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## 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 = ∫

^{M2}

_{M1}ξ(M) dm

## The Attempt at a Solution

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In our case, N = A(∫

^{8}

_{0.1}M

^{-2.35}dm + ∫

^{40}

_{8}M

^{-2.35}dm + ∫

^{100}

_{40}M

^{-2.35}dm)

∴ N = -(A/1.35) ((-22.33) + (-0.053) + (-4.88x10

^{3}))

So White Dwarf Total = 16.5 A

Neutron Star Total = 0.039 A

Black Hole Total = 3.61x10

^{-3}A

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?