Using Hurley's 2000 paper on Single Stellar Evolution, I have graphed the core mass of a star at three stages as a function of metallicity, Z, for a chosen ZAMS mass: at the beginning of the HG (MS), at the end of the Hertzprung-Gap (HG), and at the Base of the Asymptotic Giant Branch (BAGB).

All three functions have a cusp at Z = 0.0005 which I 1) do not understand physically and 2) wonder if it is incorrect? Is this expected? I would have expected that the core mass is monotonic in metallicity, Z. The cusp is present for any ZAMS mass chosen. Core mass of Star at three stages as function of metallicity

EDIT: The equations I use are...

Core mass at beginning of HG: $Mc_{MS}$ is the product of equation 29 and the core mass at the end of the HG described below ($\rho$ is always $< 1$).

Core mass at end of HG: $Mc_{HG}$ is, using equation 28 over the relevant mass range the HG ends at Helium Ignition, given by equation 44, where I solved for the time, $t$, in equation 35 and substituted that into equation 34 to find that $M_{c} = \Big(\frac{L}{D}\Big)^{1/5}$, and following the procedure given in the paragraph below equation 65 (where it references equation 44). I used equation 49b for the Luminosity here.

Core mass at BAGB: $Mc_{BAGB}$ is equation 66.

I'm only interested in stars above $10 \odot{M}$, so I do not consider the possibility of a Blue Loop phase for simplicity.

  • $\begingroup$ Can you provide or reference the equations you were referencing from this paper to make this graph? $\endgroup$
    – zephyr
    Commented Sep 19, 2018 at 1:03
  • $\begingroup$ @zephyr Edited my question to include the equations. I hope I described well enough, but fair warning that this paper is quite tedious to work with. $\endgroup$ Commented Sep 19, 2018 at 2:26
  • $\begingroup$ It's of course nice to know if I implemented the equations correctly or not, but I think they are correct (perhaps not!). Assuming so, is it physically sensible? Usually when I do things incorrectly they as a result don't make sense, but I don't have much intuition here. $\endgroup$ Commented Sep 19, 2018 at 2:29

1 Answer 1


I feel silly, feel free to laugh at this, but I found my mistake. In the Hurley paper, he uses "log" for the logarithm of base 10. I had been using the natural logarithm. With the fix, the graph looks more realistic: enter image description here


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