Square Orbits

Why do some galaxies have barred centers?

Because the stars at the center are in an orbit which closely approximates a square. It a not-all-that-uncommon solution to the restricted three body problem.

Edit: I started to do some drawing for how this works but, of course, the web knows all. Here is a treatment done much better than mine of some of the complicated shapes an orbit can assume in the 3-body problem. One bar producing solution is the Ice Cream Spoon orbit

Unfortunately, the orbits themselves aren't all that stable. What you see in a galatic bar is a statisitical sample of a large number of stars, most of which spend some of their time in a bar-like orbit, but none permanently so.

The best analogy in every day life for square orbits is the Tilt-A-Whirl. There is a central point point around which the arms orbit, and a second point further out around which the cars rotate.
If the central rotation were off, but the roation of the cars was on, you'd just spin in circles. Add it the central roation though, and you get a little circle, swinging around the end of a great big circle. The result is a pattern that, for large parts of the motion, is a nearly straight line followed by corners of high curvature (and high g-forces!). The pattern of this motion strongly resembles the orbits of galactic bar stars.


Which, all in all, is pretty cool. And, these kinds of orbits are not limited to squares. In general almost any polyhedreon can be simulated with the right set of masses and forces, although orbital stability in the general case is not assured.