Does a star fuse helium to beryllium on the main sequence?
When a star has finished fusing all its hydrogen into helium, it will then start fusing helium into beryllium and so on and so forth up until iron.
When the star is fusing to beryllium, will the star still be in the main sequence phase and will it at that point start to grow into the red giant phase, or is there no given rule for when it will start growing?
Stars don't fuse helium to beryllium, Be-8 has an *extremely* short half-life. Beryllium isotopes are produced by cosmic ray spallation.
Thx PM for highlighting my mistake, I did some more research and see Small ->H->He, Medium go up to Carbon. However massive stars go up Copper and more, I thought fusion stopped at Iron. https://www.enchantedlearning.com/subjects/astronomy/stars/fusion.shtml
You're right: stellar fusion does stop at iron / nickel. But in a hot star with sufficient neutron flux heavier species can be "cooked" by the s-process.
What defines the main sequence?
Main sequence stars are characterized by hydrogen fusion in their cores, either through the proton-proton chain (for lower-mass stars) or the CNO cycle (for stars more than about 1.5 times the Sun's mass). Outside the core, no significant fusion takes place; the outer layers are involved in radiative or convective energy transport, but not energy generation. In general, if hydrogen fusion is occurring in the core, we say that a star is still on the main sequence.
This changes in stars that evolve off the main sequence. Some low-mass red giants may fuse hydrogen to helium via the CNO cycle in a layer outside a largely non-reactive helium core; this is referred to as shell burning. In more massive stars, heavier elements (e.g. helium, carbon, etc.) are fused inside the core, and shell burning continues in the outer layers. For instance, in a fairly high-mass star that is far into the post-main sequence phase of its life, you might see oxygen, neon, carbon, helium and hydrogen being fused in successive layers farther and farther from the core.
A common misconception is that a star uses up all its hydrogen before leaving the main sequence; this is not true. It merely uses up the majority of the hydrogen in its core; there is still plenty in the outer layers, which is what makes shell fusion possible.
Post-main sequence evolution
Let's consider stars of around one solar mass. As hydrogen fusion stops in the (now degenerate) core, the source of pressure keeping the star in hydrostatic equilibrium vanishes. Hydrogen burning starts in a shell around the core. After some time, the core begins to contract, the outer envelope expands, and the star is said to be on the red giant branch. Eventually, temperatures rise to the point where the triple-alpha process can occur, and a helium flash occurs, marking the beginning of the horizontal branch and helium fusion via the triple-alpha process. Hydrogen shell burning continues.
As you'll notice - and as others have said - stars don't fuse helium to beryllium to any significant degree during any part of this process, or post-main sequence evolution in general. It's endothermic; the triple-alpha process is exothermic.
At what point does a star begin to grow? At the end of hydrogen fusion in the core?
@MiscellaneousUser Stars grow throughout their life in the main sequence. For example, our Sun was only 0.75 R☉ just after its birth, and 3-4 billion years from now it will be around 1.5 R☉. Of course, I assume you are referring to the expansion into a red giant. In that case, it is when helium begins to fuse. Hydrogen still gets fused along the edges of the core, and this is referred to as the Hydrogen-fusion shell, but most of the core will be fusing helium (or heavier elements if later along) at the point. Now, technically, the shell is actually not part of the core, but that's semantics.
@KITTENDESTROYER-9000 "In that case, it is when helium begins to fuse. " This part of your comment is not right. A star shrinks when it begins to fuse helium and terminates the first ascent red giant branch.
Re the misconception discussed in paragraph 3, pretty much no physical process is going to transform all the A into B, then transform all the B into C and so on. Rather, as A becomes less abundant, the rate of transforming A to B will slow and, as B becomes more abundant, the rate of C production will increase. It's never going to be a hard cut-off.