Surface density contrast in an eccentric ring
= Surface density contrast in an eccentric ring
A higher orbital line density at <apoapsis> does not always give a higher <surface density of a disk>: the local ring width also changes. In a narrow <aligned eccentric ring>, neglecting disc twist and keeping first-order <orbital eccentricity>, $\Sigma_{\rm peri}\propto1+a\,de/da$ and $\Sigma_{\rm apo}\propto1-a\,de/da$. Constant eccentricity therefore gives constant surface density to this order.