I Nuclear reactions in the Sun and other topics on stars

[Hak]

TL;DR

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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:

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.

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]

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.

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

 

[Hak]

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

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]

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...

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

 

[Hak]

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

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]

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.

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

 

[Hak]

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

All right. I hope to get all the answers to my questions... Thanks anyway.

 

[Vanadium 50]

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?

 

[Hak]

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

Sorry, I did not understand this statement of yours.

 

[Hak]

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

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. We want to show that processes take place inside the star that release energy to repel gravitational attraction, but the argument 'since it does not contract as much, then there is either a neutron star or there are nuclear reactions' is not very logical, also bearing in mind that 'your friend' does not know what a neutron star is. It was just to understand how this problem could be explained to someone totally inexperienced. 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? Thank you very much.

 

[Ibix]

Gravitational potential energy could become light energy; i

You are missing @Vanadium 50's point. We detect neutrinos coming from the Sun. Neutrinos are byproducts of fusion reactions and the number we see is consistent with the fusion rate needed to generate the power the Sun emits. If you deny the Sun is fusion powered you need to explain where the neutrinos are coming from.

 

[renormalize]

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.

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?

 

[Frabjous]

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.

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]

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?

I don't think it can be explained by gravitational contraction. This is probably the most fruitful way to refute the friend's thesis. However, I don't want you to think that I am trying hard to justify the gravitational argument: I was just looking for a way to refute the (obviously wrong) gravitational thesis. The one you, @Ibix and @Vanadium 50 put forward could be a very good argument. Thank you.

 

[Frabjous]

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?

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

 

[Hak]

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

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.

 

[Vanadium 50]

Sorry, I did not understand this statement of yours.

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.

 

[Hak]

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

I do not understand where the first equation I reported comes from. The professor said it is particularly difficult to justify it, but I don't think it is impossible: I would like some help from you, who are much more experienced than me and certainly know a justification or derivation. Thank you.

 

[Frabjous]

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.

Sigh. What does your textbook say?

 

[Hak]

Sigh. What does your textbook say?

Nothing, because I do not have a textbook on these topics, nor do I know of one: do you have any advice on a particularly detailed and efficient book on these types of discussions? The existence of various proofs in this regard was pointed out by this professor, but the discussion dates back a few years, so I could not find out from him what he meant. I was hoping you would clarify and present me with various proofs why the argument of gravitational contraction is wrong. One has already been presented and seems very good to me, but I think it is the most solid one as well as the one I already knew (although 'know' is a big word...).

 

[Hak]

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.

I don't understand why post #10 highlights a lack of understanding of where neutrinos come from. I had only laid out a possible refutation or counterargument from someone inexperienced in the subject who supports the gravitational argument (not even with too much conviction, given that he is inexperienced). 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, but at the time prepared in advance, specifically, by a professor, to try to highlight all the gaps in the gravitational argument and, instead, undermine (leading to convince him of its inaccuracy) the interlocutor's thesis "opponent". You are right, arguing with a "crackpot" is harmful, but this is not the case. This is just a fictitious discussion. Let's put it this way: I would just like to try to know all the evidence supporting the "nuclear reactions inside the Sun" argument that can incontrovertibly disprove the "gravitational contraction" argument. Thanks for your time.

 

[Hak]

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

This professor (not mine, he only gave one lesson) did not carry out any derivation of that formula. Now that I think about it, maybe he talked about "radiative transfer equation" (or something like that), but he didn't prove it. He only said that it is very difficult to physically justify or derive it. I would like to take it to the next level and figure out how to do it. Furthermore, the question about the white dwarf posed at the end by the professor and reported by me seems very, very difficult: indeed, it seems irreconcilable. How would you solve it? Thank you.

 

[Bandersnatch]

@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.

 

[Drakkith]

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?

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.

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.

The observed rate of contraction is unnecessary (and not observable on our timescales anyways). We can figure out how much energy is available through gravitational contraction and then show that this is not nearly enough to keep the Sun shining for its determined lifespan.

 

[Vanadium 50]

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

Actually, I think it's negative: stars get bigger as they evolve on the main sequence. The effect for the sun is about 2% per billion years.

 

[Hak]

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.

Most probably this is obvious to you, who will have a lot of experience behind you, but not to someone inexperienced in the subject. I recall that this was a preliminary question put forward so that those who wanted to answer that dilemma above would verify the veracity and reasonableness of the premises (and not, instead, that the professor had only told lies about them). With some estimates (which I, at the moment, am unable to make) one might have been able to prove what you describe as 'obvious'.
The real question for me that is irresolvable, and very difficult to answer, is the whole issue put forward by the professor.

"The fact that matter is ionized allows ions and electrons to be much closer together than they are in atoms (Bohr radius
), 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."

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

Thank you so much.

 

[Hak]

@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.

Thank you so much.
It is probably found in all books on stellar physics, but I do not know of any. Which books on stellar physics do you find most detailed, complete and efficient in this regard? The two just mentioned or also others? Thank you very much.

 

[Drakkith]

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.

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]

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.

I understand. Do you know of any sources you could direct me to for detailed calculations, even if you are not an expert in the area (any books that deal with these topics in general, so I can see if this particular topic is covered)? Do you know any experts (or, at any rate, those with more knowledge on the subject) in this area within this forum? In any case, is there anyone who has read this question and has any idea how to go about it with detailed calculations and everything with appropriate sources? Thank you.

 

[Bandersnatch]

Which books

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.