Galactokinetics II: Spiral structure

TL;DR

This paper develops a comprehensive linear theory of spiral structures in stellar disks, unifying various classic results and extending the understanding of different spatial regimes, while identifying where nonlinear effects become essential.

Contribution

It presents a unified linear response framework for spiral structures, connecting classic theories and extending their applicability across multiple spatial scales.

Findings

Derivation of a general linear response theory for thin disks.

Unification of classic spiral density wave results as limiting cases.

Identification of regimes where nonlinear physics becomes necessary.

Abstract

We present a unified theory of linear spiral structure in stellar disks. We begin by identifying the characteristic scales involved in the spiral structure problem and listing some quantitative requirements of a successful theory. We then write down the general linear response theory for thin disks, making clear the equivalence between different representations (e.g., Volterra, Landau, van Kampen) of the theory. Next, using the asymptotic expansions developed in our previous galactokinetics paper, we consider spiral structure on different spatial scales and thereby show how several classic results - including Lindblad-Kalnajs density waves, swing amplification, Lin-Shu-Kalnajs modes, and groove instabilities - emerge as limiting cases. In addition, many of our asymptotic results connect smoothly when extrapolated to intermediate regimes, rendering the analytic theory valid over a larger range of scales than naively expected. Finally, we identify situations in which nonlinear physics is unavoidable. Though many nonlinear questions remain unanswered, we hope that the theoretical synthesis developed here will allow us to both connect and distinguish the plethora of ideas that have accumulated over the last six decades of spiral structure studies, and will provide a foundation upon which a comprehensive theory might ultimately be built.