How hot would the core of the Red Giant Sun be?

Question

After the Sun becomes a red giant, it will heat up its core to 100 million kelvins, which initiates the Triple-Alpha fusion process, which heats up the star's core even further and cause it to undergo a runaway thermal reaction, a helium flash.

However, I have not been able to find the final temperature of the core. Meaning that, although the star's core would heat up to 100 million kelvin, since the electron-degenerate core cannot expand, it just gets more hotter. I remember having read a paper where the Red giant's core would reach 1 billion kelvin, but I can no longer find that. What vague info I have in mind, is that the Red Giant's core would be between 100m-1b kelvins.

What would be the core temperature of the Red Giant Sun, after the Triple Alpha process causes it to heat up?

Answer 1

According to this paper: https://iopscience.iop.org/article/10.1086/342498/meta

• The core may not be the hottest point of the star, rather that will be where fusion is happening.
• At the moment of Helium flash the core is likely to be at around $7\times10^7$K
• Core temperature will rise as per the mecahnism you posit but eventually the temperature rise will allow the core to expand (which presumably acts as a limit to the heating)

This paper: https://iopscience.iop.org/article/10.1086/319496/fulltext/006059.text.html - cited in the above suggests that temperatures at the bottom of the convection layer (the hottest point) will be of the order of $>10^8$K

Answer 2

Here is what I get when I run MESA-Web for the sun, zooming in on the red giant period (top plot: core temperature, middle: triple alpha luminosity, bottom: surface luminosity).

When the process sets in, the core temperature rises (after oscillatory transients) to 110 million K, ramping up to 147 MK near the end.

The maximum temperature is however not always in the core, but sometimes in a shell surrounding it. Plotting it versus the core temperature shows there are periods where the shell reaches 200 million K.