### What is an orbital resonance?

An orbital resonance occurs in galaxies when an orbit's epicyclic frequency —the frequency of an orbit's radial motion—is a simple multiple of a forcing frequency. The forcing frequency can be the rate at which an object encounters successive crests of spiral waves or the influence of a rotating central bar. In these cases the spiral pattern or the rotating bar can be characterized by a pattern frequency Ωb. If an orbit's angular frequency is Ω then a resonance (in the limit of a circular orbit) occurs when the rate at which an object encounters the forcing, Ω - Ωb, is commensurate with the epicycle frequency κ:

m(Ω - Ωb) = κ
.

where m is an integer. Some examples of common resonances are given below.

#### Corotation resonance

This resonance occurs when the orbit moves at the same angular speed as the forcing

Ω = Ωb

Example movies are given below. The movie on the right shows the orbital motion in the spiral-structure's corotating frame.

(click to play)

This resonance occurs when the orbit's epicyclic motion lags the forcing. Example movies in the case of a barred galaxy are shown below. The movie on the right shows the orbit in the frame corotating with the bar.

(click to play)

This resonance occurs when the orbit overtakes the forcing periodically. Example movies are given below. The movie on the right shows the orbit in the frame corotating with the bar. Warning: The fast spiral motion on the left might induce vertigo!

(click to play)