I. Gravitational Stability of Uniformly Rotating Disks

Abstract

The stability of a stratified self-gravitating rotating medium is discussed. It is found that in all cases pressure effects stabilize short waves while long waves are stabilized by rotation. When $$\pi G\bar\rho/4\Omega^2$$ is greater than a number between 1.8 and 0.7 (depending on the polytropic index) there is an intermediate range of unstable wave-lengths centred at several times the thickness of the sheet. These instabilities would lead to the break-up of the sheet into masses of definite size. This paper serves as an introduction to the following one on the stability of differentially rotating media and the formation of spiral arms.