Kinetic Theory of Stellar Systems, or, Dynamics in Translation: How the Mathematics of Nuclear Fusion Informs the Physics of Galaxies

Every high school student knows that electrostatics and gravity are intellectually adjacent subjects:

up to a sign, the Coloumbic electrical force and the Newtonian gravitational force are identical. What

is less well appreciated is that this adjacency extends much further than simple 1/r^2 force laws. In

fact, it turns out that the mathematical methods developed to harness the power of the protons and

electrons and magnetic fields in astrophysical and fusion plasmas are precisely the same as those

needed to describe the dynamics of stars, spiral arms and dark matter in galaxies like the Milky Way.

That plasma physics and galactic dynamics are closely related is not a new discovery — Lynden-

Bell’s theory of violent relaxation is now as much at home in a plasma course as it is in galactic

dynamics, whereas the mathematics of Landau damping now underpins the theory of angular mo-

mentum transport in galactic disks. But these two fields long ago went their separate ways, and in

the modern literature are separated by a near-impenetrable wall of jargon. 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.

The purpose of this tutorial article is to supply plasma physicists with this dictionary. We aim to

provide you with a jargon-free understanding of the basic properties of stellar systems, to offer you the

theoretical minimum necessary to begin reading galactic dynamics literature and to recognize where

fruitful overlap might be sought, and to convince you that stellar dynamics and plasma kinetics are,

to a deep and useful extent, the same thing.