On the Gravitational Stability of a Disk of Stars by Alar Toomre (1964, The Astrophysical Journal 139, 1217–1238)

The primary calculation treats a collisionless stellar disk and obtains the critical radial velocity dispersion $3.36G\Sigma /\kappa$. A fluid disk has a related but numerically different criterion involving $\pi G\Sigma /\kappa$. The distinction matters when a fluid dispersion relation is used to approximate stellar random motion.