Certainly Bacon's judgment that optics is the gateway to other sciences is particularly true of astronomy, since virtually all astronomical information arrives in the form of light. We devote the next two chapters to how astronomers utilize the sweetness and beauty of optical science. This chapter introduces the fundamentals.

We first examine the simple laws of reflection and refraction as basic consequences of Fermat's principle, then review the behavior of optical materials and the operation of fundamental optical elements: films, mirrors, lenses, fibers, and prisms.

Telescopes, of course, are a central concern, and we introduce the simple concept of a telescope as camera. We will see that the clarity of the image produced by a telescopic camera depends on many things: the diameter of the light-gathering element, the turbulence and refraction of the air, and, if the telescope uses lenses, the phenomenon of chromatic aberration. Concern with image quality, finally, will lead us to an extended discussion of monochromatic aberrations and the difference between the first-order and higher-order ray theories of light.

Following up on the previous chapter, in which we discussed star formation, we now address how individual stars evolve with time. As we will see below, most stars, during most of their evolutionary histories, can be considered as spherically symmetric objects with a constant mass that are in hydrostatic equilibrium. Under these conditions, the evolution of a star is almost completely determined by its mass and chemical composition through a set of ordinary differential equations that describe the structure of the star. In this chapter, we start with a brief description of the basic concepts of the theory of stellar evolution. A detailed description is beyond the scope of this book, but can be found in many monographs and textbooks on this subject (e.g. Schwarzschild, 1965; Clayton, 1983; Kippenhahn & Weigert, 1990). We then use the theory of stellar evolution to predict the properties of individual stars (e.g. spectrum, luminosity, metal production, etc.) at different evolutionary stages, and discuss how these results can be synthesized to make predictions regarding the evolution of populations of stars (e.g. galaxies). Finally, we discuss how the evolution of stars affects the chemical evolution of galaxies.

The Basic Concepts of Stellar Evolution

A stellar evolution model generally starts with two basic assumptions: (i) stars are in hydrostatic equilibrium, and (ii) stars are spherically symmetric.

In the standard model of cosmology described in the previous chapter, the Universe is assumed to be highly homogeneous at early times. The structures observed today, such as galaxies and the clusters of galaxies, are assumed to have grown from small initial density perturbations due to the action of gravity. In this scenario, structure formation in the Universe involves the following two aspects: (i) the properties and origin of the initial density perturbations, and (ii) the time evolution of the cosmological perturbations in an expanding Universe.

In this chapter we examine the origin of cosmological perturbations and their evolution in the regime where the amplitudes of the perturbations are small. We begin in §4.1 with a description of Newtonian perturbation theory in the linear regime. This applies to structures with sizes much smaller than the horizon size, so that causality can be considered instantaneous, and with a density contrast relative to the background much smaller than unity. The relativistic theory of small perturbations is dealt with in §4.2. This is an extension of the Newtonian perturbation theory, and is required when considering perturbations larger than the horizon size or when the matter content of the perturbations cannot be treated as a non-relativistic fluid. For a Universe with a given matter content, the theories presented in these two sections allow one to trace the time evolution of the cosmological perturbations in the linear regime. The nonlinear evolution will be discussed in Chapter 5.

In the previous chapters we have discussed the various physical ingredients that play a role in galaxy formation, from the growth, collapse and virialization of dark matter halos, to the formation of stars out of the baryonic material that cools within these halos. In this chapter we combine all this information to examine the structure and formation of disk galaxies.

As we have seen in Chapter 2, disk galaxies in general consist of a disk component made up of stars, dust and cold gas (both atomic and molecular), a central bulge component, a stellar halo, and a dark halo. The disk itself reveals spiral arms and often - in roughly half of all cases - a central bar component. Any successful theory for the formation of disk galaxies has to be able to account for all these components. In addition, it should also be able to explain a variety of observational facts (see §2.3.3), the most important of which are:

• Brighter disks are, on average, larger, redder, rotate faster, and have a smaller gas mass fraction.

• Disk galaxies have flat rotation curves.

• The surface brightness profiles of disks are close to exponential.

• The outer parts of disks are generally bluer, and of lower metallicity than the inner parts.

Observational astronomy has developed at an extremely rapid pace. Until the end of the 1940s observational astronomy was limited to optical wavebands. Today we can observe the Universe at virtually all wavelengths covering the electromagnetic spectrum, either from the ground or from space. Together with the revolutionary growth in computer technology and with a dramatic increase in the number of professional astronomers, this has led to a flood of new data. Clearly it is impossible to provide a complete overview of all this information in a single chapter (or even in a single book). Here we focus on a number of selected topics relevant to our forthcoming discussion, and limit ourselves to a simple description of some of the available data. Discussion regarding the interpretation and/or implication of the data is postponed to Chapters 11-16, where we use the physical ingredients described in Chapters 3-10 to interpret the observational results presented here. After a brief introduction of observational techniques, we present an overview of some of the observational properties of stars, galaxies, clusters and groups, large scale structure, the intergalactic medium, and the cosmic microwave background. We end with a brief discussion of cosmological parameters and the matter/energy content of the Universe.

Cosmology, the branch of science dealing with the origin, evolution and structure of the Universe on large scales, is closely related to the study of galaxy formation and evolution. Cosmology provides not only the space-time frame within which galaxy formation and evolution ought to be described, but also the initial conditions for the formation of galaxies. Modern cosmology is founded upon Einstein's theory of general relativity (GR), according to which the space-time structure of the Universe is determined by the matter distribution within it. This perspective on space-time is very different from that in classical physics, where space-time is considered eternal and absolute, independent of the existence of matter.

A complete description of GR is beyond the scope of this book. As a remedy, we provide a brief summary of the basics of GR in Appendix A and we refer the reader to the references cited there for details. It should be emphasized, however, that modern cosmology is a very simple application of GR, so simple that even a reader with little knowledge of GR can still learn it. This simplicity is owing to the simple form of the matter distribution in the Universe, which, as we have seen in the last chapter, is observed to be approximately homogeneous and isotropic on large scales. We do not yet have sufficient evidence to rule out inhomogeneity or anisotropy on very large scales, but the assumption of homogeneity and isotropy is no doubt a good basis for studying the observable Universe.

General relativity (hereafter GR) is the subject dealing with the structure of space-time and with how to describe physical laws in any given space-time. The perspective of space-time in GR is very different from that in Newtonian physics. In Newtonian physics, space is considered to be flat, infinite and eternal, time is considered to flow uniformly, and physical processes are considered to act in this external space-time frame. In the framework of GR, however, space-time is a four-dimensional manifold which may be curved and the properties of space-time itself are determined by dynamical processes.

This appendix provides a brief summary of the aspects of GR that are used in this book. More details can be found in the excellent textbooks by Weinberg (1972), Misner et al. (1973), Rindler (1977), and Carroll (2004).

Space-time Geometry

In order to gain some insight in how to describe space-time as a four-dimensional manifold (hypersurface), consider a two-dimensional analog. To describe a two-dimensional surface, we can construct a coordinate system and label each point on the surface by its coordinates. The geometrical properties of the surface can be obtained by considering the distance between each pair of infinitesimally close points on the surface in terms of the differences in coordinates.

Galaxies are ecosystems consisting of dark matter, stars and gas. It is useful to split the gas into three broad components according to its relation to the galaxy. The first is the interstellar medium (ISM), which is the gas that is directly associated with the galaxy. The second is the halo gas, which is distributed outside the galaxy but inside the host dark matter halo of the galaxy. The third is the gas that is not associated with dark matter halos. The latter two components combined are known as the intergalactic medium (IGM). During the formation and evolution of a galaxy, the ISM and IGM interact actively with each other. Halo gas can cool and be accreted into the galaxy to become part of the ISM. The gas in the ISM can be ejected into the halo or even into the large-scale environment by galactic winds and stripping. And finally, dark matter halos can accrete gas from the IGM in their large-scale environments.

Clearly, the IGM is a crucial ingredient of any theory of galaxy formation and evolution. In fact, by definition, all baryons were part of the IGM at sufficiently early times (before the formation of stars and galaxies). At later times, more and more material of the IGM is accreted by virialized dark matter halos, where it can be converted into cold gas (ISM) or stars. However, even at the present day, a very substantial fraction of the baryons is believed to still reside in the IGM.

This book is concerned with the physical processes related to the formation and evolution of galaxies. Simply put, a galaxy is a dynamically bound system that consists of many stars. A typical bright galaxy, such as our own Milky Way, contains a few times 1010 stars and has a diameter (~ 20kpc) that is several hundred times smaller than the mean separation between bright galaxies. Since most of the visible stars in the Universe belong to a galaxy, the number density of stars within a galaxy is about 107 times higher than the mean number density of stars in the Universe as a whole. In this sense, galaxies are well-defined, astronomical identities. They are also extraordinarily beautiful and diverse objects whose nature, structure and origin have intrigued astronomers ever since the first galaxy images were taken in the mid-nineteenth century.

The goal of this book is to show how physical principles can be used to understand the formation and evolution of galaxies. Viewed as a physical process, galaxy formation and evolution involve two different aspects: (i) initial and boundary conditions; and (ii) physical processes which drive evolution. Thus, in very broad terms, our study will consist of the following parts:

• Cosmology: Since we are dealing with events on cosmological time and length scales, we need to understand the space-time structure on large scales. One can think of the cosmological framework as the stage on which galaxy formation and evolution take place.

So far we have concentrated on the formation of structure under the influence of gravity alone. However, since the astronomical objects we are able to observe directly are made of baryons and electrons, the role of gas-dynamical and radiative processes must also be taken into account in order to understand how the structures we observe form and evolve. As demonstrated in §4.1.3, since baryons and dark matter are expected to be well mixed initially, the density perturbation fields of the baryons, δb, and dark matter, δdm, are expected to be equal in the linear regime, except for perturbations on scales smaller than or comparable to the Jeans length of the gas. In this chapter, we examine the role of gas-dynamical and radiative processes for the evolution of structures in the highly nonlinear regime. We start in §8.1 with a brief description of the basic dissipational processes. §8.2 describes the structure of gas in hydrostatic equilibrium within dark matter halos. The formation of gaseous halos in the absence of cooling and heating is discussed in §8.3, while §8.4 focuses on the impact of cooling. §8.5 describes several thermal and hydro dynamical instabilities of cooling gas, and §8.6 discusses the evolution of gaseous halos in the presence of energy sources. §8.7 gives a summary of the current status of numerical studies of the formation and structure of gaseous halos, while §8.8 discusses observations of gaseous halos associated with clusters and galaxies.