# Simulation for galaxy dynamics

Hello,

I'm trying to simulate disc galaxy dynamics with a nbody code. The main problem is to get
good initial values (positions and velocities of each star) in order to reproduce the
experimental dynamics.

For the positions, I began by generating a gaussian distribution of stars on 0x and Oy plans ( with mux=muy=0.0 and sigmax != sigmay). On 0z direction, I have generated a uniform distribution whose interval is small compared to sigmax and sigmay. ( this is supposed to reproduce the thin thickness of the disc galaxy). For the velocities of each point, I simply took the newtonian formula :

vx = - ||vnorm|| * sin(theta)

vy = ||vnorm|| * cos(theta)

vz = 0.0

with ||vnorm||=sqrt(GM/R) with R equal to the distance from the origin and M the mass parameter that we have to adjust.

Unfortunately, using the code with these initial conditions, the galaxy is not stable from a dynamics point of view.

I know the model of these conditions is too basic. Could you give me indications to generate initial conditions more accurate, which could reproduce a stable dynamics.

For example, I should take account of a central bulge.

Has anyone got some documentation on this problem and models more elaborated ?

Thanks

Unfortunately, using the code with these initial conditions, the galaxy is not stable from a dynamics point of view.

I know the model of these conditions is too basic. Could you give me indications to generate initial conditions more accurate, which could reproduce a stable dynamics.
What do you mean by this: for how long should it remain stable, until it develops its spiral arms, or further than that?

In case you want to make it stable indefinitely, I think you should use some tricks, the most common is to add a massive halo of invisible particles to it.

||vnorm||=sqrt(GM/R) , won't that produce absurd velocities?
Maybe you could do a velocity dump after so many interactions, to see if they are very high or maxing out.
Personally I'd use (1+R), or to limit it further, add a terminal velocity as well.