The Distribution of the Galaxies: Gravitational Clustering in Cosmology

William C. Saslaw's The Distribution of the Galaxies is an excellent and useful book that is especially well suited to the needs of advanced undergraduates and beginning graduate students. Researchers, as well, should welcome its comprehensive and detailed discussion of a theoretical approach that does not Figure prominently in other book-length accounts of what Edwin Hubble, in a famous series of lectures, called the realm of the nebulae. Saslaw, a pioneer in the application of thermodynamics and statistical mechanics to gravitational astrophysics, modestly but accurately describes the book as "really no more than an extended essay on aspects of galaxy clustering that I've found especially interesting."

The essay's main thesis is that galaxies can be thought of as particles of a gas that evolves through a series of quasi-equilibrium states. With this assumption, and with the gas's equation of state given by the cosmic energy equation, one can use standard methods in thermodynamics, statistical mechanics, and kinetic theory to predict functions that describe the distribution of galaxies in physical space and in velocity space. A straightforward application of thermodynamic fluctuation theory then gives the distribution of galaxy numbers in a volume of given magnitude. To predict the distribution of peculiar velocities, one needs an additional assumption: the value of the parameter "b" (mentioned below).

Roughly half the book is devoted to these and closely related theoretical matters and to discussions of computer simulations and observational evidence that bear directly on the predicted distribution functions. The book also contains a relatively brief but insightful discussion of theoretical and practical aspects of correlation functions.

Most students, and many of their mentors, pay little attention to the history of the problems they are trying to solve, assuming that it is of more interest to historians than to working scientists. In reality, nothing is more helpful to the novice scientist than a deep understanding of how his or her subject has evolved. One of the best things about the book under review is its opening 50-page history of efforts to describe and understand the spatial distribution of galaxies.

A further bonus is a cluster of five short chapters dealing with nontraditional mathematical techniques for describing nonuniform spatial distributions of points: percolation; minimal spanning trees; topology; and fractals, introduced by a brief discussion of the problem of distinguishing genuine patterns from optical illusions. Here the author's talent for clear, concise, and insightful exposition is on display. Equally impressive, and especially valuable for students, are his accounts of key ideas and results in thermodynamics, including phase transitions and kinetic theory. The author does not merely apply results from other branches of physics to the problem at hand, he either derives them from the ground up or explains their provenance in ways that encourage an interested reader to seek further enlightenment.

The author's assumption that galaxies can be treated as particles in a gas that expands through a sequence of quasi-equilibrium states allows him to put to one side the question of how cosmic structure arose and evolved. My own view is that galaxy clustering is one stage in a process of hierarchical clustering that began with the formation of the smallest self-gravitating units and proceeded through stars, multiple star systems, star clusters, and so on through galaxy superclusters. In this view, the cosmic medium is a "gas" that remains on the edge of thermodynamic instability as it expands; I raise the subject here, because it leads to a prediction about a parameter that plays a central role in Saslaw's book. The prediction is that this parameter, which in Saslaw's book varies with time, has a fixed value close to 0.75; Figure 4.1 on page 30 of the book shows that the Saslaw­Hamilton spatial distribution function fits Hubble's old galaxy counts almost perfectly, if the parameter "b" is assigned the value 0.72; numerical simulations also support a value close to 0.75.

The author and the editors have found many ways to make The Distribution of the Galaxies both attractive and reader-friendly. Cambridge University Press is to be congratulated on a splendid job of book-making. The quality of the book matches the quality of its contents.