# Initial Mass Function - how many stars are born

1. Feb 1, 2010

### hullio

Hello everyone. I have a problem listed below. I am very lost due to the fact that my teacher literally just gave us this problem to do and expects us to hand it in soon without even teaching/talking about this topic in class. I did some research over the Internet on IMF, but still am pretty confused. I really have tried my best at attempting this problem, but nothing is working since I literally don't have a clue how to approach this. I really wish my teacher explained this.

1. The problem statement, all variables and given/known data
The Initial Mass Function describes in a relative sense how likely a star of a particular mass is likely to form. It has been found from counts of starts as a function of mass that probability P(m)dm of forming stars with masses between m and m + dm (called the IMF) is given by P(m)dm = km^-a dm, where k is a normalization constant determined by requiring that P = 1 when integrated over all possible stellar masses (i.e. 0.007 M(sun) to 50 M(sun)). If you have an ensemble of N stars born all at the same time, then, the number of stars with masses between m and m + dm is N P(m)dm and the mass associated with those stars is mNP(m)dm. Suppose that a giant molecular cloud with a mass of 10^4 M(sun) converts 1% of its mass into stars. Assume that stars form according to a Salpeter IMF.

How many stars are born? What fraction of the stars will blow up as supernovae? Would you expect to see a supernova? Explain.

2. Relevant equations
P(m)dm = km^-a dm

mNP(m)dm

3. The attempt at a solution

Masses which are important for this problem are 10,000 and 100? What about the 0.07 and 50 - do they have anything to do with the problem? Also, what is 'a'? 'a' is defined as a dimensionless exponent (Wiki).

I also came across this thread: https://www.physicsforums.com/showthread.php?t=230930 in which a member 'malawi_glenn' talks about a certain formula:

"...if you want to calculate the number of stars between mass m1 and m2:https://www.physicsforums.com/latex_images/17/1703469-5.png [Broken]"[/URL]

Last edited by a moderator: May 4, 2017
2. Feb 3, 2010

### zepphira

ur in mccalls class eh