What is the movement of stars within the nucleus of a barred spiral galaxy I'm looking for visualizations that show the movement of stars in barred galaxies but not having much luck. I've found many that simulate spiral galaxy arms in general, but none that include a bar or a nucleus.

I'm trying to word my question in a way that is not dependent on my own assumptions, but some of my assumptions are:


the area that includes the bar is the nucleus.
the nucleus and the bulge are not necessarily the same thing. (Bars within the nucleus is a result of gravity waves. Bulge is an artifact of how the galaxy was formed.)
the edge boundary of the nucleus is a gravitational "tipping point".
stars are not crossing this boundary (ie: they either belong to the nucleus or to the arms, not both).


What is the movement of stars within the nucleus of a barred spiral galaxy, and how do their galactic orbits differ from stars outside the nucleus?
It's a little hard to know how to answer your question, partly because you're using "nucleus" in a confusing fashion. So let me try answering what might be your general question, which is "how do stars move in the region spanned by the bar?"

("Nucleus" is generally used to refer to the inner few hundred parsecs -- or even, these days, just the inner ten parsecs or so. Since bars extend to anywhere from several hundred parsecs to as much as ten thousand parsecs in radius, they are usually well outside the "nucleus". [I am deliberately ignoring so-called "nuclear bars" -- which are generally only a few hundred parsecs in size -- in order to keep things simple ;-)])

Stars in a disk galaxy generally all orbit in the same direction and in the same plane. Some of the orbits are close to circular, while others are more elongated. These elongated orbits precess -- that is, the axis of the apparent ellipse rotates with time, so the star traces out a rosette. In a barred galaxy, there are a lot of stars which are on elongated orbits which are aligned, and which precess at the same rate. Thus, they maintain a common oval region that is dense with stars (the "bar") which rotates as a whole at a more-or-less constant speed (even as the stars making up the bar are doing their own individual orbits at different speeds). The combined gravity of all these stars in an oval configuration is what keeps the whole thing synchronized and consistent, although there are some stars on more chaotic orbits.

There is a kind of magic radius called "corotation". This is where an imaginary star in a circular orbit would go once round the center of the galaxy in the same time that the bar as a whole make one complete turn. Stars inside corotation go once around faster than the bar turns, while stars outside this radius would go once round slower than the bar. Stars orbiting inside the corotation radius can form part of the bar (and generally have to be part of the bar if they're not on some very chaotic orbit). Stars outside corotation cannot be part of the bar; their orbits will actually tend to be elongated perpendicular to the bar, though as you get further away from the bar, its gravitational influence becomes less and less important, so that stars further out can have orbits that are pretty much circular.

There is good evidence -- both theoretical and observational -- that bars cannot extend further out than the corotation radius, and that bars in fact tend to extend about 3/4 or 4/5 of the way to corotation (with the stars further out but still inside corotation probably having very chaotic orbits).