Introduction

Since the early days of solar spectroscopy, the Solar System composition has been considered to be among the most fundamental set of parameters in astrophysics. Russell (1929) in his pioneering research succeeded in deriving the abundances of the 56 elements whose signatures he recognized in the photospheric spectrum of the Sun. Since then a significant body of research regarding the abundances of all elements in the solar photosphere has been accumulated. Much of the research on the composition of the solar photosphere is summarized in a number of review articles, e.g. Cameron (1970), Anders & Grevesse (1989), Grevesse & Sauval (1998), Grevesse et al. (2005).

The Sun, and the nebula out of which it was formed, is composed (by numbers of atoms or ions) of ~90% hydrogen, ~10% helium, and slightly over 0.1% of heavier elements. Oxygen (atomic number Z = 8), the most abundant element after H and He, has an abundance that is over three orders of magnitude lower than H. Ne (10), Mg (12), Si (14), and Fe (26) have abundances over four orders of magnitude lower than the abundance of H. The abundances of Na (11), Al (13), Ca (20), and Ni (28) are five to six orders of magnitude lower than that of H, and K (19) is almost seven orders lower. Copper (29) and other heavier elements are more than seven orders of magnitude less abundant than H. Spectral lines emitted by ions whose atomic numbers are larger than Z = 28.

In this appendix, we discuss an alternative representation of the solution for the rigidly rotating disc of dust. The underlying mathematical structure of this formulation is given through the so-called Bäcklund transformation, which is a technique that enables one to construct explicit solutions to the linear matrix problem (2.41) and the corresponding Ernst potentials f. These solutions take a particularly simple form, since they can be written as quotients of determinants in which only elementary functions and functions that can be calculated from a ‘seed solution’ f0 appear (see below for examples). The Kerr solution for a rotating black hole in vacuum, Equation (2.358), can be considered as a particular example of a Bäcklund transform, see e.g. Neugebauer (1980a). Moreover, the method allows for the construction of regular Ernst potentials, which correspond to disc-like sources of the gravitational field. In particular, it is possible to identify the rigidly rotating disc of dust as a well-defined limit of these solutions.

After the introduction of disc-like solutions, generated by Bäcklund transformations, depending on a set of parameters as well as a real analytic function, an appropriate generalization is given which allows the Ernst potentials to be written in terms of two free functions. For the rigidly rotating disc of dust, these functions take on a simple explicit form.

Introduction

In this chapter we will review the main diagnostic techniques that allow the measurement of the physical properties of optically thin plasmas. These techniques can be used to measure the electron and ion temperatures, electron density, the thermal structure of the plasma, its chemical composition and ionization state, its dynamics, and the velocity distribution of its electrons. Most, but not all, of the techniques we describe assume that the emitting plasma is (i) thermal; (ii) homogeneous and isothermal; and (iii) in collisional ionization equilibrium. The effects of the relaxation of one or more of these assumptions will be discussed when possible, although the effects of departures from ionization equilibrium are difficult to study because of the complexity of evaluating ion abundances in the dynamic environment of out-of-equilibrium plasmas.

Diagnostic techniques require atomic databases and spectral codes to be used. These codes are necessary to provide theoretical estimates of line and continuum fluxes as a function of the physical parameters of the plasma, whose comparison with observations provides the measurement of such parameters. In this chapter, we also briefly review the main spectral codes available in the literature. The diagnostic techniques we discuss can be used with either fluxes (radiances) or intensities (irradiances), but for clarity we will mostly use fluxes.

Electron density diagnostics

Line flux ratios

Measuring electron densities using the flux ratio of two spectral lines is the most popular method.

Introduction to geochemical modelling

Generally, quantitative models are considered as the most advanced, final, step in the interpretation of experimental and analytical data. Three types of chemical evolutionary Earth model may be distinguished (in order of increasing complexity): (1) transport chemical models envisaging distinct homogeneous reservoirs and applying mainly mass-balance considerations (e.g. O'Nions et al., 1979; Jacobsen and Wasserburg, 1979); (2) transport chemical models that take the temporal preservation of chemical and isotopic heterogeneities within reservoirs into account, highlighting the behaviour of the species within each reservoir (Kellogg et al., 2002); (3) physical models with chemical tracers in them (Christensen and Hofmann, 1994; van Keken et al., 2002; Samuel and Farnetani, 2003).

The models are best applied progressively, increasing the complexity only when simpler approaches and their deficiencies are understood. In this chapter we discuss the simplest model involving the transfer of material and species between distinct principal long-lived terrestrial reservoirs. The model includes two major stages of Earth history, accretion (Chapters 18 to 20) and post-accretion evolution. The data related to the isotopic systems modelled, 244Pu–Xe(Pu), 129I–129Xe(I), 40K–40Ar, U–Th–He–Ne, 147Sm–143Nd, 87Rb–87Sr, 176Lu–176Hf and 87Rb–87Sr, were discussed in the previous chapter.

It should be emphasized that neither the model itself (Section 28.2) nor its reference solution (Section 28.3) are unique: they only illustrate one possible way to describe the Earth's materials, and the processes transferring and developing them, within the frame of a self-consistent semiquantitative concept, applying reasonable input parameters.

This book is a cross between a textbook and a monograph, and it was started as an attempt to link depth with breadth in cosmo- and geochemistry. The need for this becomes obvious when one sees the two opposing trends in this science. On the one hand, much excellent research goes into great depth in a relatively narrow field, unnoticed except by specialists and, on the other hand, wide-ranging textbooks capture the imagination of a broader audience but cannot do justice to the actual data-gathering and interpretation. Thus, if one is interested in cosmochemistry, or the solar system or planetary formation and evolution, one can readily find a number of specific, well-written, textbooks. However, those who want to examine critically how these issues are related, and who would like to see the “big picture” and realize how it came to be, have to dive into the often rather complicated original literature.

As is the case with most branches of science, cosmochemistry and geochemistry have made huge leaps forward in the last 20 years but have become more fragmented. A bewildering amount of isotopic evidence has amassed that links Earth's history to that of the early solar system and, in turn, early solar system history to the evolution of the Galaxy and of the Universe itself. The many papers in which these data have appeared necessarily address specialized issues and although the connection to a grand unifying theme is normally made clear, there is mostly no direct contact with other specialized work that relates to the theme from another niche.

Introduction

As seen in the preceding chapters, the giant impact fundamentally affected the history of the Earth. This event has been postulated to explain the existence of the Moon, and the parameters for modelling it have been tuned to produce a Moon with the right mass and metal/silicate ratio, and the right angular momentum for the Earth–Moon system.

One of the impressive results of the Luna and Apollo missions is a chronology of the magmatic evolution of the Moon: major planetary-scale differentiation occurred ∼4.45 Gyr, followed by mare basaltic magmatism within ∼ 4.0 to 3.0 Gyr ago. Unlike terrestrial materials, the ancient rocks of the Moon have preserved a record of its very early evolution.

Within the framework of this book, it would have been attractive to exploit this record in order to understand the early history of our planet better. However, from the following sections we shall see that, although the existence of the Moon is essential evidence for the standard model of planetary accretion and although there is an underlying partial similarity of chondrite-like volatile-depleted initial matter to that of the Earth (Section 21.2), the Moon's evolution was fundamentally different from what happened on the early Earth. An exception is the record of frequent impacts on the Moon with a late heavy bombardment lasting up to ∼ 3.8 Gyr ago, which therefore must also have occurred on Earth.

The expanding Universe and the Big Bang hypothesis

Friedmann (1922) was the first to postulate the model of an expanding Universe that originated in one explosion-like event. Soon afterwards Hubble (1929) discovered the relationship between the redshifts, due to the Doppler effect, in the spectra of distant stars, galaxies or galactic clusters and the distances to these objects: the further the object the larger the redshift, i.e. the greater the outward velocity (see Section 4.3). These relationships were considered as the first important confirmation of Friedmann's model, which is now generally accepted.

Later, further supporting evidence was found. The uniform He/H ratio in astrophysical objects with low metallicity, discussed in Section 3.1, was shown to be identical to that predicted by the Big Bang nucleosynthesis (BBN) model. Further, important support for the Big Bang hypothesis was the observation of the cosmic microwave background radiation (Penzias and Wilson, 1965), which had been predicted by Gamow's Big Bang model. From recent high-precision satellite-based measurements of this radiation, several important cosmological parameters including the Hubble parameter and the primeval D/H ratio have been inferred, and these are in excellent agreement with the values actually observed (Spergel et al., 2003). Also, all independent estimates of the age of BBN and of the most ancient objects formed in the Galaxy are remarkably consistent (Sections 4.3 and 7.2).

Introduction to chondritic meteorites: compositions and taxonomy

The most primitive meteorites are aggregates consisting of a fine-grained heterogeneous matrix, in which are embedded small (generally from 0.2 to 1.0 mm) droplet-like silicate particles termed chondrules, which have given the name to this meteorite class, chondrites. The chondrules and the matrix comprise distinct and different assemblies of chemical elements, e.g. volatile-depleted chondrules coexist with a volatile-enriched matrix. Some chondrites also contain metal grains. The third component of chondrites, Ca–Al-rich inclusions, was discussed in Chapter 10.

Chondrites preserve a unique record of processes and conditions in the early nebula. Although never molten after their agglomeration, chondrites have variably undergone metamorphism that has in some cases altered their mineralogy and composition. The relative abundances of involatile major and trace elements in bulk chondrites are generally similar to the solar abundances (see Section 3.4). However, in sharp contrast with the solar composition, only four elements, oxygen, silicon, magnesium and iron, are the major chondritic components, contributing almost 90% by mass, and these same four are also the major constituents of the terrestrial planets (Tables 11.1 and 17.1). There are clear reasons for the high contributions of these elements to the meteoritic and planetary compositions. First of all, the most abundant isotopes of O, Mg and Si are the so-called α- or primary isotopes (16O, 24Mg and 28Si), characterized by a high binding energy per nucleon (Chapter 1).

Introduction: principal reservoirs of the post-accretion Earth

Modelling of the compositional development of the Earth in the course of the giant Moon-forming impact predicts the loss of a minor fraction of the material of the merged bodies, within a few per cent of the total mass (Cameron, 2001b). This means that the terrestrial abundances of most elements were not substantially affected. However, the great amount of energy deposited by this and preceding impacts triggered two fundamental irreversible processes, which changed the chemistry of our planet. These were the segregation of the metal core (Chapter 18) and the loss of much of the primary content of atmophile species (Chapter 20).

After the giant impact, the enormous amount of heat generated by the impact itself and by the sinking of metal through the mantle would have led to a global magma ocean. However, in contrast with the Moon (Chapter 21), the Earth shows no chemical and isotopic evidence of fractionation such as would be expected if a magma ocean had existed. The answer to this problem lies in the nature of convection in the terrestrial magma ocean; this is discussed in Section 17.5.

The mixing of late-accreting chondritic matter (with a higher Fe-content, and thus higher density, than terrestrial silicate rocks) with post-segregation metal-free silicates in the mantle or protocrust could have generated material with an intermediate density.