# What is the most appropriate way to estimate the helium composition of a star?

Say we have to estimate the helium content in Proxima Centauri.

We begin by calculating the content of helium in the Sun (source): $$24.85$$% of $$2.10^{30}$$ kg.

Mostly all the energy is generated due to the product of nuclear fusion of hydrogen into helium by way of the proton–proton (PP) chain mechanism and the luminosity of Proxima Centauri is $$0.00005\ L_☉$$.

Thus, would it be a good approximation to say that the helium content is $$0.00005 * 0.2485 * 2 * 10^{30}$$?

Would you suggest a better way of estimating the helium content?

• Well can you explain where you got the number 28%? If you know where that arises then you're on the way to an answer. Your estimate is way out. Commented Apr 5, 2020 at 17:08

## 1 Answer

Nearly all the helium in the photosphere of the sun comes from the helium in the interstellar gas that collapsed to form the sun. That helium was produced shortly after the Big Bang (in about the first 20 minutes) while the universe was hot and dense enough for hydrogen to fuse to helium. That produces a universe in which ordinary matter is about 25% helium and 75% hydrogen. (by mass) Over the eons, the gas is enriched in helium somewhat by previous stars to about 27% helium.

The outer layers of the sun still have this 25%-75% composition. Some of the helium has settled under gravity, reducing the composition of the photosphere to your 24.85% helium. The core is enriched in helium by fusion reactions. It isn't constant. The outer core is about 30% helium. The inner core has as much as 65% helium. The average composition is about 28% helium, only slightly more than what it started with.

Proxima Centauri is fully convective, which means that helium from the core gets mixed up through the whole star. But it is such a dim candle that it has hardly produced any more helium than when it formed: about 27%.

So for any star, no matter how bright or dim (with a few exceptions) the helium composition is about 25%, or a little more.

• OTOH, because red dwarfs are fully convective they do eventually fuse a much higher percentage of their hydrogen over their lifespan than larger stars do. But the slower rate of fusion & convective mixing mean that they have extremely long lifespans. Commented Apr 6, 2020 at 12:46