Understanding the Luminosity of Radiative Stars

[Fantasist]

It is extremely surprising that it [the luminosity] depends only on the mass, in the sense that it is surprising it does not depend on either R or the fusion physics.

OK, assume you have a randomly varying radiation source in the center. What would the luminosity look like then?

 

[Fantasist]

Any ideal gas sphere with no inner heat source, no matter how small its mass, would keep contracting at Kelvin-Helmholz timescale to arbitrarily small size and arbitrarily high internal temperature.

Only if it is losing energy i.e. if it is luminous (and then it is strictly speaking not an ideal gas anymore).

 

[Ken G]

OK, assume you have a randomly varying radiation source in the center. What would the luminosity look like then?

If you had different physics than an actual star, you could get a different luminosity than actual stars have. But the way fusion really works is, it self-regulates to replace whatever heat is lost by the mechanism I describe. This is why fusion is stable-- if it didn't do this, our Sun would be a very large H-bomb.

 

[Fantasist]

If you had different physics than an actual star, you could get a different luminosity than actual stars have. But the way fusion really works is, it self-regulates to replace whatever heat is lost by the mechanism I describe. This is why fusion is stable-- if it didn't do this, our Sun would be a very large H-bomb.

Your comparison of fusion with a thermostat appears to be paradoxical to me: a thermostat decreases the energy production when the temperature increases, but fusion, on the contrary, increases it, so it is potentially destabilizing. The star is only stabilized by the fact that it expands when it is heated, and in the process cools again due to the work done against its own gravitational field.

Irrespective of the stability issue, the bottom line is that only (and only) radiation is lost from the star which has been produced by some kind of radiative process in the first place, whatever the structure and physics of the star may be (and whatever mass-luminosity relationship you may derive from this).

 

[Ken G]

Your comparison of fusion with a thermostat appears to be paradoxical to me: a thermostat decreases the energy production when the temperature increases, but fusion, on the contrary, increases it, so it is potentially destabilizing. The star is only stabilized by the fact that it expands when it is heated, and in the process cools again due to the work done against its own gravitational field.

Yes, but you have to include the entire situation. Fusion, in an environment that expands when it gets hot, acts like a stable thermostat. That's all that has to be true for the situation I described to occur.

Irrespective of the stability issue, the bottom line is that only (and only) radiation is lost from the star which has been produced by some kind of radiative process in the first place, whatever the structure and physics of the star may be (and whatever mass-luminosity relationship you may derive from this).

Yes, radiation is created by processes that create radiation, that is true. But we know that, what I'm saying is something very few people realize: the physics of fusion has little effect on the luminosity of a star that transports energy radiatively and obeys ideal-gas physics. Hopefully, more people know this now.

 

[Drakkith]

Your comparison of fusion with a thermostat appears to be paradoxical to me: a thermostat decreases the energy production when the temperature increases, but fusion, on the contrary, increases it, so it is potentially destabilizing. The star is only stabilized by the fact that it expands when it is heated, and in the process cools again due to the work done against its own gravitational field.

It's always best not to take analogies too far. Both a thermostat and the physics of a star result in the same effect: the regulation of temperature.