<p>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:
<a href="https://i.sstatic.net/coCJR.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/coCJR.jpg" alt="enter image description here"></a></p>

CC BY-SA 4.0
2018-09-19T23:12:50.837Z
2018-09-19T23:12:50.837Z
Daddy Kropotkin
<p>Using Hurley's <a href="https://arxiv.org/abs/astro-ph/0001295" rel="nofollow noreferrer">2000</a> 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). </p>

<p>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. <a href="https://i.sstatic.net/NqmiR.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NqmiR.jpg" alt="Core mass of Star at three stages as function of metallicity"></a></p>

<p>EDIT: The equations I use are...</p>

<p>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 $&lt; 1$).</p>

<p>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.</p>

<p>Core mass at BAGB:
$Mc_{BAGB}$ is equation 66.</p>

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

CC BY-SA 4.0
2018-09-19T01:03:23.033Z
Can you provide or reference the equations you were referencing from this paper to make this graph?
zephyr
CC BY-SA 4.0
2018-09-19T02:26:16.000Z
@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.
Daddy Kropotkin
CC BY-SA 4.0
2018-09-19T02:29:39.813Z
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.
Daddy Kropotkin
<star><stellar-evolution>
Stellar core mass as a function of metallicity
Daddy Kropotkin
# Stellar core mass as a function of metallicity

(Asked by: username_0 on 2018-09-18)

Using Hurley's [2000](https://arxiv.org/abs/astro-ph/0001295) 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](https://i.sstatic.net/NqmiR.jpg)](https://i.sstatic.net/NqmiR.jpg)

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.

**Tags:** star, stellar-evolution

> **Comments:**
> **username_1**: Can you provide or reference the equations you were referencing from this paper to make this graph?  
> **username_0**: @username_1 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.  
> **username_0**: 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.  

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## 1 answers

### Answer by username_0 on 2018-09-19. Score: 4 | Accepted answer

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](https://i.sstatic.net/coCJR.jpg)](https://i.sstatic.net/coCJR.jpg)


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