Questions about Nuclear Fusion in the Sun

[enceladus_]

This excerpt is from "The Universe and the Atom" by Don Lichtenburg:

The two released positrons in these fusion reactions annihilate
against two electrons via the electromagnetic interaction, producing
energetic photons. The photons are absorbed in the sun, and less energetic
photons are emitted. Many absorption and reemission processes
take place, degrading the energies of the photons. Eventually,
most of the electromagnetic energy is radiated out into empty space,
much of it in the form of visible light.

I was under the impression that photons made in the nuclear fusion bounced off of particles for a long time, before they inexplicably were able to escape from the sun. Why does the sun absorb the most energetic photons?

Also, before Einstein discovered the equivalence of matter and energy, how exactly did physicists of the world think that the Sun functioned (or any star for that matter)?

 

[Pagan Harpoon]

I was under the impression that photons made in the nuclear fusion bounced off of particles for a long time

The way I read the passage that you pasted, that's exactly what he's saying. The nuclear reactions create high energy photons, they bounce around and eventually reach the surface of the sun and escape into space. It's important to think about what "bouncing around" means, though. The photons produced are gamma rays. They don't scatter elastically from the matter in the sun, if they did then they'd still be gamma rays when they leave the sun. No, the energy spectrum thermalises to the sun's temperature and what comes out is a blackbody distribution of energies.

As for what people thought happened before E=mc², I don't really know. There is a thing called the Kelvin-Helmholtz mechanism (see http://en.wikipedia.org/wiki/Kelvin–Helmholtz_mechanism ) which refers how a large collapsing body releases its gravitational energy. You can calculate the timescale for how long the sun would last if this were the source of its energy and (unsurprisingly), it's much too short. I don't really know if this was ever considered to be the source of the sun's energy, though.

 

[Nugatory]

Also, before Einstein discovered the equivalence of matter and energy, how exactly did physicists of the world think that the Sun functioned (or any star for that matter)?

They didn't - this was one of the important unanswered questions of that time.

 

[enceladus_]

The way I read the passage that you pasted, that's exactly what he's saying. The nuclear reactions create high energy photons, they bounce around and eventually reach the surface of the sun and escape into space. It's important to think about what "bouncing around" means, though. The photons produced are gamma rays. They don't scatter elastically from the matter in the sun, if they did then they'd still be gamma rays when they leave the sun. No, the energy spectrum thermalises to the sun's temperature and what comes out is a blackbody distribution of energies.

Ahh, I read the passage wrong then. I thought some of the photons we re-absorbed for some reason. This clears up some errors in my understanding.

Thanks to both of you for the answers.

 

[PeterDonis]

The way I read the passage that you pasted, that's exactly what he's saying.

Not really. The passage quoted explicitly says "absorption and reemission processes", indicating that the gamma rays from nuclear reactions in the Sun's core get absorbed, not just scattered. I believe our best current understanding is that both processes are going on.

There is a good point to raise here, though, which you may have been trying to get at when you mentioned inelastic scattering. A gamma ray is only going to get absorbed by a nucleus inside the Sun, and pretty much the only thing that can happen next is for the nucleus to re-emit a gamma ray of the same frequency. This is because a given nucleus will only absorb gamma rays of specific frequencies; nuclei have definite energy levels just as electrons in atoms do. The frequencies that get emitted are the same as the frequencies that get absorbed; there may be cases in which there is some intermediate nuclear energy level so that one absorbed gamma ray would be re-emitted as two gamma rays (each of lower frequency), but that's probably very rare (I would have to look up the nuclear energy levels involved to be sure).

So in order for the light radiated by the Sun to be thermalized by the time it is emitted at the surface, the gamma rays *have* to be inelastically scattered, gradually transferring energy and momentum to the matter inside the Sun. This energy and momentum then gets re-radiated by the matter inside the Sun; one gamma ray photon released by a nuclear reaction in the Sun's core ends up producing millions of visible light photons emitted at the surface. So virtually all of the photons we see from the Sun were not produced in the core; they were produced somewhere in between.

(Btw, it's quite possible that *none* of the gamma rays produced in the core ever make it to the surface; they may just be scattered back and forth in the core until they are absorbed by a nucleus, then re-emitted again, absorbed again, re-emitted again, etc. The key point is that there *must* be inelastic scattering going on to thermalize the spectrum.)

 

[PeterDonis]

I thought some of the photons we re-absorbed for some reason.

Some of them are. See my post in response to Pagan Harpoon.

 

[enceladus_]

Great post Peter, thank you. My book also touched on instances when a photon strikes an electron or positron before they can annihilate. What kind of process occurs when this happens?

 

[PeterDonis]

My book also touched on instances when a photon strikes an electron or positron before they can annihilate. What kind of process occurs when this happens?

This would just be an example of scattering, probably inelastic.

 

[phyzguy]

As for what people thought happened before E=mc², I don't really know. There is a thing called the Kelvin-Helmholtz mechanism (see http://en.wikipedia.org/wiki/Kelvin–Helmholtz_mechanism ) which refers how a large collapsing body releases its gravitational energy. You can calculate the timescale for how long the sun would last if this were the source of its energy and (unsurprisingly), it's much too short. I don't really know if this was ever considered to be the source of the sun's energy, though.

It certainly was considered a realistic theory of where the sun's energy came from, and it led to a classic debate between Lord Kelvin and Thomas Huxley, who was espousing Darwin's theory of evolution. If gravitational contraction were the source of the sun's energy, the Earth could only be 10's of millions of years old, which is not old enough for complex creatures like us to evolve, and which was considered a strike against Darwin's theory. See, for example, http://m.teachastronomy.com/astropedia/article/Kelvin-and-the-Suns-Age. Of course, today we know that the sun is powered by nuclear fusion, and Earth is in fact ~4.5 billion years old, ample time for the evolution of the life we see.

 

[ImaLooser]

Also, before Einstein discovered the equivalence of matter and energy, how exactly did physicists of the world think that the Sun functioned (or any star for that matter)?

There have been some very nice answers here already. I can add that it has been estimated that it takes about 300,000 years for photons to exit the sun.

That stars are powered by fusion was proved by Landau or Bethe, I think. One of those excellent scientists who never became famous. The ancient Greeks thought it was fire. Then gravitational contraction. Lord Kelvin was unfortunate to live in an era in which much that was known was incomplete, so many of his very good theories did not work out. What can you do?