<p>The mean molecular mass per electron is very close to 2.0 for lighter elements (ignoring hydrogen), but rises to around 2.5 for heavier elements.</p>
<p>If you think that the interior of the stellar object is mostly heavy elements, then 2.5 would be appropriate.  I believe in 1931, the composition of such objects was not settled.</p>

CC BY-SA 4.0
2023-03-04T20:08:40.220Z
2023-03-04T20:08:40.220Z
BowlOfRed
<p>The mean molecular mass per electron and its influence on the maximum mass of a star supported by <a href="https://en.wikipedia.org/wiki/Electron_degeneracy_pressure" rel="noreferrer">electron degeneracy pressure</a> is discussed in detail by <a href="https://academic.oup.com/mnras/article/92/7/662/996908" rel="noreferrer">Stoner (1932)</a>. It was in fact Stoner, who had first clearly established the necessity of a maximum mass, though his treatment assumed a uniform density and so the specific value was incorrect.</p>
<p>In that discussion it is quite clear that astronomers at the time didn't have any idea what stars were made of and in what proportions. Stoner makes the somewhat prescient prediction that the molecular mass per electron is likely to be somewhere between 1.5 and 2.5 (a value that might only be true if a star is made out of something like uranium). Stoner presents calculations using a range of mean molecular masses from 1 to 2.5.</p>

CC BY-SA 4.0
2023-03-05T11:23:19.400Z
Thanks. What puzzled me originally was 0.9 solar masses (rather than some 1.4) for the limit (Chandrasekhar 1931 paper), which nevertheless corresponds to the molecular mass per electron 2.5.
Leos Ondra
CC BY-SA 4.0
2023-03-05T18:59:34.750Z
ProfRob, is there anything you *don't* know!? ;-)
Peter - Reinstate Monica
CC BY-SA 4.0
2023-03-06T00:02:28.703Z
I use a version of Stoner's treatment in a course on Compact Objects (since I'm too lazy to cover polytropes) @Peter-ReinstateMonica
ProfRob
CC BY-SA 4.0
2023-03-05T08:19:45.290Z
2023-03-06T19:04:01.820Z
2023-03-06T19:04:01.820Z
ProfRob
<p>I understand that the history of the Chandrasekhar limit is complicated (see, for example, Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs, Michael Nauenberg, JHA 39:297, 2008 / <a href="http://physics.ucsc.edu/%7Emichael/stonerchandra.pdf" rel="noreferrer">PDF</a>) but what puzzles me is the physics rather than the history. In his 1931 paper (<a href="https://ui.adsabs.harvard.edu/abs/1931ApJ....74...81C/abstract" rel="noreferrer">The Maximum Mass Of Ideal White Dwarfs, ApJ 74:81</a>), Chandrasekhar used a value of 2.5 for mean molecular mass. Why? I thought that it is 2.0 for metals and much less for hydrogen and helium.</p>

<white-dwarf>
Why did Chandrasekhar use 2.5 for molecular weight in 1931?
Leos Ondra
# Why did Chandrasekhar use 2.5 for molecular weight in 1931?

(Asked by: username_0 on 2023-03-04)

I understand that the history of the Chandrasekhar limit is complicated (see, for example, Edmund C. Stoner and the Discovery of the Maximum Mass of White Dwarfs, Michael Nauenberg, JHA 39:297, 2008 / [PDF](http://physics.ucsc.edu/%7Emichael/stonerchandra.pdf)) but what puzzles me is the physics rather than the history. In his 1931 paper ([The Maximum Mass Of Ideal White Dwarfs, ApJ 74:81](https://ui.adsabs.harvard.edu/abs/1931ApJ....74...81C/abstract)), Chandrasekhar used a value of 2.5 for mean molecular mass. Why? I thought that it is 2.0 for metals and much less for hydrogen and helium.

**Tags:** white-dwarf

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## 2 answers

### Answer by username_2 on 2023-03-05. Score: 22 | Accepted answer

The mean molecular mass per electron and its influence on the maximum mass of a star supported by [electron degeneracy pressure](https://en.wikipedia.org/wiki/Electron_degeneracy_pressure) is discussed in detail by [Stoner (1932)](https://academic.oup.com/mnras/article/92/7/662/996908). It was in fact Stoner, who had first clearly established the necessity of a maximum mass, though his treatment assumed a uniform density and so the specific value was incorrect.

In that discussion it is quite clear that astronomers at the time didn't have any idea what stars were made of and in what proportions. Stoner makes the somewhat prescient prediction that the molecular mass per electron is likely to be somewhere between 1.5 and 2.5 (a value that might only be true if a star is made out of something like uranium). Stoner presents calculations using a range of mean molecular masses from 1 to 2.5.

> **Comments:**
> **username_0**: Thanks. What puzzled me originally was 0.9 solar masses (rather than some 1.4) for the limit (Chandrasekhar 1931 paper), which nevertheless corresponds to the molecular mass per electron 2.5.  
> **username_3**: ProfRob, is there anything you *don't* know!? ;-)  
> **username_2**: I use a version of Stoner's treatment in a course on Compact Objects (since I'm too lazy to cover polytropes) @Peter-ReinstateMonica  

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### Answer by username_1 on 2023-03-04. Score: 13

The mean molecular mass per electron is very close to 2.0 for lighter elements (ignoring hydrogen), but rises to around 2.5 for heavier elements.

If you think that the interior of the stellar object is mostly heavy elements, then 2.5 would be appropriate. I believe in 1931, the composition of such objects was not settled.


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