The sun is completely ionized, though, so there exist only electrons and nuclei. Ignore the electrons, because they're small (they don't count and don't collide with anything), and give it another shot.

Here's the complete story. A star contracts and heats until its core reaches something in the neighborhood of 10 million Kelvin, at which point nuclear burning sets in and the star reaches a long-lasting equilibrium state. At this point, we don't know the exact core temperature, but we do know it roughly because that's the temperature where you start to get a lot of nuclear burning. According to the force balance in the star, at that temperature it must have a certain radius to have pressure balance gravity. If you know the temperature and the radius, you know the radiative energy content. To go from there to luminosity, you only need to know the time photons take to escape on average from the star. None of that requires any detailed understanding of the nuclear burning rate, yet we have a good estimate of the luminosity. Now we use that luminosity to calculate what the core temperature would need to be to supply that luminosity, and iterate any smal errors we encounter. It converges very quickly. However, if you were to try it the other way, and use your rough core temperature estimate to get the luminosity, you'd be way off and you could never get the right answer to converge, because you've inverted the logic that the star itself, in some sense, is using.

To see that the star itself is using the logic I claim, imagine that the physics of fusion suddenly changes, and you need a 10% higher temperature to give the same luminosity you had before. Would the star's luminosity just drop because the new fusion rate is lower, or would the core temperature just jump up the necessary 10% to re-establish the old luminosity? It would be kind of a combination of the two, but the extreme temperature sensitivity of fusion would guarantee that the result would me more like the latter case. So that's what I mean by luminosity causing the core temperature. And I do mean luminosity, not flux density.
The temperature profile must be consistent with both the luminosity and the fusion rate, that's certainly true. The issue is, which needs to know about the other? Luminosity does not need to know anything about nuclear fusion, and if fusion was turned off in the Sun tomorrow, the luminosity wouldn't really change, the Sun would just start evolving faster. But the fusion rate does need to know what the luminosity is, and if you increased the opacity so that light had a harder time escaping, both the luminosity and the nuclear burning rate would go down as they readjust to the new opacity.

This seems overstated, or over-interpreted . The luminosity of a 100w light bulb has no causal effect on the amperage through the filament, nor does my bathroom scale cause me to be a certain mass. However, they both are great indicators of what is really there.

I believe you are thinking in a math sense? Since we can't directly measure core energy production - maybe neutrino meters will be effective someday - but we can measure luminosity, then luminosity becomes the main variable to help solve for core activity, right?


I would assume the latter would be the case. You have a given - luminosity. If the equation of state is altered and the luminosity is known, the core's energy production rate, from the equation, would jump up the 10% (not necessarily temperature).

Why would luminosity change? Luminosity doesn't care what equation we have wrong, so it won't adjust. It simply radiates all the energy that is produced, if in a steady state.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

And that is exactly why a star does not work like a 100w light bulb! I'm not just making up analogies, I'm describing the way stars work when you analyze the equations that govern them. In a light bulb, the energy generation controls the luminosity, you look at the first to calculate the second, but in a star the luminosity controls the energy generation, for the reasons I've explained. A star is a self-regulating system, a light bulb is not. The difference there is what people's intuition always overlooks.

No, it has nothing to do with what we can measure. If we lived in the cores of stars and only saw the fusion, all my conclusions would still be the same. We'd ask, "why is the fusion we are observing going on at the rate it is?", and the answer would be, "because we are surrounded by a star that is shining out light at a given rate that is determined by the gross attributes of the star (not the physics of nuclear fusion)."

Yes, that's exactly it. Can you see how different that is from a light bulb?
Ah, but that last little "if in a steady state" speaks volumes! The issue is, what is an allowable steady state for the star? Not just anything! It must carry the right luminosity for the gross attributes of the star. Nuclear fusion is more flexible, it is happy to produce whatever is necessary, and is robustly stable at doing so.

I think I'm seeing your point now. Because the object is a star and subject to its own attributes, such as mass and opacity, the luminosity is the best variable to measure - and easiest, I suppose - in order to define the star. This is also true in regards to the core's paramaters as the luminosity reveals what it must be doing since the core is subject to the stars mass and size (assuming the atomic ratios are known and understood).

If I were to borrow your wand and suck-out all the energy from the outer layers of the star, it would eventually restore itself to its previous luminosity since its mass and composition are the same. We don't know the mass of a lone star from any direct measurement, but the luminosity will reveal it. This begs the question of whether or not it is the mass of the star you are indirectly addressing. Only the luminosity reveals what is there, I suppose.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

I rather think of the mass as an independently determinable variable, in fact it is the truly crucial attribute. You can imagine a binary system, and infer the mass, but measurement is not really the issue here-- the star has some mass whether we know it or not. The mass will ultimately determine everything, radius, luminosity, and core temperature, but my point is that first the mass determines the radius, subject to the need to get the core to something like 10 million K. Then the mass and radius determine the luminosity (since we know what stars are made of), and finally, the luminosity sets the self-consistent core temperature. Following this logic, you can converge to a solution by iteration. None of this has anything to do with what we can measure, this is the logic of the equations themselves, taken from the point of view of how you would need to make fine tuned adjustments to get the structure to converge to a steady state (i.e., what the star actually does). The crucial ingredient is the extreme temperature sensitivity of fusion rate, but note this does not make the core temperature determine the luminosity-- quite the opposite.

[This reminds me of solving heat transfer problems. I only remember how simple and innocent the equations were, but was then surprised at how much squeeze (including iterations) it took to get the juice. ]

I still think I'm getting closer to understanding what you are saying. The star's opacity creates a feeback system that helps regulate the core's activity. This is not true in my lightbulb analogy which simply allows, essentially, all the energy from the filament to be radiated from the bulb. The mass of the star, radius, and the insulation effect of the outer zones will dictate what is happening within the core. The core will simply respond to these parameters.

Is this closer?

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

That's basically it, in a nutshell. The other key point is that it is the extreme sensitivity of the fusion rate to the temperature that makes this true, even though that fact is often used to try and argue the opposite perspective. That's the interesting irony in all this.

Yes it is. [I knew this thread would be interesting.]

Once something causes the temperature to rise a little, a lot of energy is suddenly produced causing the fusion region to expand and reduce its rate of fusion. Is this another explanation for it?

If so, what happens when something dramatic does happen to a star? For instance, when a 10 Jupiter mass planet roars inward through the outer atmospheres of a star, will a shock wave or something cause the core to rev-up? I'm mindful of those few flashing stars known (e.g. V838 Mon). One idea has the planet's deuterium fusing and creating the flash.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Yes, exactly, fusion is so temperature sensitive it makes it extremely stabilizing for a gas pressure supported star, so it is both a very good thermostat and a very good way to help the star find its steady equilibrium.
Possibly, though the influence might not really make it down to the core. Stars respond on various timescales when you bang on them, but they return to their equilibrium.
Yeah, there are some instabilities present in some stars, typically involving how the ionization fraction is also sensitive to temperature.

Ok, I think I got it.

The banging should be a nightmare in modeling.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Thanks for staying with it, I'm sure it made it helpful as well for anyone lurking.
One example of "banging" is the tidal influences of an elliptical companion. Modelers like that sort of thing-- puts their computer codes through the paces. I prefer the simpler version.

Remember, I'm not changing the fusion of this new bizarre species at all, I'm just changing the mean molecular weight. There's no need here to speculate about what the new particle actually could be, it doesn't exist, it's just hypothetical for the purpose of understanding what mean molecular weight actually does in a star (it's widely misunderstood).

And here is a totally off the wall suggestion
on something I have wondered about. The
sensitivity of the fusion rate to any energy
input. Suppose the neutrino bursts from
Supernovae dumps an amount of extra energy in
the core to affect the rate temporarily? Yes
the very very very faint sweep of these
particles through the star. Its the only
weather in space really. I am thinking of
two nearby supernova 1000 years ago and the
Maunder Minimum a few hundred years later!
Worth trying out on the models perhaps.

This is an excellent test case for the kind of thinking I'm talking about. When you understand this thread, you will understand why small externally imposed heating of the core of a main sequence star will have zilch impact on the star's luminosity.

Not even a teeny weeny blip? Ah well..I will
wait for a newer model that might tell me I
have something

Something to consider.

As the gas cloud is condensing due to gravity, pressure is built up in the center, as gravity and pressure become stronger and stronger, just before ignition (fusion) takes place...

At this point, it would seem that the internal pressure, heat, fusion would be the 'cause' of the stars luminosity...but Ken G could have a different and more correct view here.

But, then the question would become...once ignited, does the luminosity then take over as the controling factor?

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!