In this series of lectures I discuss the basic principles and the modelling of the chemical evolution of galaxies. In particular, I present models for the chemical evolution of the Milky Way galaxy and compare them with the available observational data. ¿From this comparison one can infer important constraints on the mechanism of formation of the Milky Way as well as on stellar nucleosynthesis and supernova progenitors. Models for the chemical evolution of elliptical galaxies are also shown in the framework of the two competing scenarios for galaxy formation: monolithic and hierachical. The evolution of dwarf starbursting galaxies is also presented and the connection of these objects with Damped Lyman-α systems is briefly discussed. The roles of supernovae of different type (I, II) is discussed in the general framework of galactic evolution and in connection with the interpretation of high redshift objects. Finally, the chemical enrichment of the intracluster medium as due mainly to ellipticals and S0 galaxies is discussed.

Basic parameters of chemical evolution

Galactic chemical evolution is the study of the evolution in time and space of the abundances of the chemical elements in the interstellar gas in galaxies. This process is influenced by many parameters such as the initial conditions, the star formation and evolution, the nucleosynthesis and possible has flows.

In these lectures I present a highly opinionated review of the observed patterns of metallicity and element abundance ratios in nearby spiral, irregular, and dwarf elliptical galaxies, with connection to a number of astrophysical issues associated with chemical evolution. I also discuss some of the observational and theoretical issues associated with measuring abundances in H II regions and gas and stellar surface densities in disk galaxies. Finally, I will outline a few open questions that deserve attention in future investigations.

Introduction

The measurement of element abundances in galaxies other than our own has a roughly forty-year history, beginning with early attempts to measure helium abundances in giant H II regions in the Magellanic Clouds and M33 (Aller & Faulkner 1962, Mathis 1962) and pioneering studies of heavy element abundances from forbidden lines in extragalactic H II regions (e.g. Peimbert & Spinrad 1970, Searle 1971, Searle & Sargent 1972). Since then this field has grown tremendously, with high quality oxygen abundance data in some 40 nearby spiral galaxies and more than 100 irregular and compact dwarf galaxies. The amount of data for other elements (C, N, Ne, S, and Ar) has also improved tremendously, thanks largely to improvements in visible-wavelength detectors and the launching of spacecraft observatories, such as IUE, HST, and ISO, which have opened up the UV and IR spectral regions for spectroscopy.

The methods of abundance determinations in H ii regions and planetary nebulae are described, with emphasis on the underlying assumptions and inherent problems. Recent results on abundances in Galactic H ii regions and in Galactic and extragalactic Planetary Nebulae are reviewed.

Introduction

H ii regions are ionized clouds of gas associated with zones of recent star formation. They are powered by one, a few, or a cluster of massive stars (depending on the resolution at which one is working). The effective temperatures T* of the ionizing stars lie in the range 35 000 – 50 000 K. The nebular geometries result from the structure of the parent molecular cloud. Stellar winds, at evolved stages, may produce ring-like structures, but the morphology of H ii regions is generally rather complex on all scales. Typical hydrogen densities n are 103 – 104 cm–3 for compact H ii regions. The average densities in giant extragalactic H ii regions are lower, typically 102 cm–3 since giant H ii regions encompass also zones of diffuse material. The total supply of nebular gas is generally large, so that all (or at least a significant fraction) of the ionizing photons are absorbed.

Planetary nebulae (PNe) are evolutionary products of so-called intermediate mass stars (initial masses of 1 – 8 M⊙) as they progress from the asymptotic giant branch (AGB) to the white dwarf stage.

The distribution of elements in the cosmos is the result of many different physical processes in the history of the Universe, from Big Bang to present times. Its study provides us with a powerful tool for understanding the physical conditions of the primordial cosmos, the physics of nucleosynthesis processes that occur in different objects and places, and the formation and evolution of stars and galaxies. Cosmochemistry is a fundamental topic for many different branches of Astrophysics as Cosmology, Stellar Structure and Evolution, Interstellar Medium, and Galaxy Formation and Evolution.

The advances made in the last decade of the XXth century in the study of the chemical evolution of the Universe have been really spectacular. On one hand, they have been brought by the availability of large-aperture ground-based telescopes and space borne telescopes (working in both the visible and other regions of the electromagnetic spectrum), and on the other hand by advances in theory and numerical modelling techniques in many fields of astrophysics such as stellar evolution stellar atmospheres, the physics of ionised plasmas and atomic and molecular physics.

According to the predictions of the most commonly accepted cosmological models, most of the light elements, especially deuterium and helium, were produced during the first minutes after the Big Bang. Comparison between observed and predicted lightelement abundances is one of the classical fundamental tests of cosmological models. Stellar evolutionary models have advanced considerably in recent years.

Of the light nuclides observed in the universe today, D, 3He, 4He, and 7Li are relics from its early evolution. The primordial abundances of these relics, produced via Big Bang Nucleosynthesis (BBN) during the first half hour of the evolution of the universe provide a unique window on Physics and Cosmology at redshifts ∼ 1010. Comparing the BBN-predicted abundances with those inferred from observational data tests the consistency of the standard cosmological model over ten orders of magnitude in redshift, constrains the baryon and other particle content of the universe, and probes both Physics and Cosmology beyond the current standard models. These lectures are intended to introduce students, both of theory and observation, to those aspects of the evolution of the universe relevant to the production and evolution of the light nuclides from the Big Bang to the present. The current observational data is reviewed and compared with the BBN predictions and the implications for cosmology (e.g., universal baryon density) and particle physics (e.g., relativistic energy density) are discussed. While this comparison reveals the stunning success of the standard model(s), there are currently some challenges which leave open the door for more theoretical and observational work with potential implications for astronomy, cosmology, and particle physics.

Introduction

The present universe is expanding and is filled with radiation (the 2.7 K Cosmic Microwave Background - CMB) as well as “ordinary” matter (baryons), “dark” matter and, “dark energy”.

The horizon for studies of element abundances has expanded dramatically in the last ten years. Once the domain of astronomers concerned chiefly with stars and nearby galaxies, this field has now become a key component of observational cosmology, as technological advances have made it possible to measure the abundances of several chemical elements in a variety of environments at redshifts up to z ≃ 4, when the universe was in its infancy. In this series of lectures I summarise current knowledge on the chemical make-up of distant galaxies observed directly in their starlight, and of interstellar and intergalactic gas seen in absorption against the spectra of bright background sources. The picture which is emerging is one where the universe at z = 3 already included many of the constituents of today's galaxies—even at these early times we see evidence for Population I and II stars, while the ‘smoking gun’ for Population III objects may be hidden in the chemical composition of the lowest density regions of the intergalactic medium, yet to be deciphered.

Introduction

One of the exciting developments in observational cosmology over the last few years has been the ability to extend studies of element abundances from the local universe to high redshifts.

After recalling general knowledge about nuclear reactions and stellar evolution, we highlight aspects of stellar nucleosynthesis and the underlying physics of stellar evolution where progress has been achieved during the last years. In §2, we discuss the bulk nucleosynthesis in massive stars, especially of oxygen which is the most prominent massive star tracer, before we outline effects of rotation in those stars. §3 describes some recent developments in the field of s-process nucleosynthesis, §4 deals with the relevance of close binary systems for nucleosynthesis, and §5 is concerned with the most massive stars.

Introduction

We know 290 stable isotopes. With the exception of the nine lightest ones, they are all synthesised in the deep interior of stars. In order to study the evolutionary history of the abundance of all these nuclei, it is most efficient to group them such that the formation of the isotopes in each group can be understood through the same process. Following the legendary approach of Burbidge et al. (1957), one can break down the nucleosynthesis into half a dozen processes, which can be split further considering more details, but which leave only very few nuclei unexplained. While in what follows we will connect nucleosynthesis processes with evolutionary stages of stars, it is worth pointing out that Burbidge et al.

Introduction

The origins of the chemical elements must rank highly in any intelligent citizen's list of questions about the natural world. Thanks to the efforts of observers and theoreticians over the last half-century, the citizen may now be provided with answers to ‘Where, when, and how were the elements made?’ This remarkable achievement of astrophysics provides one focus for this set of lectures. It is impossible to tell in the available space the complete story of nucleosynthesis from hydrogen to uranium (and beyond) with full justice to the observational and theoretical puzzles that had to be addressed.

Nucleosynthesis began with the Big Bang (see Steigman's contribution to this volume). According to the standard model of this event, nucleosynthesis completed in the first few minutes of the Universe's life resulted in gas composed of 1H, and 4He with 1H/4He ≃ 0.08 by number of atoms, and trace amounts of 2H, 3He, and 7Li. The inability of the rapidly cooling low density Big Bang to synthesise nuclides beyond mass number 7 is due to the fact that all nuclides of mass number 5 and 8 (i.e., potential products from 1H + 4He and 4He + 4He) are highly unstable.

Ashes of the Big Bang cooled. The photons of the cosmic microwave background radiation were set free to roam the Universe. Then came what is known as ‘The Dark Ages’ before galaxies were formed.

Introduction

Most readers of this volume will know that the ancestry of gauge field theories extends back to Hermann Weyl's 1918 theory of ‘gravitation and electricity’. Since papers of Yang and others in the 1970s recovered this lineage from obscurity, considerable interest has been shown, and a few years ago a new English translation of Weyl's original paper appeared. The broad outline of the story is now common currency and need not be rehearsed in any detail here. Yet there are several largely unacknowledged aspects that arguably have more than incidental interest for those interested in philosophical issues of the significance of local symmetries. First of all, Weyl did not start out with the objective of unifying gravitation and electromagnetism, but sought to remedy a perceived blemish in Riemannian ‘infinitesimal’ geometry. The resulting ‘unification’ was, as it were, serendipitous. Then there is the not insignificant matter of Einstein's ‘pre-history’ objection, commonly affirmed to have sealed the unhappy fate of Weyl's theory. Just several weeks after hailing Weyl's theory as ‘a stroke of genius of the first magnitude’, Einstein reasoned that it was in blatant contradiction with the known constancy of the spectral lines of the chemical elements.

I think the real situation has to be described as follows. Relative to a complete system of reference not only the points in space but also all physical quantities can be fixed by numbers. Two systems of reference are equally admissible if in both of them all universal geometric and physical laws of nature have the same algebraic expression. The transformations mediating between such equally admissible systems of reference form the group of physical automorphisms; the laws of nature are invariant with respect to the transformations of this group. It is a fact that a transformation of this group is uniquely determined by that part of it that concerns the coordinates of space points. Thus we can speak of the physical automorphisms of space. Their group does not include the dilatations, because the atomic laws fix an absolute length, but it contains the reflections because no law of nature indicates an intrinsic difference between left and right. Hence the group of physical automorphisms is the group of all proper and improper congruent mappings. If we call two configurations in space congruent provided they are carried over into each other by a transformation of this group, then bodies which are mirror images of each other are congruent. I think it is necessary to substitute this definition of congruence for that depending on the motion of rigid bodies, for reasons similar to those which induce the physicist to substitute the thermodynamical definition of temperature for an ordinary thermometer.

Leibniz's principles made for an elegant and coherent philosophy. In part meta-physical, in part methodological, they addressed fundamental questions – in the treatment of symmetry, in the relationship of physics to mathematics, in logic – that are if anything even more pressing today than they were in Leibniz's time. As I shall read them, they also expressed a distinctive and uncompromising form of realism, a commitment to the adequacy of purely descriptive concepts. This doctrine has been called ‘semantic universalism’ by van Fraassen (1991), and the ‘generalist picture’ by O'Leary-Hawthorne and Cover (1996): it will become clearer in due course just what it entails.

The principles that I shall consider are the Principle of Sufficient Reason (PSR) and the Principle of the Identity of Indiscernibles (PII). In the first instance I shall take them both to be methodological principles. The former I shall read as requiring that the concepts of physics be entirely transparent. Analysis and explanation are to proceed without any limits. The perspective is impersonal: any epistemological limitation, to do with our human situation or perceptual apparatus, is to be viewed as a purely practical matter, reflecting no fundamental constraint. This puts in place a part of the generalist picture.

The PSR clearly promotes the use of mathematical concepts in physics. The PII, in contrast, depends on a sharp distinction between purely mathematical concepts, and physical ones.

Introduction

In sections 6 and 7 of their paper in this volume, French and Rickles raise the question of the logical relations between the indistinguishability postulate (IP) and the various senses in which particles might fail to be individuals. In section 6 they refer to the convincing arguments of French and Redhead (1988) and of Butterfield (1993) that IP does not logically entail non-individuality, understood several ways – even though, as all seem to concede, there is something perverse about taking bosons and fermions to be individuals. Going the other way, the possibility of IP violating ‘quons’ (Greenberg, 1991) shows that if non-individuality is taken to mean the absence of continuous distinguishing trajectories, characteristic of standard quantum mechanics (QM), then non-individuality does not entail IP. Nor, as French and Rickles point out, do substance or haecceity views of individuality.

But what if we conceive of individuality in terms of the Principle of the Identity of Indiscernibles (PII)? First, French and Redhead (1988) and Butterfield (1993) have given theorems showing that bosons and fermions violate PII, while the former have also demonstrated violations of PII in the case of a certain paraparticle state. But these cases, as I will explain (and as French and Rickles point out), cover just a very few of the possible kinds of quantum particles, and so for each kind the question arises as to whether it violates PII.

Introduction

The term ‘gauge’ refers in its most general everyday connotation to a system of measuring physical quantities, for example by comparing a physical magnitude with a standard or ‘unit’. Changing the gauge would then refer to changing the standard. The original idea of a gauge as introduced by Weyl in his (1918) in an attempt to provide a geometrical interpretation of the electromagnetic field was to consider the possibility of changing the standard of ‘length’ in a four-dimensional generalization of Riemannian geometry in an arbitrary local manner, so that the invariants of the new geometry were specified not just by general coordinate transformations but also by symmetry under conformal rescaling of the metric. The result was, in general, a non-integrability or path dependence of the notion of length which could be identified with the presence of an electromagnetic field. In relativistic terms this meant that, unacceptably, the frequencies of spectral lines would depend on the path of an atom through an electromagnetic field, as was pointed out by Einstein.

With the development of wave mechanics the notion of gauge invariance was revived by Weyl himself (1929) following earlier suggestions by Fock and by London, so as to apply to the non-integrability of the phase of the Schrödinger wave function, effectively replacing a scale transformation eα(x) by a phase transformation eiα(x).

Introduction

It is difficult to overstate the significance of the concept of symmetry in its many guises to the development of modern physics. Indeed one could reasonably argue that twentieth-century physics with its pillar achievements of successful physical theories of spacetime/gravitation and the electromagnetic and nuclear interactions merits calling that century the ‘Century of Symmetry’. For symmetry played a key part in each of these developments. Of particular significance are symmetries described by continuous (Lie) groups of transformations. Such symmetry groups play a central role both in our current understanding of fundamental physics and in various attempts to go beyond this understanding. Today such continuous symmetries are often assigned a, if not the, fundamental role in the worldview of modern physics. The precise nature of this role, though, is not entirely unambiguous. Just what significance – physical, philosophical, and otherwise – is to be ascribed to the preeminent role of such symmetry groups in fundamental physics?

This paper aims to provide a brief and necessarily selective survey of the historical development of the place of continuous symmetries in physical theory.