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For stars around the mass of the sun, helium fusion occurs concurrently with late hydrogen shell burning.

For stars smaller than the sun, is their a subset that first burn all their hydrogen store before initiating helium fusion in their cores?

Is this possible, or is the environment during hydrogen shell burning more preferential than during late gravitational collapse?

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The only way for a star to fuse (most) of its hydrogen, without being stripped by, or colliding with, another object, is to have a fully convective hydrogen burning stage. Unless there is some exotic stellar composition and dynamics I am unaware of, the only stars which are fully convective during their hydrogen burning phase are red dwarfs (under half a solar mass or thereabouts). All higher mass stars have a mix of radiative and convective zones.

In the higher mass stars, by continuity of the pressure and temperature gradients there will always be a region of the star where hydrogen burning is possible. Once you establish a meaningful "helium core", the star not being fully convective, combined with this region, means there will necessarily be a shell of hydrogen burning going on around it, both before and after helium fusion initiates.

Red dwarfs, however, while fully convective, will never be capable of helium fusion. They simply can't reach the necessary temperatures and pressures. Given a prodigious amount of time (trillions of years), they will fuse a vast proportion of their hydrogen into helium and then essentially just shut down all fusion.

Maybe a collision and merger of two thusly exhausted red dwarfs could produce helium burning with no significant hydrogen burning shell. I'm not sure if that's been modeled (not nearly enough time has passed for such objects to exist within our universe), and am not sure it would not result in a supernova of some form.

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  • $\begingroup$ I would suggest this answer needs to take into account the observed helium white dwarfs. $\endgroup$
    – Joshua
    Commented Dec 20, 2021 at 18:33
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    $\begingroup$ @Joshua As helium white dwarfs are understood to be formed via mass loss in a binary system, the "without being stripped" line in the answer addresses them. Though they do offer up an opportunity for an observable collision between such objects. $\endgroup$ Commented Dec 20, 2021 at 21:55
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We observe hydrogen-depleted stars that appear to be burning helium, for example R Coronae Borealis variables and Wolf–Rayet stars.

These are rare objects, apparently not part of common stellar evolution histories. They may be the product of mixing in very rapidly rotating stars, which would burn the entire hydrogen envelope, or they may have lost their hydrogen via ejection or binary mass transfer.

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  • $\begingroup$ It may be worth noting that these first two (very interesting) types of stars likely had some part of their evolution, including pre-merger objects, with a hydrogen burning shell involved. I'm not sure if the OP wishes to discount a prior history of shell burning. If not, these are great examples of the cool sort of stuff you can get with mergers and mass loss. $\endgroup$ Commented Dec 20, 2021 at 22:21
  • $\begingroup$ @zibadawatimmy Well, if you burn all the hydrogen before you ignite the helium, you get a different history. Helium ignition results in a type Ia supernova. $\endgroup$
    – John Doty
    Commented Dec 20, 2021 at 22:49

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