Kinetic theory of stellar systems: A tutorial

Stellar systems—globular and nuclear star clusters, elliptical and spiral galaxies and their surrounding dark matter haloes, and so on—are ubiquitous characters in the evolutionary tale of our Universe. This tutorial article is an introduction to the collective dynamical evolution of the very large numbers of stars and/or other self-gravitating objects that comprise such systems, i.e., their kinetic theory. We begin by introducing the basic phenomenology of stellar systems, and explaining why and when we must develop a kinetic theory that transcends the traditional two-body relaxation picture of Chandrasekhar. We then study the individual orbits that comprise stellar systems, how those orbits are modified by linear and nonlinear perturbations, how a system responds self-consistently to fluctuations in its own gravitational potential, and how one can predict the long-term evolutionary fate of a stellar system in both quasilinear and nonlinear regimes. Though our treatment is necessarily mathematical, we develop the formalism only to the extent that it facilitates real calculations. Each section is bolstered with intuitive illustrations, and we give many examples throughout the text of the equations being applied to topics of major astrophysical importance, such as radial migration, spiral instabilities, and dynamical friction on galactic bars. Furthermore, in the 1960s and 1970s, the kinetic theory of stellar systems was a fledgling subject which developed in tandem with the kinetic theory of plasmas. However, the two fields have long since diverged as their practitioners have focused on ever more specialized and technical issues. This tendency, coupled with the famous obscurity of astronomical jargon, means that today relatively few plasma physicists are aware that their knowledge is directly applicable in the beautiful arena of galaxy evolution, and relatively few galactic astronomers know of the plasma-theoretic foundations upon which a portion of their subject is built. Yet, once one has become fluent in both Plasmaish and Galacticese, and has a dictionary relating the two, one can pull ideas directly from one field to solve a problem in the other. Therefore, another aim of this tutorial article is to provide our plasma colleagues with a jargon-light understanding of the key properties of stellar systems, to offer them the theoretical minimum necessary to engage with the modern stellar dynamics literature, to point out the many direct analogies between stellar- and plasma-kinetic calculations, and ultimately to convince them that stellar dynamics and plasma kinetics are, in a deep, beautiful and useful sense, the same thing.