# Initial Mass Function problem

1. Dec 30, 2008

### grahammtb

Hi, I've got a solution to this problem but I don't know if it's correct. My lecturer hasn't given us any examples but I had a go and the answer seems fine. Here it is:

The IMF of a cluster of stars is: dN$$\propto$$m-2.5dm
There are 5 stars in the cluster with mass greater than 10 solar masses.
What is the number of stars with mass greater than 2 solar masses?

I put in 5 for dN, and solved the integral from 10 to infinity, to get the proportionality constant: 237.
Now using the constant, I solved the integral from 2 to 10 to find N in this range of masses. Then I added the 5 stars which are more massive than 10 solar masses.

Seems plausible to me, but I have no way right now of checking the answer.
Thanks a lot for any help!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 30, 2008

### Redbelly98

Staff Emeritus
Welcome to PF

I agree with your math, though I am not familiar with mass distributions of stars and will take your word for it that part is valid.

FYI, you could also do the integral from 2 to ∞, and that will include the 5 stars with m>10.

3. Dec 30, 2008

### grahammtb

thank you for your opinion. I've been working away at a few different problems and I seem to have them sorted out now
I found some examples on my physics department website which helped.

I did agree with you about solving the integral from 2 to $$\infty$$ but I tried it and it doesn't give the right answer. I think this is since the question only says there are 5 stars above 10 solar masses, and so these could be very massive or only a little more than 10 solar masses. So I think the method is to integrate from 2 to 10 then simply add on the remaining 5 to give the correct answer

thanks again

4. Dec 31, 2008

### Redbelly98

Staff Emeritus
That's weird, I definitely get 56 using 2 to ∞ for the integral.