main sequence lifetime problem

[kranav]

Hello.
The question states that
We have a globular cluster with total mass 10^6 times sun's mass.
Assume that the main sequence lifetime of a solar mass star is 10 gigayear, and a main sequence lifetime scales with mass as M^-2. What is the mass of the most massive main sequence stars in the cluster after 1 gigayear? (answer - 3.2 times sun's mass)

we have t ~ M^-2

Does this require me to do a differential and find out the maxima (of the mass) by putting it to zero?
or by cutting of the massive stars which would die out within the 1 gigayear and somehow see the masses left.

[twofish-quant]

1) Hint 1: The cluster mass is extraneous information that you can ignore.......

(stop reading before you get to hint 2)


2) Hint 2: set it up like a ratio problem.

[kranav]

so,

T/t = M/m

where t = 10 gy and T = 1 gy and
m = 1 solar mass

is this correct?

thanks.

[twofish-quant]

so,

T/t = M/m

where t = 10 gy and T = 1 gy and
m = 1 solar mass


Close. What you've set up is the equation for T proportional to M. You are looking for T proportional to M**-2