Toomre wavenumber
= Toomre wavenumber
{c}
{title2=$k_T=\kappa^2/(2\pi G\Sigma)$}
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 $\lambda_T=2\pi/k_T=4\pi^2G\Sigma/\kappa^2$. 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 $|k|=2k_T$.