Question regarding fusion in main sequence stars

[Manto]

Hey guys,

I'm new to the forum, and I am just gonna jump straight into a few questions regarding fusion in main sequence stars that I hope you guys may elucidate for me:

1) In the first step of proton-proton process involves taking two protons and make a deuteron, while releasing a positron and neutrino in the process. As far as I understand, both the positron and neutrino are matter and not pure energy (like photon in the gamma radiation). But since the positron will most likely annihilate with a free flying electron very soon after it's released, does this energy get counted towards "energy created" in the overall proton-proton fusion process?

2) The mass of a neutron is heavier than that of a proton - so how do two proton come together to form a deuteron yet still have enough excess energy to release a positron and neutrino in the process? Does this have anything to do with the kinetic energy of the fast-moving protons before them combine into a deuteron?

3) The CNO cycle can happen in main sequence stars when the core reaches a certain temperature. However, the proton-proton fusion only generates helium as its by product; carbon, nitrogens, and oxygens are not created until later in the life of a star where it's hot enough in the core to conduct helium fusion. How do stars early in the main sequence have access to C, N and O - are they already present in the interstellar medium before the protostar is even formed? If that's the case, is it correct in thinking that main sequence stars that can perform CNO cycle can only born out of the remnants of a previously dead/failed/exploded star?

Thanks guys!

Shawn

[ShinAce]

I'll answer number 2 for you. It boils down to the fact that a neutron and proton together in a nucleus weigh less than the combined weight of a free proton and free neutron. This is the binding energy.

I didn't have the exact numbers, so I pulled them from wiki.
atomic mass of deuterium = 2.01410178 u
atomic mass of hydrogen = 1.00794(7) u
atomic mass of a positron = 0.00055 u

So if we start with two atoms of hydrogen, so two protons and two electrons, we have a total of 2*1.00794 = 2.01588 u .

Now we're left with deuterium, plus a positron and a neutrino. I'm going to ignore the neutrino for now. So we had 2.01588 u to start with and now we're left with 2.01410 + 0.00055 = 2.01465 u. That means there's still 0.00123 u to be found. This is in the form of the neutrino and kinetic energy(of all particles), along with any gamma rays.

It seems odd to think that two things stuck together weigh less than the parts total, but that's exactly what happens. It's the strong nuclear force. We don't see it in our normal lives, but that's what it does. When protons and neutrons get stuck in a nucleus, it's because the strong nuclear force allows them to shed away energy. That's why atoms don't spontaneously disintegrate. You have to give them back the energy that's been shed in order to get the free floating pieces again. It might seem that they only have to shed a small amount of energy when bound, but that energy is actually huge. Think of trying to lift a 5 pound rock, it's not that bad. Now try to lift a 5 pound rare earth magnet stuck to iron. Much harder, but maybe you'll get it. The strong nuclear force is like the best glue available. You're not getting that stone to move if you have to fight the strong force. You'll break every bone in your body trying to lift it.

They come together with kinetic energy, but stay together thanks to a whole new force, the strong nuclear force. That kinetic energy is the energy they need to fight the static electricity(called coulomb repulsion) that pushes resists their union.

[WayneFrancis]

First, welcome to BAUT Manto.

The following is my understanding of the process. I'm sure others will come by to expand on what I say or correct any of my errors.

Hey guys,

I'm new to the forum, and I am just gonna jump straight into a few questions regarding fusion in main sequence stars that I hope you guys may elucidate for me:

1) In the first step of proton-proton process involves taking two protons and make a deuteron, while releasing a positron and neutrino in the process. As far as I understand, both the positron and neutrino are matter and not pure energy (like photon in the gamma radiation). But since the positron will most likely annihilate with a free flying electron very soon after it's released, does this energy get counted towards "energy created" in the overall proton-proton fusion process?

I'd count the positron as part of the energy released because it is part of the loss of mass of the new nuclei

2) The mass of a neutron is heavier than that of a proton - so how do two proton come together to form a deuteron yet still have enough excess energy to release a positron and neutrino in the process? Does this have anything to do with the kinetic energy of the fast-moving protons before them combine into a deuteron?

From my understanding the kinetic energy alone isn't enough if you look at it in isolation. From memory it is about 1 order of magnitude off. That said that is the average kinetic energy. Some will have higher energy some lower. The other thing is that a lower kinetic energy then normally required can get 2 nuclei close enough where quantum tunnelling effects actually become more statistically relevant. These 2 reasons combined with the large volume of material create the conditions for the sustained nuclear reactions at a lower temperature then one would expect if you look at the nuclei in isolation.

3) The CNO cycle can happen in main sequence stars when the core reaches a certain temperature. However, the proton-proton fusion only generates helium as its by product; carbon, nitrogens, and oxygens are not created until later in the life of a star where it's hot enough in the core to conduct helium fusion. How do stars early in the main sequence have access to C, N and O - are they already present in the interstellar medium before the protostar is even formed? If that's the case, is it correct in thinking that main sequence stars that can perform CNO cycle can only born out of the remnants of a previously dead/failed/exploded star?

Thanks guys!

Shawn

Most of the metallicity of a star comes from the source material. Remember population I stars are produced from the remnants of older stars thus have have material that has already been through, often, a much larger star that can produce the heavier material. There will be some elements that are created during the normal hydrogen fusing process but statistically the amount will be VERY low.

[WayneFrancis]

I just noticed, after I read ShinAce's post, that I answered a different question in number 2.

You ask a interesting question. That kinetic energy isn't lost in the process. Some of the energy released by the new nuclei is simply the mass difference from the original 2 particle compared to the final product but that kinetic energy still has to be conserved some how. So some of that will go into the kinetic energy of the newly formed nuclei I would imagine and some would be radiated away.

[ctcoker]

For number 3, WayneFrancis got most of it. The carbon, nitrogen, and oxygen for CNO burning in today's stars comes from the previous generations of stars that spewed it all over the place when they died. Population I stars only had access to hydrogen and helium (and a tiny bit of lithium, which they would destroy) at first, and burned hydrogen through the p-p chain, no matter how massive.

However, if the star is massive enough, I believe helium and hydrogen burning can take place at the same time in a core with a pure hydrogen and helium mix*. Once enough carbon is formed, CNO burning of hydrogen would take over. This is provided, of course, that the helium can burn fast enough before the core hydrogen is all used up.

*CNO burning has such a steep temperature dependence that the central temperature of today's stars is never high enough to burn helium on the main sequence. P-p fusion, however, has a low enough temperature dependence that very high central temperatures are possible while still on the main sequence.

[WayneFrancis]

For number 3, WayneFrancis got most of it. The carbon, nitrogen, and oxygen for CNO burning in today's stars comes from the previous generations of stars that spewed it all over the place when they died. Population I stars only had access to hydrogen and helium (and a tiny bit of lithium, which they would destroy) at first, and burned hydrogen through the p-p chain, no matter how massive.

However, if the star is massive enough, I believe helium and hydrogen burning can take place at the same time in a core with a pure hydrogen and helium mix*. Once enough carbon is formed, CNO burning of hydrogen would take over. This is provided, of course, that the helium can burn fast enough before the core hydrogen is all used up.

*CNO burning has such a steep temperature dependence that the central temperature of today's stars is never high enough to burn helium on the main sequence. P-p fusion, however, has a low enough temperature dependence that very high central temperatures are possible while still on the main sequence.

Slight correction. " Population I stars only had access to hydrogen and helium" should be "Population III stars only had access to hydrogen and helium"

Population III stars are the first generation of stars in the universe.
Population II stars are 2nd generation stars with low metallicity.
Population I stars are 2nd+ generation stars with high metallicity.

The names are more when the "group" was discovered...tho we still, to my knowledge, have not discovered a population III type star but they've made the category because it was the only one left.

[chornedsnorkack]

I just noticed, after I read ShinAce's post, that I answered a different question in number 2.

You ask a interesting question. That kinetic energy isn't lost in the process. Some of the energy released by the new nuclei is simply the mass difference from the original 2 particle compared to the final product but that kinetic energy still has to be conserved some how. So some of that will go into the kinetic energy of the newly formed nuclei I would imagine and some would be radiated away.

It is not only the energy which must be conserved - momentum must also be conserved.

If the centre of mass of the two protons has no momentum relative to the star - the protons happen to be moving in opposite directions with equal speed - then all the kinetic energy must go to the energy of the products.

A deuteron has no excited states. Thus the binding energy of the deuteron PLUS the kinetic energy of the protons must go to kinetic energies.

Since deuteron is massive, it can only have very little energy from the recoil - if the neutrino and the positron are emitted in the same direction. The bulk of the energy is distributed randomly between the neutrino and the positron - thus pp process neutrinos have wide continuous energy distribution all the way to zero.

Since the neutrino escapes, its energy is not available to heat the star. Whereas the positron is soon annihilated, its rest mass plus any kinetic energy it shared is given to the photons which are in their turn absorbed and heat the star.

There is an alternative to pp, namely pep. This three particle collision is somewhat less common in Sun.

When it does happen, only 2 particles result. Now, the conservation of momentum requites that almost whole of the available energy - fusion energy and the kinetic energy of protons and electron - must be carried away by the neutrino, leaving only tiny recoil energy to deuteron. The pep process neutrinos thus form a sharp line, with only small Doppler tails, mostly bluewards.

[Cougar]

Population III stars are the first generation of stars in the universe.

Right. That makes sense, doesn't it? NOT! Another example of perfectly backwards nomenclature in our beloved field....

[ngc3314]

But that way we get to be Pop I. (Or more seriously, when Baade et al. recognized the populations, the age distinction only came later, when it was too late to change the Roman numerals.) On of my favorite questions to snarl discussion into a complete loop at meetings is "when are we justified in revising our nomenclature to make more physical sense, albeit completely breaking decades or more of existing use?" More examples: when are we really justified in talking only about core-collapse and white-dwarf SN, instead of the type I/II (and subtypes) which are defined in purely observational terms? Should we have gotten rid of "planetary nebula" at some point?

[antoniseb]

... when are we justified in revising our nomenclature to make more physical sense ...

Or say the charge of an electron is positive, or stop calling ellipticals "early type galaxies".

[ctcoker]

Population III stars are the first generation of stars in the universe.
Population II stars are 2nd generation stars with low metallicity.
Population I stars are 2nd+ generation stars with high metallicity.

Oh, right, duh. Brain fart on my part.

[Manto]

From studying astronomy, I've come to realize that astronomers are not the best at naming things or phenomenon (except perhaps galaxy harassment)

[Manto]

Thanks for the prompt and informative answers guys!

[ngc3314]

From studying astronomy, I've come to realize that astronomers are not the best at naming things or phenomenon (except perhaps galaxy harassment)

although following some paleontological discussions on nomenclature makes me think astronomers are geniuses at it! (Even though this is the community that built a very large array of radio telescopes and named it the VLA, or a very large telescope in Chile and called it the VLT - at least instrument builders are getting more slack now to have genuine names.)