= Softened Toomre dispersion relation
{title2=$\omega^2=\kappa^2-2\pi G\Sigma_0k e^{-k\epsilon}+c_s^2k^2$}
Linear axisymmetric compressive modes of a <barotropic closure of a razor-thin disk> combine radial epicyclic restoration, softened <self-gravity> and <pressure>. The <off-plane razor-thin Poisson kernel> supplies the exponential gravity reduction. Here $k$ is the nonnegative radial <wavenumber> magnitude. The full linear system also has an <axisymmetric geostrophic mode>.
Back to article page
