What is the Initial Mass Function problem and its solution?

In summary, the IMF of a cluster of stars is 5dN\proptom-2.5dm. There are 56 stars with mass greater than 10 solar masses.
  • #1
grahammtb
10
0
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[tex]\propto[/tex]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.
Final answer: 56 stars.

Seems plausible to me, but I have no way right now of checking the answer.
Thanks a lot for any help!
 
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  • #2
Welcome to PF :smile:

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

I did agree with you about solving the integral from 2 to [tex]\infty[/tex] 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 :smile:

thanks again :smile:
 
  • #4
That's weird, I definitely get 56 using 2 to ∞ for the integral.

http://www.google.com/search?hl=en&q=237*(2^(-1.5))%2F1.5&btnG=Search
 
  • #5
Redbelly98 said:
That's weird, I definitely get 56 using 2 to ∞ for the integral.

http://www.google.com/search?hl=en&q=237*(2^(-1.5))%2F1.5&btnG=Search

Oh, I probably made a silly mistake when I did the integral. At least it confirms my answer of 56 :smile:
 

Related to What is the Initial Mass Function problem and its solution?

1. What is the Initial Mass Function (IMF) problem?

The Initial Mass Function problem is a long-standing puzzle in astrophysics that relates to the distribution of masses of stars in a given population. It refers to the fact that the number of stars in a certain mass range is not consistent with what is predicted by theoretical models.

2. How does the IMF affect the evolution of galaxies?

The IMF plays a crucial role in the evolution of galaxies. The distribution of stellar masses determines the amount of energy and elements that are released into the interstellar medium through stellar evolution. This, in turn, affects the formation of new stars and the overall structure and dynamics of galaxies.

3. What are the current theories that attempt to explain the IMF problem?

There are several theories that have been proposed to explain the IMF problem, including the turbulent fragmentation theory, the competitive accretion theory, and the primordial fragment theory. Each of these theories offers a different explanation for the observed distribution of stellar masses.

4. How do scientists study the IMF problem?

Scientists use a combination of observations and theoretical models to study the IMF problem. They analyze the distribution of stellar masses in different regions of the universe, such as star clusters and galaxies, and compare these observations to predictions from various theoretical models.

5. What are the implications of solving the IMF problem?

Solving the IMF problem would not only provide a better understanding of the formation and evolution of stars and galaxies, but it could also have broader implications for our understanding of the universe as a whole. It could also have practical applications, such as improving our ability to predict and study the properties of exoplanets and their potential for hosting life.

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