Unstable wavenumber band of a rotating gas sheet
= Unstable wavenumber band of a rotating gas sheet
{title2=$q_-<|k|<q_+$}
Put $Q=2|\Omega|c/(\pi G\Sigma_0)$. The <uniformly rotating gas-sheet dispersion relation> has growing waves precisely for $Q<1$, at $q_-<|k|<q_+$ with $q_\pm=(\pi G\Sigma_0/c^2)(1\pm\sqrt{1-Q^2})$. <Pressure> stabilizes short waves and rotation stabilizes long waves. Equality $Q=1$ is marginal; $Q\geq1$ is the gas <Toomre stability criterion>.