Why did Chandrasekhar use 2.5 for molecular weight in 1931?

Question

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) 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), 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.

score 22 · Accepted Answer · edited Mar 06 '23 at 19:04

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The mean molecular mass per electron and its influence on the maximum mass of a star supported by electron degeneracy pressure is discussed in detail by Stoner (1932). 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.

edited Mar 06 '23 at 19:04

Peter Mortensen

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answered Mar 05 '23 at 08:19

ProfRob

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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 Mar 05 '23 at 11:23
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ProfRob, is there anything you don't know!? ;-) – Peter - Reinstate Monica Mar 05 '23 at 18:59
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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 Mar 06 '23 at 00:02

score 13 · Answer 2 · answered Mar 04 '23 at 20:08

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.

Why did Chandrasekhar use 2.5 for molecular weight in 1931?

2 Answers2