 Spiral density wave

A collective perturbation of surface density and gravitational potential in a galactic disk. Material can cross its spiral-shaped crests; the pattern angular speed need not equal the local material angular speed. A tightly wound fluid approximation has $(\omega -m\Omega {)}^2={\kappa }^2+c_s^2{k}^2-2\pi G\Sigma |k|$, while a collisionless stellar disk requires its own response function.