# Initial Mass Function Question (white dwarfs, neutron stars and black holes)

## Homework Statement

Calculate the number of white dwarf, neutron star and black holes the galaxy will have after 5Gyr of evolution.

M<8(solar mass) for white dwarf

8(solar mass) < M < 40(solar mass) for neutron star

M > 40(solar mass) for black hole

Initial mass function is ξ(M) = AM-s where s = 2.35 in the Milky Way, M is the mass in solar units and A is a normalisation constant.

## Homework Equations

Total number of stars formed with masses between M1 and M2 is

N = ∫M2M1 ξ(M) dm

## The Attempt at a Solution

[/B]
In our case, N = A(∫80.1M-2.35dm + ∫408M-2.35dm + ∫10040M-2.35dm)

∴ N = -(A/1.35) ((-22.33) + (-0.053) + (-4.88x103))

So White Dwarf Total = 16.5 A
Neutron Star Total = 0.039 A
Black Hole Total = 3.61x10-3A

How do I account for the 5Gyr of evolution within my answer as at the moment I believe all I have calculated is the number of stars formed between the masses specified?

## Answers and Replies

mfb
Mentor
I'm not sure if the questions is asking about that, but (a) you might have to determine A or (b) you should take into account existing stars and stellar remnants, or even (c) take into account that some stars live longer than 5 Gyr.

And keep in mind that the present distribution of stellar masses and the distribution of stellar masses of new stars are completely different things due to the different lifetime.