Kyle Barbary

Astro 120

Spring 2002

Homework 3

III) More Dynamics

A) Two Plummer Spheres colliding

The general behavior here is that the two spheres come together and appear to basically just pass through each other, mostly intact. Then when gravity starts slowing them down, the faster stars escape while the slower ones don’t and the dispersion of both spheres increases. They start to move back toward each other, and thus start a large-scale oscillation. This dies down as the spheres become more diffuse, and they settle into a final state of one sphere, a bit more diffuse than either original sphere. Below is shown the first 9 frames and then the final 4 frames (frames 10-27 are skipped).

The velocity dispersion for the final case is shown below on the left and the dispersion for one of the original spheres is shown on the right. They have the same basic shape, but the velocity dispersion is lower in the final equilibrium state. The system reached this state after 1500 iterations of dt = .01, however long that is equivalent to.

B) Plummer spheres colliding at various impact parameters

Here, I set the plummer spheres apart from each other by 4, 3, 2, and 1 units of offset of their initial x position. Some graphs are shown below.

B = 4:

Here, the galaxies don’t pull many stars off each other at all. The path of the moving galaxy is certainly deflected though. Estimated loss = 25 stars (out of 300 total per galaxy).

B = 3:

Here the galaxies are definitely interacting. They seem to practically grab hold of each other and swing each other around. This would probably be a strong interaction, since the velocity of the darker galaxy seems to have almost totally changed direction. Estimated star loss = 40 stars

B = 2:

Here the interaction is even stronger as the galaxies seem to merge for a second before separating again. Estimated star loss = 100 stars

B = 1:

For this case, I think it will suffice to show the final state:

Nearly all of the stars from the darker galaxy have been absorbed into the initially stationary galaxy. Estimated star loss = 250 stars

This is a very very rough graph, but from it, it seems that the tidal limit is around b = 2.5 or 3. It is certainly less than 4 and greater than 1 though.

C) Angular momentum in tidal interactions

Using b = 2.5 but spinning the incident galaxy in the direction of motion with spin –1, I found something very strange and unintuitive:

The spin seemed to make both galaxies separate. I don’t really know what’s going on here. It doesn’t seem like spin should create negative gravity though. Lets try spinning it the other way:

Wow! This time the spin causes it to move in a whole new direction entirely! Oh, I think I see what is going on here. The program give the entire system an angular momentum, not just the incident galaxy around its own axis. This makes more sense. So, in this picture and the last one, the angular momentum dominates over the incident velocity and causes the galaxies to fling each other away from each other, with very minimal star loss.

D) Tidal Tail Galaxy

I tried several different starting points to get this to work and this is the best I could come up with:

Initial Conditions:

Galaxy 1: 700 particles. Shift = (2,2,0) velocity = (-.25,-.25,0)

Galaxy 2: 700 particles. Shift = (-1,0,0) Velocity = (.25, ,25, 0)

No spin. 1500 iterations at dt = .01

There seems to be somewhat of a circular tail at some points, but it really isn’t very satisfying. I would like to be able to do it with whatever values look best. I did this with plummer spheres. The model in the book was done with spirals I believe, but when I tried it with spiral or even disk galaxies, it always just dissipated.