I agree. I read the 5000 years time a few times and I don't like it.

When you have a transparent medium like water or glass, the photon that enters and the photon that exit share a lot of properties, in particular energy/color/frequency. Perhaps they have a shift in the phase or a different polarization (like in water with sugar or if you want to be fancy a quarter wave plate). You can still split a beam before in enter and make interference experiments after half of it passed though water or glass, and other weird experiments, so I think it's fair to call them "the same photon".

But in the Sun, the original photons in the center of the Sun have a few very specific values of energy/color/frequency, that are totally lost. (But the neutrinos have so few interactions that they don't lose this information, and it's possible to do neutrino spectroscopy!)

Also, the photons emitted by the "surface" of the Sun have a wide spectrum of energy/color/frequency that is very close to black body radiation at something like 5000K-6000K.

So in my opinion it's better to think that the original photon in the center is absorbed shortly after it's emitted, and transformed into heat. The heat takes 5000 years to get to the surface. And then the hot surface emits a few new photons unrelated to the original one.

I'm not sure what is the main transmission method inside the Sun: conduction, convection or radiation.

belated edit: My comment about “whatever, the temperature is high” is silly. The mean photon energy is about 2.7kT, which scales in direct proportion the interest bits of the Maxwell-Boltzmann and Bose-Einstein distributions (see [0] and [1]). At 2.7kT, the curves are pretty close, but you don’t have to go down that far to get a big difference. So tagging all the light would cause a substantial change in the sun’s color.

[0] https://scholarship.haverford.edu/cgi/viewcontent.cgi?articl... Eq. 16 [1] Handy plot at https://commons.wikimedia.org/wiki/File:Quantum_and_classica...

The canonical Q/A pair "Why does the Sun shine?"/"Fusion in its core" perhaps contributes confusion here? Where the question is silently swapped out for "Why is the Sun still shining after 4+ Gyr?". You're primed for a close connection between core and surface photons. Asking "Why is there fog over the uncovered corner of the pool?", one seems unlikely to appreciate "the fog comes from a small aquarium heater somewhere on the bottom!" (IIRC the magnitudes). "The Sun is hot, and hot things glow" creates less of that association between core and light.

> You could calculate how long it would take to notice anything if the core suddenly stopped fusing.

FW(little)IW (very not my field, just AI, quick&sloppy), for a Sun magically switched to contraction-dominated heating, I'm sloping order 10^6-7 yr for a 1% increase in surface temp, with core contraction dynamics being just one uncertainty.