclude my examination of the geology of multi-ring basins by speculating on the role of basins in the early geological evolution of the planets. Many of the ideas offered in this chapter are subjects of ongoing research and answers to some of the questions raised by such speculation may be forthcoming with additional work.

The building blocks of planetary surfaces

The recognition of regional patterns of landforms on the Moon led to the discovery of multi-ring basins; this pattern recognition of “the big picture” out of the chaos of detail displayed by the lunar surface is well described by Hartmann (1981). The use of such perception techniques in planetary photogeology has shown us that basins are also present on Mercury, Mars, and the icy satellites of the jovian planets. Moreover, such discovery is not yet complete; ongoing analysis of planetary images adds every year to the basin inventory of the Solar System.

From the evidence described and analyzed in this book, I believe that basins are the fundamental building blocks of early, planetary crusts.

Multi-ring basins are the largest impact craters on Solar System bodies. They form in the earliest stages of planetary history by the collision of asteroid-sized bodies with planets and affect the subsequent evolution of these latter objects in many profound ways. Many scientists have expended great effort in attempting to understand these features; a casual glance at the literature of planetary science over the last 30 years reveals no less than several hundred entries dealing with some facet of multiring basins.

Planetary scientists studying the problem of multi-ring basins approach it from many different directions. Some are physicists, describing the mechanics of basin formation on the basis of known theory. Other workers make geological maps from photographs, searching for clues to the processes that have shaped the surface of the planet. Still others study the chemistry and mineralogy of terrestrial and lunar samples, using the rock record to reconstruct the physical extremes of heat and pressure produced during large impacts. The basin problem is multi-disciplinary; answers to the many questions raised by these features require knowledge from geology, chemistry, physics, and other fields of study. No one person has the expertise to understand all aspects of the basin problem: So why this book?

The only other book available on the problems posed by basins is the proceedings of a topical conference held at the Lunar and Planetary Institute, Houston, in November, 1980 (Multi-ring Basins: Formation and Evolution, P.H. Schultz and R.B. Merrill, editors, Supplement 15 of Geochimica et Cosmochimica Acta, Pergamon Press, New York, 1981).

The Nectaris basin is located on the lunar near side (Figure 1.1), south of Mare Tranquillitatis and west of Mare Fecunditatis. An origin by impact for the Nectaris basin was advocated first by Baldwin (1949, 1963), who paid particular attention to the development of the Altai scarp, the southwestern topographic rim of the basin (Figure 4.1). The basin is relatively well preserved and served as a prototype multi-ring basin in the pioneering study of Hartmann and Kuiper (1962). More recent systematic studies of the Nectaris basin are those of Whitford-Stark (1981b), Wilhelms (1987), and Spudis et al., (1989). The Apollo 16 mission to the Descartes highlands in 1972 collected samples and orbital data that are directly applicable to comprehension of Nectaris regional geology. In this chapter, I describe the geology of the Nectaris basin and synthesize various data into a geological model for its origin and subsequent development.

Regional geology and setting

The Nectaris basin formed in typical crust of the near side highlands and interacted with two older basins. The average thickness of the crust in the region is about 70 km (Bills and Ferrari, 1976). The surrounding terrain consists of heavily cratered highlands, except where buried by later mare basalts. Nectaris deposits are well preserved to the south and west of the basin, but have been buried to the north and east by the lavas of Maria Tranquillitatis and Fecunditatis (Figure 4.1).

Ever since their recognition, multi-ring basins have fascinated and vexed scientists attempting to reconstruct the geological history of the Moon. As the other terrestrial planets were photographed at high resolution, it became apparent that basins are an important element in the early development of all planetary crusts. This importance spurred research into the basin-forming process and yielded a plethora of models and concepts regarding basin origin and evolution. In this chapter, I outline the general problem areas of basin formation and describe the approach taken by my own work on lunar basins.

Multi-ring basins and their significance

Multi-ring basins are large impact craters. The exact size at which impact features cease to be “craters” and become “basins” is not clear; traditionally, craters on the Moon larger than about 300 km have been called basins (Hartmann and Wood, 1971; Wilhelms, 1987). Basins are defined here as naturally occurring, large, complex impact craters that initially possessed multiple-ring morphology. This definition purposely excludes simulated, multi-ring structures that result from explosion-crater experiments on the Earth and whose mechanics of formation differ from impact events (e.g., Roddy, 1977), although important insights into the mechanics of ring formation may be gained from these studies. The qualification that basins initially possessed multiple rings is in recognition of the fact that many older, degraded basins display only one or two rings, even though their diameters of hundreds of kilometers indicate that they had multiple rings when they originally formed.

The Orientale basin (Figure 3.1) is located on the western limb of the Moon; most of the basin and its deposits extend over the lunar far side. The name “Orientale” (eastern) is derived from the old astronomical practice of displaying telescopic photographs of the Moon with south at the top and east-west convention derived from terrestrial coordinates. The first studies of the Orientale basin utilized Earth-based telescopic photographs; because of the basin's location on the extreme limb, these photographs were geometrically rectified at the Lunar and Planetary Laboratory (University of Arizona) to create a vertical viewing perspective (Hartmann and Kuiper, 1962). These rectified photographs also served as the primary data base for an early geological study of Orientale as the prototype lunar basin (McCauley, 1968).

Because of the spectacular success of the Lunar Orbiter spacecraft, particularly a series of high-quality photographs by Orbiter IV that provide contiguous coverage, the number of detailed geological descriptions of the Orientale basin increased dramatically in the years immediately following the Apollo missions (Hartmann and Wood, 1971; Head, 1974a; Moore et al., 1974; McCauley, 1977; Scott et al., 1977; Spudis et al., 1984b). In this chapter, I review the regional and local geology of Orientale and, in conjunction with data from photogeology and remote sensing, integrate these data into a geological model for the formation and evolution of the basin.

Regional geology of the Orientale impact site

The Orientale basin is sparsely filled by mare basalt and located in rugged highland terrain on the western limb of the Moon (Figure 3.1).

Multi-ring basins are features produced by the collision of solid bodies with the planets, so the basin problem is a subset of the more general problem of impact cratering, a vast field of study. This chapter briefly describes the impact process from theoretical considerations, from the evidence of some well studied terrestrial impact craters, and from the observed morphology of impact craters on the Moon and their systematic changes with increasing crater size.

The cratering process

Impact mechanics

Our understanding of what happens when a solid body hits a planetary surface at high speeds has increased greatly over the past 25 years. The study of the physical processes occurring during impact events is called impact mechanics. Although the details of this complex process are not understood, laboratory experiments, explosion craters, natural impact craters, and computer simulations have given us a general outline of the main stages that characterize the formation of an impact crater.

Solid bodies collide with planetary surfaces at very high speeds; such impact speeds are in the range called hypervelocity. Encounter velocities can vary from lunar escape velocity (about 2.5 km/s) at a minimum, up to many tens of kilometers per second (on the basis of velocities of bodies in heliocentric orbits). On the Moon, the mean impact velocity is about 20 km/s (Shoemaker, 1977). At the moment of contact between an impactor and a planet, the kinetic energy of the impacting body is transferred to the planetary surface target. A shock wave propagates into the target and projectile, resulting in intensive compression of both objects. In hypervelocity impacts, the quantities of energy produced greatly exceed the heat of vaporization for geological materials.

The formation of multi-ring basins dominated the early geological evolution of the Moon. The five basins described in the preceding chapters represent a spectrum of basin ages, sizes and morphologies. By comparing the similarities and differences among these basins, some general inferences may be made regarding the process of formation of multi-ring basins on the Moon. I here synthesize the information described in the previous chapters to develop a model for the formation and geological evolution of multi-ring basins on the Moon. This model is incomplete, but several puzzling aspects of basin geology can be explained satisfactorily through this approach. At various points in the following discussion, please refer to preceding sections in the text.

Composition and structure of the lunar crust

The crust of the Moon is heterogeneous on a local and a regional scale; the impact targets for lunar multi-ring basins were similarly heterogeneous. The crustal thickness at the basin target sites was widely varied, ranging from 50 km thick for parts of the Imbrium basin to over 120 km thick for the Orientale highlands (Bills and Ferrari, 1976). Moreover, lithospheric conditions during the era of basin-forming impacts changed with time in response to rapidly changing thermal conditions within the Moon 4 Ga ago (Hubbard and Minear, 1975; Solomon and Head, 1980). The older basins formed in a relatively thin, easily penetrated lithosphere that gave rise to extensive post-impact modification.

The Serenitatis basin is on the near side of the Moon, east of Mare Imbrium and north of Mare Tranquillitatis (Figure 1.1). The basin is almost completely flooded by mare basalts (Figure 6.1) and displays a mascon gravity anomaly (Sjogren et al., 1974). The Serenitatis basin was recognized as multi-ring in the studies of Hartmann and Kuiper (1962), Baldwin (1963), Hartmann and Wood (1971) and during systematic geological mapping of the Moon (Wilhelms and McCauley, 1971). Because of the large amount of mare flooding and generally degraded appearance of the basin, Serenitatis was once considered to be one of the oldest basins on the Moon (Hartmann and Wood, 1971; Wilhelms and McCauley, 1971). This view has changed, primarily because of ages obtained for some Apollo 17 samples considered to represent impact melt of the Serenitatis basin (James et al., 1978; Wilhelms, 1987). I will describe the regional geology of the Serenitatis basin and some aspects of Apollo 17 site geology that relate to problems in the interpretation of its formation and subsequent evolution.

Regional geological setting and basin definition

The Serenitatis basin is close to the Imbrium basin and the effects of Imbrium on the morphologic evolution of Serenitatis have been significant. Most interpretations of basin geology rely on the well exposed highlands to the east of Mare Serenitatis (Figure 6.1). Thus, the morphological data available for interpreting the geology of the Serenitatis basin are limited compared with those for some of the other basins described in this book.

The Imbrium basin (Figure 7.1) is probably the most studied multi-ring basin on the Moon. Prominently located on the lunar near side, west of Mare Serenitatis and east of the large maria Oceanus Procellarum (Figure 1.1), the Imbrium basin first attracted the attention of G.K. Gilbert (1893) in his historic analysis of lunar craters. Gilbert recognized the extensive pattern of radial texture associated with Imbrium and postulated that Mare Imbrium had formed by the collision of a large meteorite with the Moon. The impact origin of the Imbrium basin was also recognized by Dietz (1946), Baldwin (1949; 1963), Urey (1952), and Hartmann and Kuiper (1962). The landmark paper of Shoemaker and Hackman (1962) proposed a global stratigraphic system for the Moon based on the deposition of ejecta from the Imbrium basin as a marker horizon. The Imbrium impact was considered such a key event in lunar geological history that two Apollo missions (Apollo 14 and 15) were sent to landing sites specifically chosen to address problems of Imbrium basin geology.

Regional geology and setting

Imbrium is one of the youngest major basins on the Moon, but extensively flooded by mare basalt (Figure 7.1). Even so, as one of the largest lunar basins (main topographic rim 1160 km in diameter), it has an ejecta blanket so extensive that almost all of the near side may be dated relatively with respect to the time of the Imbrium impact (Wilhelms, 1970).

The formation of multi-ring basins was an important process in the early histories of Solar System bodies. Thus, study of basins on the other planets potentially can give us insight into the early geological evolution of the planets. Although occurring on all of the terrestrial planets, the most and best preserved basins occur on planets that display remnants of their early crusts, i.e., Mercury, Mars, and the icy satellites of Jupiter and Saturn. In this chapter, I discuss the geology of basins found on the terrestrial planets in relation to the geological model for basin formation and development on the Moon discussed above.

Earth

Most of the recognized impact structures on the Earth are either simple, bowlshaped craters or complex craters displaying central peaks (Grieve and Robertson, 1979; Masaitis et al., 1980; Grieve, 1987). However, several of Earth's larger craters have multiple rings; seventeen craters display at least two rings (Table 9.1; Pike, 1985 and references therein). The paucity of terrestrial multi-ring basins doubtless reflects the relatively youthful average surface age of the Earth, as compared with the more primitive terrestrial planets, such as Mercury and Mars.

Impact craters of the Earth show the morphological transitions with increasing size, as do craters on the planets, but changes in form occur at different diameters (Pike, 1985). Complex craters on the Earth range in size from about 4 km to about 25 km in diameter.

Large solar flares are probably the most spectacular eruptive events in cosmical plasmas. Though rather weak in absolute magnitude compared for instance with the enormous energies set free in a supernova explosion, they outshine all other cosmic events for a terrestrial observer. According to the generally accepted picture, a flare constitutes a sudden release of magnetic energy stored in the corona and is therefore primarily an MHD process, though the various nonthermal channels of energy dissipation and deposition, which give rise to the richness of the observations, require a framework broader than MHD theory.

Since the major part of this book is concerned primarily with phenomena in laboratory plasmas, it seems to be convenient for the generally interested reader to find a somewhat broader introduction to this astrophysical topic. The engine driving the magnetic activity in the solar atmosphere is turbulent convection in the solar interior. Section 10.1 therefore gives an overview of our present understanding of the convection zone, in particular magnetoconvection. In section 10.2 we consider the solar atmosphere, its mean stratification, the process of magnetic flux emergence from the convection zone and the magnetic structures in the corona, in particular in active regions. In section 10.3 we then focus in on the MHD modelling of the flare phenomenon.