What is the Constant 'a' in the Initial Mass Function for a Globular Cluster?

[kranav]

Homework Statement

the question says, consider a newly formed globular cluster, with a total mass 10^6 times mass of the sun and an initial mass function dN/dm = a.m^-2.35 in the mass range 0.1 - 20 times mass of the sun, where m = M/mass of the sun.
find the constant a. (answer : 1.9 x10^5)
thanks.

Homework Equations

The Attempt at a Solution

the number of stars in a globular cluster are between 10^4 - 10^6. but N from the above equation should be smaller as the mass range is from 0.1 to 20 times sun's mass. If I can find that N the equation is a piece of cake.

 

[gabbagabbahey]

Is there a reason why you felt the need to disobey forum rules and create another thread for the exact same problem you asked a week and a half ago?

 

[kranav]

I'm really sorry about that ... wasn't aware of that. I thought if I could reframe the question and start afresh

 

[gabbagabbahey]

After looking up "initial mass function", it looks like the number of stars in the mass range $m_0$ to $m_1$ is given by

$$N=\int_{m_0}^{m_1}\frac{dN}{dm}mdm$$

Have you tried performing this integration?

 

[kranav]

Yes this time I got it. Thank you very much