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Homework Help: Initial Mass Function Question (white dwarfs, neutron stars and black holes)

  1. Apr 13, 2016 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

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

    N = ∫M2M1 ξ(M) dm

    3. The attempt at a solution

    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?
  2. jcsd
  3. Apr 16, 2016 #2


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    2017 Award

    Staff: 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.
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