Why aren't the <v^2> and <vr^2> curves different in my Hernquist model?

In summary, the speaker is seeking help with generating equal mass initial conditions for a Hernquist model. They explain their method of solving the inverse equation for radius and drawing velocities using a rejection method. They also mention calculating and comparing <v^2> and <vr^2> in a logarithmic scale, but are facing a problem where the two curves are the same instead of differing by a factor of 3 as expected due to the model's isotropy. They are asking for ideas on how to resolve this issue.
  • #1
LordV
7
0
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?
 
Astronomy news on Phys.org
  • #2
Hmmm, any ideas?
 

What is the velocity dispersion problem?

The velocity dispersion problem is a phenomenon observed in astrophysics where the velocities of stars within a galaxy do not follow a predictable pattern, but rather show a wide range of velocities. This is in contrast to what is expected based on the mass distribution of the galaxy.

What causes the velocity dispersion problem?

The causes of the velocity dispersion problem are still not fully understood, but it is believed to be a result of interactions between stars and dark matter within the galaxy. Other possible factors include the presence of supermassive black holes and mergers with other galaxies.

How does the velocity dispersion problem impact our understanding of galaxies?

The velocity dispersion problem challenges our current understanding of galaxy formation and evolution. It suggests that there may be other factors at play that influence the dynamics of galaxies, such as the presence of dark matter and interactions with other galaxies.

What research is being done to address the velocity dispersion problem?

Scientists are using a variety of techniques, such as simulations and observations, to study the velocity dispersion problem. This includes studying the properties of dark matter, the distribution of mass within galaxies, and the effects of galaxy mergers.

Are there any proposed solutions to the velocity dispersion problem?

While there is no definitive solution to the velocity dispersion problem, some proposed solutions include modifying the laws of gravity, or considering alternative theories of dark matter. However, more research and observations are needed to fully understand this phenomenon.

Similar threads

  • Mechanics
Replies
20
Views
862
  • Introductory Physics Homework Help
Replies
6
Views
891
  • Astronomy and Astrophysics
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
31
Views
1K
  • Astronomy and Astrophysics
Replies
1
Views
1K
Replies
4
Views
1K
Replies
8
Views
2K
Replies
1
Views
525
  • Astronomy and Astrophysics
Replies
1
Views
2K
  • Astronomy and Astrophysics
Replies
6
Views
1K
Back
Top