# Homework Help: Cloud Collapse/Degeneracy

1. Oct 2, 2011

### AnniB

1. The problem statement, all variables and given/known data
1. Consider a cloud that consists entirely of molecular hydrogen. The temperature is a uniform 15 K and the number density of particles is 5x109 m-3. Assuming a 100% efficient collapse, subsequent star birth and normal evolution, what type of degenerate remnant will result? Justify your answer with appropriate calculations.

2. For the same cloud in problem 1, assume that the cloud is able to form multiple stars of various masses. Calculate the initial mass of a star whose main sequence lifetime will equal the free fall timescale for the cloud.

2. Relevant equations
N=Mcloud/mH
M=(4/3)$\pi$r3$\rho$
r=(3M/(4$\pi$$\rho$))1/3
tff=$\sqrt{}3\pi/32Gρ$

3. The attempt at a solution
The first thing I did, since I was given the number density N, was to solve for the mass of the cloud by rearranging the first equation that I gave up above. However, when I do that, I get a really low number for the mass of the star, and I don't think it's actually possible. The only thing I can think of is that it's actually ρ, not N, but that doesn't seem right. Also, if I do that it looks like there will be a lot of messy calculation to acquire the mass and radius, and I'm not sure if I need to do all that to get the answer.

Last edited: Oct 2, 2011