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Understanding the origin and evolution of galaxies is one of the most fascinating unsolved problems in astrophysics. In recent years, there has been an abundance of new observational results that are pertinent to galaxy formation. At the same time, major advances have been made in one or two theoretical areas, notably involving application of particle physics to cosmology and numerical simulations of galaxy mergers and clustering. It is therefore timely for a review of galaxy formation. Our emphasis will be on recent developments in both observation and theory that have occurred since the last major reviews were written by Jones (1976) and Gott (1977).

We begin with a discussion of the observational aspects of galaxies and large-scale structure that are relevant for understanding the origin of galaxies. In Section 2.1, we discuss elliptical galaxy properties and in Section 2.2 we summarize the relevant data on luminosity profiles and rotation of disc systems. The luminosity function is reviewed in Section 2.3, and in Section 2.4 we discuss galaxy clustering, superclustering and estimates of the mean mass density of the Universe. Observations of the microwave background radiation are also reviewed (Section 2.5).

Next, we turn to the evolution of density perturbations in an expanding universe. Results are summarized on the linear theory (Section 3.1) and on the origin (Section 3.2) and spectrum (Section 3.3) of fluctuations. Adiabatic (Section 4.1) and isothermal fluctuations (Section 4.2) are introduced, and the evolution of an initially featureless power-law spectrum described. In Section 4.3, we discuss how the residual radiation anisotropy provides a probe of primordial fluctuations, over both large and small angular scales. Complications associated with reionization after decoupling are also described (Section 4.4).

Large-scale structure in the galaxy distribution provides a useful constraint on the initial fluctuation spectrum. The Newtonian theory for the growth of irregularities is reviewed and is applied to the formation of "pancakes" (Section 5.2) and to the evolution of the galaxy correlation function in hierarchical clustering theories (Section 5.3). We also review results from large computer simulations which have recently been applied to the problem of galaxy clustering.

In Section 6.1 we describe dissipationless collapse and violent relaxation. Various authors have speculated that elliptical galaxies may have formed by dissipationless collapse. If this were true, the observed shapes and rotational properties of ellipticals may be related to initial conditions in a simple and tractable way. Numerical simulations designed to test this idea are reviewed in Section 6.2. Angular momentum provides a direct test of dissipationless collapse models. The acquisition of angular momentum by tidal interactions is reviewed in Section 6.3 and the theoretical predictions are compared with the rotational properties of ellipticals and spirals.

One exciting idea that has gained in popularity recently is that collisions and mergers between galaxies may occur quite frequently. A discussion of encounter cross sections and merger rates is given in Section 7.1. Numerical simulations indicate that mergers between two similar disc galaxies result in remnants with density profiles and dynamical properties similar to those of elliptical galaxies (Section 7.2). The general issue of whether ellipticals form via mergers is addressed in Section 7.3.

The role of dissipative processes in galaxy formation is considered in Section 8. Of course, it is impossible to present a detailed treatment of the gas dynamical processes likely to have been important at the time of galaxy formation. For example, a major uncertainty is the role of star formation, a process that we do not understand even in our immediate environment. Nevertheless, there are some general arguments (Section 8.1) concerning dissipation and radiative cooling which can be applied in an attempt to understand the characteristic masses and sizes of galaxies. Angular momentum is conserved in dissipationless collapse, so the rotational properties of galaxies provide an important test of theoretical models (Section 8.2). In the pancake theory of galaxy formation, galaxies must form by the dissipative collapse and fragmentation of much larger systems. A discussion of the amount of cold gas that can condense to form galaxies in a collapsing pancake is given in Section 8.3. As we shall see, the characteristic masses of fragments that condense from the cool gas turn out to be much smaller than the masses of typical galaxies. Galaxy formation must therefore proceed by the coagulation of much smaller gas clouds. In Section 8.4 we de-describe a scheme in which galaxies form by the coagulation and disruption of small gas clouds which may be applicable to both the pancake and hierarchical clustering theories. In Section 8.5 we briefly discuss the role of pregalactic stars in galaxy formation.

Finally, we turn to one of the most dramatic recent developments in cosmology, which has arisen from the realization that particle physics has a unique laboratory in the very early universe, where energies are attained that provide a regime where grand unification theories apply. The implications for fluctuation theory are noteworthy (Section 9.1), but the most revolutionary aspect has been the realization that neutrinos (Section 9.2) and other fermions [such as gravitinos (Section 9.3)] may have rest-masses that suffice to dominate the present mass-density of the universe.

We assume that the reader has had an introductory course in General Relativity and is familiar with the Friedmann-Robertson-Walker metric and with the general details of the standard, unperturbed, hot big bang cosmology. For those readers who lack this basic knowledge we would recommend the books by Peebles (1971a) and Weinberg (1972, particularly Section 15). For readers interested in more detail on some aspects of the material covered in this article but who do not yet wish to dive into the original literature we would recommend the following recent books and reviews: Observations of galaxy structure and dynamics are reviewed by Kormendy (1982). A survey of observations of large-scale structure and superclusters is given by Oort (1983) and the origin of large-scale structure is discussed by Fall (1979a) and in detail by Peebles (1980a). Observational limits on the mean mass density of the Universe are reviewed in depth by Faber and Gallagher (1979) and by Peebles (1980b). Galaxy mergers and the effects of environment on galactic structure are discussed by White (1982). Particle physics and cosmology are reviewed by Barrow (1983).

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