# Increased fusion in the sun's core: How long to reach the surface?November 15, 2013 1:41 PM   Subscribe

If hydrogen fusion in the center of the sun suddenly increased by a factor of 10^3 to 10^10, how long would it take until the energy burst reaches the surface and is radiated away? As I understand it, energy is transfered via convection and radiation within the sun and may take tens of thousand of years until reaching the surface and being radiated away. Would this hold even when the energy flux is much bigger?

I've only found examples for a sudden cessation of fusion, in which case a number of several years is given. Does an energy flux exist which would certainly eradicate humanity as soon as it reaches the surface and is radiated towards the earth, but might take decades to do so?
posted by Triton to Science & Nature (8 answers total) 1 user marked this as a favorite

If something like that happened, the Sun would explode.
posted by Chocolate Pickle at 2:01 PM on November 15, 2013

Probably yes! But how fast?

Small changes would probably be self-corrected and not even be noticed except for the neutrinos. Very big changes would probably result in an instant explosion. But how small is small? How big is very big? Can any physicists help me find better boundaries?
posted by Triton at 2:06 PM on November 15, 2013 [1 favorite]

This is a good question for http://what-if.xkcd.com/.
posted by ubiquity at 2:46 PM on November 15, 2013

I haven't studied this stuff in a *long* time, but the Sun would start undergoing very rapid mass loss if it exceeded the Eddington luminosity, which is 32,000 times its current luminosity. The newly-bright Sun's gravitational binding energy would be radiated on the Kelvin-Helmholtz timescale, which is 1,000 years if it's radiating at the Eddington rate. Basically, it would turn into eta Carinae.
posted by lukemeister at 4:20 PM on November 15, 2013 [2 favorites]

Thanks lukemeister, this is interesting!
Would the mass loss happen immediately?
I'm looking for a scenario where scientists know humanity is doomed because of the higher neutrino flux, but it might take years or decades until the radiation reaches the surface of the sun. Is this possible?
posted by Triton at 6:41 AM on November 16, 2013

Triton,

Yes! The neutrinos will still escape immediately (at the speed of light), but the photons will take longer. I don't know about years or decades specifically, but I think the basic idea works.
posted by lukemeister at 9:11 AM on November 16, 2013

might take years or decades until the radiation reaches the surface of the sun.

Yeah, it doesn't really work that way. I know a lot of times people are told that it takes X years for a photon to go from the center of the sun to the surface, but that's actually a sort of made up scenario that doesn't really make much sense. You can't follow "a single photon" that way, not even conceptually, since there's a continuous process of absorption and emission going on amongst lots of hot atoms, and so this "random walk time" really just conveys that 1) the sun is large 2) the opacity is high and 3) random walks are slow. It's not really indicative of how the sun behaves.

If I suddenly make the center of the sun very hot, the relevant timescale is set by the sound speed. Ignore the photons (let's also ignore supersonic shocks, to make life easier), what matters is that you have a hot ball of gas that was previously in equilibrium with the weight of the rest of the sun on top of it, but now it's hotter and the pressure is greater, so the entire sun is going to adjust to accommodate that, and it's going to do so at the sound speed. This is on the order of hundreds of kilometers per second, so the right timescale is probably about an hour or so. As the core expands it puffs up the envelope, which actually makes the temperature at the surface drop. At this point there's a ton of atomic physics that comes into play: the ionization state of the photosphere sets the surface opacity, which will set the equilibrium structure that the star needs to reorganize itself towards in order to accommodate the increased energy production, and all of this will set the final temperature and luminosity of the star. I know that's not very satisfying or intuitive, but if you look at the evolution of stars as they go through different phases of nuclear burning they exhibit all kinds of strange behaviors in temperature and luminosity, much of which makes no intuitive sense unless you run detailed models.

So if I had to give an answer to the question as presented, I'm going with an hour, but exactly what happens at that hour mark is very uncertain.

Appendix A: I said at the top let's assume no shocks, which requires that the energy deposition is not so great that it destroys the sun entirely. If that were to happen, it would occur in minutes. You can probably get away with a ~10^5 change in energy generation without destroying the star, just judging from other cases where similar mass stars are undergoing different fusion processes, but beyond that I don't think we have any examples to draw on. The problem is that most stars that undergo exotic phases like this are all high mass, so there's not much to draw on for solar-type stars. The best analogy I can think of is the Helium flash. AGB stars also might be an interesting comparison, but again there's just a ton of different physical processes going on that it's hard to extrapolate much from them.

Appendix B: This is a good time to point out that stars have negative heat capacity: in the most simple treatment, if you add energy to a star, it gets cooler. That's the sort of weird effects you're up against when trying to understand how a scenario like this would play out.
posted by kiltedtaco at 10:39 AM on November 16, 2013 [2 favorites]

Wow kiltedtaco, that's impressive!

Thanks for the time frame and the detailed explanation!
posted by Triton at 10:27 AM on November 18, 2013

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