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Advanced Physics Homework Help
Initial Mass Function Question (white dwarfs, neutron stars and black holes)
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[QUOTE="J_M_R, post: 5441709, member: 503732"] [h2]Homework Statement [/h2] 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[SUP]-s[/SUP] where s = 2.35 in the Milky Way, M is the mass in solar units and A is a normalisation constant. [h2]Homework Equations[/h2] Total number of stars formed with masses between M1 and M2 is N = ∫[SUP]M2[/SUP][SUB]M1[/SUB] ξ(M) dm [h2]The Attempt at a Solution[/h2] [/B] In our case, N = A(∫[SUP]8[/SUP][SUB]0.1[/SUB]M[SUP]-2.35[/SUP]dm + ∫[SUP]40[/SUP][SUB]8[/SUB]M[SUP]-2.35[/SUP]dm + ∫[SUP]100[/SUP][SUB]40[/SUB]M[SUP]-2.35[/SUP]dm) ∴ N = -(A/1.35) ((-22.33) + (-0.053) + (-4.88x10[SUP]3[/SUP])) So White Dwarf Total = 16.5 A Neutron Star Total = 0.039 A Black Hole Total = 3.61x10[SUP]-3[/SUP]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? [/QUOTE]
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Initial Mass Function Question (white dwarfs, neutron stars and black holes)
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