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Astronomy

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  • $\begingroup$ I think there's a small error in lower bound of the integral for $N_\mathrm{WD}$; shouldn't it be 0.9 rather than 1, according to what you write in the beginning (and according to your result of 0.027). But why do you start at 0.9, and not at 0.1? Is it because stars of M<0.9 are all assumed to be still on the MS? $\endgroup$
    – pela
    Commented Oct 16, 2019 at 13:40
  • $\begingroup$ Yes, it should be 0.9. Of course it is (slightly) composition dependent. The lower limit is indeed set by the lifetime on the main sequence. Lower mass stars are not white dwarfs (yet) - that is spelled out in the brackets at the end of para. 3. $\endgroup$
    – ProfRob
    Commented Oct 16, 2019 at 14:28
  • $\begingroup$ Ah yes, sorry, I missed the "…as are all stars born with lower masses". Thanks! And yes, a shallower IMF at low masses would yield a smaller number of WDs. But I thought actually the number was larger? Salpeter assumed 10% WDs, but that's probably outdated. Do you happen to have any references for observed numbers? $\endgroup$
    – pela
    Commented Oct 16, 2019 at 14:56
  • $\begingroup$ @Pela Well the mass function isn't Salpeter down to the lowest masses and so low mass stars are over-represented in my calculation I expect. I could do something more realistic and it might bump the WD density up by a factor of 2, but wouldn't change the NS and BH numbers. $\endgroup$
    – ProfRob
    Commented Oct 16, 2019 at 16:46
  • $\begingroup$ Yes, that's what I meant. Anyway, thanks for a great answer. $\endgroup$
    – pela
    Commented Oct 16, 2019 at 16:47