II. Spiral Arms as Sheared Gravitational Instabilities

This paper treats examples of gravitational instability in differentially rotating media. The particular cases dealt with include polytropic, stratified sheets of gas, as well as the infinite homogeneous media. Application of the results is made to the formation of spiral arms in a differentially rotating disk galaxy. Relations are derived which connect the thickness of the galactic disk, its density, and the velocity dispersion perpendicular to the galactic plane with Oort's differential rotation parameters A and B . Sections 1 and 2 discuss requirements of any theory of spiral arms. Sections 3 to 8 give a mathematical treatment of gravitational instability in a sheared rotating stratified medium. Section 9 discusses these results qualitatively and proposes a theory of spiral arm formation based on them. Section 10 gives the observational tests and consequences of the theory. Finally Section 11 gives a very brief discussion of barred spirals and points to the many problems left unsolved by the present work.