What is the Initial Mass Function problem and its solution?

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Homework Help Overview

The discussion revolves around the Initial Mass Function (IMF) in astrophysics, specifically concerning the calculation of the number of stars within certain mass ranges in a cluster. The original poster presents a problem involving the IMF and attempts to calculate the total number of stars with masses greater than 2 solar masses based on given data.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to solve an integral to find the number of stars with mass greater than 2 solar masses, starting from a known quantity of stars with mass greater than 10 solar masses. Some participants question the method of integration limits and the assumptions regarding the distribution of the stars' masses.

Discussion Status

Participants are engaging in a back-and-forth regarding the validity of different integration approaches and the implications of the assumptions made about the mass distribution. While some express agreement with the calculations, there is no explicit consensus on the correct method to use, and multiple interpretations are being explored.

Contextual Notes

There is mention of a lack of examples from the lecturer, which may contribute to uncertainty in the methods being discussed. The original poster also notes difficulty in verifying their answer, indicating a potential gap in resources or guidance.

grahammtb
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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\proptom-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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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.
 
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 \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 :smile:

thanks again :smile:
 
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
 
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:
 

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