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Many sources claim that the Sun is around $70-74\%$ hydrogen and $25-27\%$ helium by mass, or $91\%$ and $9\%$ by atom count, without any further caveats - e.g. 1, 2, 3. I believe these sources are incorrect. (Especially bad ones will report photospheric atom ratios as mass ratios, like space.com here.)

More careful sources like this (from which I think many of the less-good sources above derive) or Wikipedia (citing this page) give the same numbers, but clarify that they only measure the composition in the photosphere, where we can analyze the spectral lines. I'm curious about the overall distribution across all radii (which ought to have more helium, since it's produced in the core and my impression is that there isn't a ton of mixing between layers - sources like this paper seem to suggest that would be true, but don't mention concrete numbers).

This helpful answer linked to some informative plots of the distribution by radius from this paper, which mostly answers my question, but the paper doesn't actually provide the relevant integrals of their plots weighted by radial density - just going off of the fact that the core contains around $34\%$ of the mass within $0.2$ solar radii and eyeballing the plot, it looks to me like the overall composition is something like $65\%$ hydrogen and $35\%$ helium, but if someone has worked out the actual numbers from our current best models I'd love to see those instead.

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    $\begingroup$ Good question. I've often wondered what proportion of the Sun's heavier elements are in the core & radiative zone, compared to what we see in the photosphere. We have a few existing questions on the Sun's convective & radiative zones, eg astronomy.stackexchange.com/q/30222/16685 but that's mostly qualitative, I can't find one that's more quantitative. $\endgroup$
    – PM 2Ring
    Oct 17, 2022 at 19:39
  • $\begingroup$ The Standard Solar Model (BP2004) has radial data for density, pressure, temperature, and total mass fraction, as well as individual mass fractions for H, He-3, He-4, C-12, N-14, O-16. I put it on Github, with a simple Python script that can read & plot the data. $\endgroup$
    – PM 2Ring
    Feb 12, 2023 at 6:35

3 Answers 3

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Both your estimate and @ProfRob's answer are roughly in the right area. I've done the integration on an older standard solar model, Model S (Christensen-Dalsgaard J., et al., 1996, Sci, 272, 1286) and get average values for the hydrogen, helium and metal mass fractions of $$ \bar{X}=0.671 \\ \bar{Y}=0.309 \\ \bar{Z}=0.020 \\ $$

Model S admittedly has the older, higher, Grevesse & Noels (1993) abundance of $Z\approx0.02$, compared to the more recent (e.g. Asplund et al. 2009) values of $Z\approx0.014$, so there's about $0.006$ wiggle room there, but the metallicity remains contentious.

If anyone is especially interested and knows Python, I created a Python package called tomso for working with stellar models (in their obscure formats) that makes this calculation quite straightforward.

import numpy as np
from tomso import fgong

# fetch Model S
S = fgong.load_fgong('https://users-phys.au.dk/jcd/solar_models/fgong.l5bi.d.15c', G=6.67232e-8)

# integrate the X and Z abundances over the fractional mass co-ordinate q
# negative because stellar models are usually ordered from surface to centre
X = -np.trapz(S.X, x=S.q)                                                                                                                                                          
Z = -np.trapz(S.Z, x=S.q)

print('X =', X)
print('Y =', 1-X-Z)
print('Z =', Z)
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  • $\begingroup$ What were the initial Y and Z in this model? $\endgroup$
    – eshaya
    Feb 12, 2023 at 0:17
  • $\begingroup$ I couldn't find this in the paper but from the data file itself, it looks like the initial composition was X₀=0.709, Y₀=0.271 and Z₀=0.020. $\endgroup$
    – Warrick
    Feb 14, 2023 at 21:25
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I think you are right.

Metals are not produced in the Sun (though lithium is destroyed), so will be distributed throughout. To first order you can ignore radiative diffusion and chemical stratification - these take a long time in a star like the Sun.

The core is radiative and will not be well-mixed. That is why the Sun's lifetime will be about 10 billion years, even though it has enough hydrogen to burn for 5 times as long at its main sequence luminosity. Thus at this roughly halfway stage in its life, about 10% of the hydrogen has been turned into helium. So the overall composition will be about 63% H, 36% He and the rest heavier elements.

A more exact number would have to come from detailed evolutionary models. Such models exist, but don't usually report what you want to know.

Edit:

Warwick has supplied the "right answer" from the standard solar model. It is interesting to think about why it differs a bit from the numbers I argued above - 67% H, 31% He and 2% metals.

Ignore the difference between 1% and 2% metals - that just depends on whether you use the older (Warwick) or newer (me) estimates of the solar metallicity. It is basically whatever the initial metallicity of the Sun was and it's also the photospheric abundance.

The interesting difference is that less hydrogen has turned into helium. I think this is simply because the Sun is actually a little less than halfway through its main sequence life and, because the luminosity increases by a factor of 2 during the full main sequence, it is in fact only about a third of the way through its use of hydrogen.

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The composition is… pretty close to the photospheric composition.

Red dwarves are well-mixed, being too small and light to support ‘differentiation’ in the stellar sense. Plasma dynamics is able to overcome stratification. Supergiants are able to stratify, which is partly why they burn quicker and die sooner.

So, where is our Sun along this scale? Decades of study, both of the Sun and other, nearby “boring” stars, has put us closer to the red-dwarf regime. This study includes general plasma physics, boundary conditions from spectrometries and isotopes, helioseismology, and more recently asteroseismology. Stars are ‘poked’ and we watch them jiggle. Only certain interiors will give certain jiggles.

All told, heterogenity doesn’t appear to be high enough to be an issue.

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    $\begingroup$ How does this square with sources like this paper or this page from the Stanford solar center, which indicate majority-helium composition in the core? Are they just incorrect or outdated? From my perspective it seems that multiple fairly-reputable-looking sources make pretty different claims, and I'm unsure how to reconcile them or identify which ones are correct. $\endgroup$ Oct 18, 2022 at 0:50
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    $\begingroup$ Differentiation is not the main relevant process and a star like the Sun is not well-mixed. You seem to have discounted nuclear processes that ensure (for instance) that the core of the Sun is helium-rich but should contain no lithium at all. $\endgroup$
    – ProfRob
    Oct 24, 2022 at 7:34
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    $\begingroup$ Stack Exchange answers are posted on the public web for anyone to read, not just for the asker's private edification, and should be written with this entire potential audience in mind. When (as is common) there are several possible answers depending on the reader's background knowledge and desire for detail, a good answer should (at a minimum) provide accurate information at the level the asker is seeking, while also noting its approximate nature and taking care not to mislead readers seeking more detail. A very good answer may also provide several explanations at different levels. $\endgroup$ Oct 27, 2022 at 17:04
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    $\begingroup$ … As a non-expert in this field myself, I cannot say for sure that your answer isn't correct or accurate enough for the OP's purposes, but I also certainly cannot confidently say that it is. Indeed, the fact that that OP has not accepted your answer, and has looked for and found sources that seem at a glance to contradict it, makes me think that it likely isn't. If those sources are incorrect or misunderstood or simply irrelevant due to the discrepancies being lost in the overall uncertainty of available data, a good answer from an expert should note and demonstrate this. Yours does not. $\endgroup$ Oct 27, 2022 at 17:14
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    $\begingroup$ @caInstrument Note that I cite these lower-quality sources specifically as examples of the kind of scholarship I'm not looking for, and as evidence for widespread confusion on the internet about the distinction I'm trying to make in the post. I'd be happy to read through any relevant papers if linked, and if the academic sources that led me to the conclusions in the original post are wrong or I misinterpreted them, I'd love to learn why! $\endgroup$ Oct 27, 2022 at 18:22

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