Nuclear reactions in the Sun and other topics on stars

The fact that matter is ionized allows ions and electrons to be much closer together than they are in atoms (Bohr radius ##a=0.5 \cdot 10^{-10}m##), and the result is that some stars, including white dwarfs, have a very small radius and a very high density that could not be had if matter were not ionized.

A white dwarf, however, is a star that has run out of nuclear fuel; therefore, it slowly cools down. At some point the temperature becomes so low that matter would tend to regroup into non-ionized atoms. But to do that it would have to increase its radius and decrease its density, and this it cannot do because the change in gravitational energy it would take is greater than all the energy it has left.

So, in a sense, the star would get to a situation where it does not have enough energy to cool down again. In other words, the temperature would stop decreasing without the star being in equilibrium with the part of the universe that surrounds it, and that is obviously not possible.

Hak said:

TL;DR Summary: /

I don't know if the Forum in which I am posting is right, if it is not please freely move my question to the Forum you think is most appropriate.

You argue that nuclear reactions occur in the Sun, which produce the energy that spreads out into space in the form of light. A friend of yours disagrees, and argues that the Sun's energy might come from the gravitational potential energy that the Sun loses as it contracts. How do you change his mind without using overly complicated arguments that he would not understand?
Do you have any arguments or ideas to make the question more elucidating? This question is emblematic of a cross-examination between a professor and some students, at the end of which the former sketches an equation saying that it is derived from the assumption that the only way energy propagates in the star is by radiative transport (i.e., photons that are absorbed and re-emitted by atoms), an assumption that is not always true:

$$\frac{dT(r)}{dr}=-\frac{3L(r)}{16 \pi al(r)cr^2T(r)^3}$$

Where a is a constant called the blackbody constant and such that the energy density in a blackbody at temperature ##T## is ##aT^4##; ##l(r)## is the free mean path of photons at distance r from the center; ##c## the speed of light.

The professor himself says it is not easy to get there: how to justify this equation? Do you have any opinions or advice on this?

At the end of it all, the professor debuts with this other question:
How to approach the question? How to understand whether it is true that matter in white dwarfs is ionized? How to understand that if the kinetic energy of particles (should be of the order of ##k_BT##) is much larger than the ionization energy, then matter is ionized?

Thank you to anyone who would like to answer me and clarify this question, which I consider complex and not at all trivial.

Frabjous said:

Check out https://en.wikipedia.org/wiki/Kelvin–Helmholtz_mechanism

Hak said:

OK, thank you very much. It is certainly a very interesting source, but at a very first glance, however, there is no reference to the formula I quoted...

Frabjous said:

When you stick numerous questions in a post, it is the responders choice on which to respond to

Hak said:

OK, I had no idea. How do I make sure that all questions are taken care of? I put them in one post because they are closely related and all refer to one event from some time ago... Thanks.

Frabjous said:

PF is not designed to replace the literature, so I do not believe it is possible.

1. PF is not for arguing with others by proxy. This is ineffective and just makes people grumpy.
2. If the sun is not powered by nuclear fusion, where are all the solar neutrinos coming from?

Vanadium 50 said:

1. PF is not for arguing with others by proxy. This is ineffective and just makes people grumpy.

Vanadium 50 said:

1. If the sun is not powered by nuclear fusion, where are all the solar neutrinos coming from?

Hak said:

Gravitational potential energy could become light energy; i

Hak said:

Gravitational potential energy could become light energy; if we want to go into microscopic detail, atoms, by collapsing, could acquire enough kinetic energy to go into an excited state (emit a photon) when they collide with each other.

Hak said:

Gravitational potential energy could become light energy; if we want to go into microscopic detail, atoms, by collapsing, could acquire enough kinetic energy to go into an excited state (emit a photon) when they collide with each other. There are cases where a star remains with the same radius, on average, for a certain period of time, i.e. gravity, which is supposed to still be there, is counteracted by a repulsive force.
This is not enough to prove that energy does not come from gravitational contraction. Your 'friend' (referring to the statement of the question) might well not trust it and say that the Sun is contracting, but at such a slow speed that we do not notice it.

renormalize said:

But neutrinos are not light, nor are they emitted by excited atoms. Neutrinos come from the nucleus, so solar neutrinos imply that nuclear reactions (like fusion) are occurring within the sun. How can this be explained by slow gravitational contraction?

Hak said:

But anyway, what interests me most are the following questions: where did those formulas come from? How can we solve the paradoxical situation presented at the end of my query?

Frabjous said:

Did you even bother to read the link about the Kelvin-Helmholtz mechanism? Gravity gives you millions of years of energy. You need billions.

Hak said:

Sorry, I did not understand this statement of yours.

Frabjous said:

Why don’t you write down your profs derivation and tell us what steps bother you?

Hak said:

Yes, of course. As I said, I know that the gravitational argument is wrong. It is just a question of understanding what are the various and numerous reasons why this argument is fallacious and erroneous (as I understand it, there are many, all interrelated). Thank you for your intervention.

Frabjous said:

Sigh. What does your textbook say?

Vanadium 50 said:

Which word didn't you understand?

Your post #10 shows a lack of understanding where neutrinos come from, nor the quantitative argument: we don't just see neutrinos, we see them in the right energies and rates to within about 3%,

Creating one's own explanation on of what is going on without knowing the evidence for the conventional view is practically the definition of crackpottery. It is unwise to argue with a crackpot: people may not be able to tell the difference.

Frabjous said:

Why don’t you write down your profs derivation and tell us what steps bother you?

Hak said:

How to understand whether it is true that matter in white dwarfs is ionized? How to understand that if the kinetic energy of particles (should be of the order of kBT) is much larger than the ionization energy, then matter is ionized?

Hak said:

This is not enough to prove that energy does not come from gravitational contraction. Your 'friend' (referring to the statement of the question) might well not trust it and say that the Sun is contracting, but at such a slow speed that we do not notice it.

Drakkith said:

The observed rate of contraction is unnecessary (and not observable on our timescales anyways)

Drakkith said:

Your question is unclear. If the KE of the particles is much larger than the ionization energy, then it seems obvious that the particles would have to be ionized.

Bandersnatch said:

@Hak you can find a mostly self-contained derivation of the radiative flux equation from the OP e.g. in Dina Prialnik's 'An Introduction to the Theory of Stellar Structure and Evolution'. In the 2nd edition it's in Chapter 3.7 ('Radiative transfer') with a more rigorous derivation provided in Appendix A.
I can also see a shorter treatment in A.R. Choudhuri's 'Astrophysics for Physicists', in Ch. 3.2.3 ('Energy transport inside stars', with references to earlier chapters). I'll venture a guess that you're likely to find the same in virtually any textbook dealing with stellar physics.

Hak said:

A white dwarf, however, is a star that has run out of nuclear fuel; therefore, it slowly cools down. At some point the temperature becomes so low that matter would tend to regroup into non-ionized atoms. But to do that it would have to increase its radius and decrease its density, and this it cannot do because the change in gravitational energy it would take is greater than all the energy it has left.

So, in a sense, the star would get to a situation where it does not have enough energy to cool down again. In other words, the temperature would stop decreasing without the star being in equilibrium with the part of the universe that surrounds it, and that is obviously not possible."

Sounds like a dilemma to me. A question that is very difficult and complex to answer. Even the professor himself thought so.

Drakkith said:

I'm not an expert in this area, but I expect that the tremendous pressures prevent the material from reforming into atoms and molecules. This wouldn't mean that it would remain hot, just that it would cool down into a very different material than that of ordinary matter. The detailed calculations involved in this are well outside my area of expertise though, and are probably not something that can be easily given over an online forum.

Hak said:

Which books

Bandersnatch said:

I don't know all that many, but of the two mentioned the first one is a better choice, as it's narrower in scope. It's also rather clearly written, if at times wordy - good for self-studying. As with any textbook, you'll find a bibliography section at the back, should you find yourself in need of further reading. It should also give you good enough lay of the land, so to speak, to be able to look up specific topics elsewhere.

But let me call @Ken G . He might have better recommendations and/or insights.

Bandersnatch said:

But let me call @Ken G . He might have better recommendations and/or insights.

Hak said:

I would like to point out once again that these arguments regarding gravitational contraction were not created by me, they are not mine. It is now an imaginary discussion,

Bandersnatch said:

But let me call @Ken G . He might have better recommendations and/or insights.

phinds said:

And THAT is the problem that @Vanadium 50 referred to. Arguing with a crackpot is futile in any case and doing it through a third party is just silly, ESPECIALLY when the third party ALSO doesn't understand the physics involved.