Toomre wavenumber ($k_T={\kappa }^2/(2\pi G\Sigma )$)

In the razor-thin fluid disk dispersion relation, the cold limit is ${\omega }^2={\kappa }^2-2\pi G\Sigma |k|$. Rotation therefore suppresses wavelengths above ${\lambda }_T=2\pi /k_T=4{\pi }^{2}G\Sigma /{\kappa }^2$. With this convention, $k_T$ is the cold-disk boundary of instability, not the fastest-growing wave number when finite pressure is present. At marginal fluid stability $Q=1$, the minimum occurs at $|k|=2k_T$.