Star Nuclear Reaction: P+P, D+P, He3 and CNO Cycle

[Stephanus]

Dear PF Forum,
I'm just wondering about P+P reaction in star.
Because of its pressure, in the core of the star, hydrogens fuse to become deuterium.
Its the complete reaction
P + P -> D
D + P -> He3
He3 + He3 -> He3 + P + P
and if the star is big enough, it can undergo CNO cycle,
But what if the star is smaller.
Can it only able to process
P + P -> D
and it can't continue to D + P -> He, etc...?
What if the star is somewhat bigger.
Can it continue to Carbon and then stop. It can't produce nitrogen, or the once initiated CNO cycle automatically completed?

 

[marcus]

Dear PF Forum,
I'm just wondering about P+P reaction in star.
Because of its pressure, in the core of the star, hydrogens fuse to become deuterium.
Its the complete reaction
P + P -> D
D + P -> He3
He3 + He3 -> He3 + P + P
and if the star is big enough, it can undergo CNO cycle,
But what if the star is smaller.
Can it only able to process
P + P -> D
and it can't continue to D + P -> He, etc...?
What if the star is somewhat bigger.
Can it continue to Carbon and then stop. It can't produce nitrogen, or the once initiated CNO cycle automatically completed?

minor typo, you meant to write He4
He3 + He3 -> He4 + P + P
http://en.wikipedia.org/wiki/Proton–proton_chain_reaction

You ask if a star could build up a deuterium core, and not proceed to make He3 and He4.
I don't think so. I think the hardest step is the first one and after you have D, the rest of the proton-proton chain is comparatively easy. Maybe someone else will step in here.

I suppose it is possible for He3 to build up. but at least the D+P -> He3 is going to happen very quickly once there is D. In that Wippy article it says:
" under the conditions in the Sun's core, a newly-created deuterium nucleus exists for only about 4 seconds before it is converted to He-3."

whereas the half life for the first step is a billion years.
the first step is very hard because it involves a beta decay (weak force) where a proton has to decay into a neutron and that has to happen before the two protons which are temporarily stuck together decide to split up. protons do not just automatically decay into neutrons very often!

 

[SteamKing]

Dear PF Forum,
I'm just wondering about P+P reaction in star.
Because of its pressure, in the core of the star, hydrogens fuse to become deuterium.
Its the complete reaction
P + P -> D
D + P -> He3
He3 + He3 -> He3 + P + P
and if the star is big enough, it can undergo CNO cycle,
But what if the star is smaller.
Can it only able to process
P + P -> D
and it can't continue to D + P -> He, etc...?
What if the star is somewhat bigger.
Can it continue to Carbon and then stop. It can't produce nitrogen, or the once initiated CNO cycle automatically completed?

Stars are dynamic objects. Their cores are stable because of a balance between the energy evolved from nuclear fusion, which tends to expand the core, and the gravitational attraction generated by the mass of hydrogen being fused, which tends to contract the core.

A stellar core will fuse material until it reaches a point where the amount of energy being generated no longer is capable of preventing gravitational contraction. When the core starts to contract, its internal density and temperature both increase, and if further fusion reactions are able to start, then the contraction will be arrested temporarily.

There are several different reactions in the P-P chain, and some exist only at higher temperatures:

http://en.wikipedia.org/wiki/Proton–proton_chain_reaction

Some of the reactions, especially in the initial stages of the P-P chain, take astoundingly long times to occur:

http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

While an initial P-P reaction might take a billion years to occur, He-4 results in a relatively short interval afterward. It is not clear that a star could be so structured as to permit P-P reactions but not P-D reactions. In any event, not much He-4 is produced in stars until the stellar core reaches a temperature > 10⁷ °K. In the meantime, the He-3 keeps accumulating in the core.

There is evidence that once the P-P chain starts, eventually all of the different reaction permutations will occur, more or less simultaneously.

Even though the sun, for example, is too small to support the CNO cycle, a small amount of the helium (< 2%) created in the sun's core results from the CNO cycle.