Question

Is it true that stars the size of the sun will never have a core hot enough to fuse carbon?

Answer 1

Yes, stars the size of the Sun aren't hot enough for carbon fusion.

Explanation:

A star needs to have a core temperature of over `10^9K` to start the carbon fusion process. This requires the star to be at least 8 times the mass of the Sun.

The Sun is currently fusing hydrogen into helium, with a core temperature of `1.5*10^6K`. This means that helium is building up in the Sun's core.

When the hydrogen runs out in the core the star collapses to the point where hydrogen fusion can start in the region outside of the core. The star expands into a red giant at this stage.

Once the core temperature reached `10^8K`, helium fusion can begin. AT this point the star contracts and is no longer a red giant. This produces the elements oxygen and carbon.

For stars less than 8 times the mass of the Sun, then the supply of helium is dexhausted, they end up as white dwarf stars with an oxygen carbon core and no further fusion reactions taking place.