# Velocity dispersion problem

1. Jul 13, 2011

### LordV

Hello, I would appreciate very much some help on this problem.

I have a Hernquist model (distribution function) and I am trying to generate equal mass initial conditions. The way I do it is this. I have the mass profile M(r) and I pick say 10^6 random numbers between 0 and 1=M(r->inf). Then I solve the inverse equation r=r(m_random) to find the radius. The next step is to draw the velocities. For each radius I calculate f(v) = f(ri,v)=f(0.5*v^2+V(r))=f(E) and then I use a rejection method to draw the velocity from f(v). Then I divide the space r (radius) in a logarithmic scale and within each bin I calculate the <v^2> from all the v's within this bin therefore I have the function <v^2>(r) and draw it and compare it with <vr^2>(r) form analytic from of the paper.

THE PROBLEM IS that the two curves are THE SAME but they shouldn't because v^2=vr^2+vphi^2+vth^2 => <v^2>=3<vr^2> because the model is isotropic i.e. <vr^2>=<vphi^2>=<vth^2>. Therefore there should be a difference by a factor of 3 in the 2 curves but there isn't any difference.

Any ideas?

2. Jul 14, 2011

### LordV

Hmmm, any ideas?