What sets the fusion rate in a main-sequence star?

[Ken G]

A few years back I started a thread to make the point that there is a common misconception about main-sequence stars that their fusion rate sets their luminosity, in the sense that to know what the luminosity of the star will be, you need to know what the fusion rate is. In particular, you would need to know the details of fusion physics that set that rate. I argued that you actually don't need to know many details about fusion, except that it sets in quite suddenly around 10 million Kelvin, to get the luminosity of a main-sequence star fairly accurately. Furthermore, the reason for this is that the luminosity is actually what sets the fusion rate, because fusion is a self-adjusting process that will do whatever it needs to resupply whatever heat the star is losing. Finally, the rate a star loses heat can be known fairly well without knowing much about fusion, beyond the temperature at which it sets in.

Apparently I did not present my arguments well, because that thread was closed. I mention this only because I do not want to appear to be sidestepping the mods, this new thread can be viewed as completely independent and involves a different basic question that can be posed very straightforwardly, and dodges the whole dodgy issue of "which sets which". The question is this:

If you imagine that all the physics of the Sun is the same, but the rate of hydrogen fusion is uniformly doubled in all cases (say by doubling all the fusion cross sections), what does it seem like should happen to the main-sequence luminosity of the Sun?

An exact answer is not needed and would be difficult, let me just ask what people think is the general answer here and why, and let that serve to address the issue in place of claims about whether fusion rates set luminosity or luminosity sets fusion rates.

 

[Drakkith]

I would say that neither luminosity nor fusion rate are the cause of one another. Instead, both seem to depend on the various conditions inside the star.

 

[snorkack]

I believe that luminosity does depend on the details of fusion. Which is why, for example, giants have a very different luminosity than main sequence, and luminosity changes during main sequence with core protium content.

 

[Bandersnatch]

In the hypothetical scenario, increasing fusion rates momentarily increases temperature and radiation pressure, and the star swells up and cools down until it reaches a new equilibrium.
Since continuity of energy must be obeyed, the amount of energy leaving the outer shell of the star must be equal to the amount produced in the hydrogen-fusing shell.
At the new equlibrium the increased fusion rates still produce more energy than the old ones did(otherwise the star would recollapse), so the total luminosity of the star would be higher than it was originally.

You end up with larger, more diffuse stars with less pressure in the core and higher luminosity.

 

[snorkack]

In the hypothetical scenario, increasing fusion rates momentarily increases temperature and radiation pressure, and the star swells up and cools down until it reaches a new equilibrium.
Since continuity of energy must be obeyed, the amount of energy leaving the outer shell of the star must be equal to the amount produced in the hydrogen-fusing shell.
At the new equlibrium the increased fusion rates still produce more energy than the old ones did(otherwise the star would recollapse),

Not sure about that reasoning!

so the total luminosity of the star would be higher than it was originally.

You end up with larger, more diffuse stars with less pressure in the core and higher luminosity.

Look at what actually happens when protium is consumed in Sun.
One consequence is that, for given temperature and density, the fusion rates fall (because a proton is less likely to encounter another proton and more likely to encounter an α, to no effect).
This would cause the core of Sun to cool... except that the cooling would cause contraction and heating.
The end result is that the new balance is achieved where the core is denser and hotter, so much so that the diminishing fraction of protium fuses at an increasing rate, and the luminosity grows!
I´d therefore argue that increasing the protium fusion cross-section might, like adding protium, cause the core to expand, cool and lose luminosity.

 

[D H]

If you imagine that all the physics of the Sun is the same, but the rate of hydrogen fusion is uniformly doubled in all cases (say by doubling all the fusion cross sections), what does it seem like should happen to the main-sequence luminosity of the Sun?

I'm the one who closed your last thread on this subject, and I'm closing this one as well.

What causes the rate of fusion to double? Magic pixie dust suddenly appearing in the star's core that changes the laws of physics?

You are ignoring that the rate at which fusion occurs and the amount of energy produced by fusion is dictated by conditions at the center of the star. It doesn't "uniformly double" for no good reason. What happens at the surface of the star indirectly affects conditions in the core, and what happens in the core indirectly affects what happens at the surface. Luminosity and fusion rate form a feedback relationship.