Astronomy, fraction of stars to have ever lived

[Chronos000]

Homework Statement

The question asks for the fraction of all 2M(sun) stars ever made in the Galaxy that are still burning on the main sequence. It assumes star formation at constant rate. The age of the Galaxy is 10GYRS

To do this I imagine you use the salpeter IMF and find the constant epsilon by equating the total mass per year to be 1 M(sun) - value taken from earlier question, don't know if this is correct to do this.

once a value for epsilon is found, I have found the total number of stars with masses from 2M(sun) to 100M(sun) - I don't know how to isolate just the 2M(sun) stars

The value I get says for every 1 star >2M(sun) there has to be 20M(sun) worth of stars made.

So in ten billion years there will have been 10G M(sun) worth made. divide by 20M(sun) gives approx 500M stars with 2M(sun).

I don't know how I go about getting the fraction that are still on the main sequence.
It also wants the same fraction is the star formation rate decreases with some exponential. Do I just equate the total mass to this instead?

 

[ideasrule]

Unless I'm misunderstanding, you don't need to do any of the calculations you've done. Just assume that k 2M stars form every year. You can easily calculate the total number formed over the galaxy's lifetime. If you know how long a 2M star lasts on the main sequence--and I don't see how you can do the question without this information--you can also find out how many have left the main sequence over the galaxy's lifetime.

You'll find that for the final answer, the k cancels out; you don't need to know its value.