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I was reading about the "Lithium problem" and I came across this Physics SE post: Discrepancy problem in lithium?

The answer mentioned

On the other hand, measurements of the $\rm Li$ abundance present in the photospheres of the oldest stars ("halo stars") in our Galaxy suggest that the primordial abundance was actually about $1.2×10^{−10}$.

How was this conclusion made? What data supports this and how was it measured?

I've read about how the element composition of distant bodies is measured using absorption and emission spectrum after accommodating for redshifts/blueshifts; do measurements needed here involve similar techniques?

I'd love to see an answer which includes a somewhat detailed description of the math needed to compute historical levels based on whatever observations we can make now.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Aug 27 '18 at 15:08
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The idea is that you measure the present day Li abundance in the oldest stars you can find. An underlying assumption is that this abundance nearly represents the abundance of the gas from which the star was made and that if the stars are old enough, then this is also equal to the primordial Li abundance created by big-bang nucleosynthesis.

That's it. The techniques for estimating the Li abundance from a high resolution spectrum are absolutely standard. They involve measuring the strength of the Li 670.8 nm absorption line due to atomic lithium and comparing that to the predictions of stellar atmosphere models.

If you think any of these steps might be suspect, then join the club. Everyone is questioning these assumptions and techniques. A probability is that the photospheric Li abundance in the oldest stars is slightly below the primordial abundance because of "non-standard" mixing that dredges up Li-depleted material from the hot interior where it has been processed in nuclear reactions. Other possibilities are discussed in my answer that you linked to.

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