The spiral in the bar in the spiral (APOD 22 Jun 2008)

[henk21cm]

Thanks Art for your reply.

A gravitational force of EXACTLY : - K * z defines an harmonic oscillator such that all the objects will have the same periodicity. (Note also that stars on the back & front sides of the bar will get a gravitational pull back to the center.)

Right, if the distance between a star and the center of the galaxy is too far, the attractive force pulls it inward towards the center of the galaxy. It will start oscillating around the center of the galaxy. That explains the inversion symmetry around the center of the galaxy.

Now, for simplicity sake, i introduce a coordinate system, which rotates, fixed to the bar. As to speak: it rotates synchronously with the galaxy. The derivative of φ with respect to time is therefore zero. Due to interaction between stars in the bar, some stars will get a lateral (in the φ direction) velocity. In the z direction they still ocillate around the center. In φ direction they will drift out of the cylinder shaped bar, not at the top or bottom of the cylinder, but through the curved (side) walls.

What I have given is just a hand waving argument that suggests how a bar galaxy might maintain itself (to first order) if the bar stars are distributed so as to emulate a simple harmonic oscillator gravitational field along the bar.

for which i must give you credit: i would not have been able to come up with such nice explanation.

[neufer]

What I have given is just a hand waving argument that suggests how a bar galaxy might maintain itself (to first order) if the bar stars are distributed so as to emulate a simple harmonic oscillator gravitational field along the bar.

for which i must give you credit: i would not have been able to come up with such nice explanation.

Actually this is simply an extension of our previous (planetary) discussion involving stable self gravitating incompressible fluid:

1) slowly rotating oblate spheroids and
2) moderately fast rotating prolate ellipsoids.

However, rather than dealing with an
a) incompressible fluid of constant density

we are dealing here with an
b) infinitely compressible fluid of variable density.

The fact that the latter (infinitely compressible) case also allows for stable RAPIDLY rotating very oblate spheroids whereas the former (incompressible) case did NOT would seem to be an encouraging sign that a large number of infinitely compressible rotating prolate fluid ellipsoids can also be found to be stable.