Equipartition of magnetic fields and turbulence?

[Jimbecile]

Homework Statement

You observe a molecular cloud core with the following properties:
T = 5K
R = 1pc
M = 10 M⊙
n = 102 cm^-3
B = 1µG
RΩ = 200 cms^-1

A. Assuming equipartition of B fields and turbulence, what is the turbulent velocity of the cloud?

Homework Equations

Emag=1/6((B^2R^3)/μo)

Eturb=1/2Mv^2

The Attempt at a Solution

I can't attempt a solution because I don't understand the question. What does it mean to "assume the equipartition of B fields and turbulence?" My understanding of the equipartition theorem was that it related the temperatures of a system to its average energies, so I'm sure the energies for turbulence and magnetic fields are involved, but I don't know what to do with them. Maybe set them equal to each other?

 

[mark726]

And what does the turbulent velocity have to do with any of this? I'm sorry, but I need more clarification before I can attempt a solution. Can you provide more information or context for this question?

Dear student,

Thank you for your question. In this case, the phrase "assuming equipartition of B fields and turbulence" means that we are assuming that the magnetic field energy and the turbulent kinetic energy are equal. This is a common assumption in astrophysics when studying molecular clouds, as both magnetic fields and turbulence play important roles in shaping the structure and dynamics of these clouds.

To solve this problem, we can use the equations given in the homework statement. The first equation relates the magnetic field energy (Emag) to the magnetic field strength (B) and the size of the cloud (R). The second equation relates the turbulent kinetic energy (Eturb) to the mass of the cloud (M) and the turbulent velocity (v). Since we are assuming that Emag and Eturb are equal, we can set these two equations equal to each other and solve for v.

I hope this helps clarify the problem. Let me know if you have any further questions or need more assistance. Best of luck with your calculations!