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AFAIK the photons inside a star essentially perform a random walk until they leave. Considering these factors:

  • closer to the core the curvature of the sphere that seperates "closer to the core" from "further from the core" is higher, so initially a step in the random walk will be more likely to increase the distance from the core than later on, where I am assuming the seperating surface locally get flatter and flatter, and such the probability of "random walk gets closer to core" and "random walk gets closer to star surface" will get increasingly equal.

  • density closer to the core is higher, so a step in the random walk towards the core will statistically be a little shorter until the photon gets reabsorbed than if the step is towards the surface.

Taking these two together I would guess that there is, or could be, a shell from r1 to 2*r1 (probably somewhere near the core) where photons from the core stay longer during their random walk than in the radius r1. Since the volume grows cubically with distance, it's probably not hotter in that volume than inside r1.

Is r1 > 0 and if yes, what is it? And does it have any physical implications?

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There is no random walk. Such a photon immediately is aborbed by the 15 million degree plasma. The resulting heat diffuses out over a long period. Finally it appears in the photosphere and where thermal radiation manages to escape and keep us warm.

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  • $\begingroup$ Ok, there are two gradients that I mentioned that influence this diffusion (the diffusion being exactly the process I asked about, I guess?), and the influence of which I am interested in. Or are you saying it makes no sense to talk about the random walk of a photon because the diffusion process doesn't mainly work through radiation? $\endgroup$
    – kutschkem
    Commented Nov 19, 2020 at 14:39
  • $\begingroup$ @kurschkem Indeed, there are no photons until you reach the photosphere, except for the very short lived ones from fusion. $\endgroup$
    – my2cts
    Commented Nov 19, 2020 at 14:53
  • $\begingroup$ What’s the main mechanism is energy transport in the plasma to the further out layers in the star? I guess what you are staying is that the mean free path of photons in the plasma is much much smaller than the mean free path of the mechanism by which energy is transport beyond the plasma layer? Such that photons are not important to consider in these regions. $\endgroup$
    – boyfarrell
    Commented Nov 21, 2020 at 17:21

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