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I don't feel that way myself but some might find it really strange and wierd that it has differential rotation and feel that it's a contradiction. They may say "How is it possible?" I am asking on behalf of others who might have that question what assumptions they are making and how to break them.

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In principle, differential rotation can refer to (at least) two different things:

  1. The sun (or any star) rotates about an axis and so are not perfectly spherical, but rather oblate: flatter at the poles and bulging at the equator, similar to the Earth! I think the OP is not referring to this.

  2. Any star composed of multiple layers (i.e., not very low mass main sequence stars), can experience different rotation rates for each layer, I think this is what the OP is referring to. It is known as "internal differential rotation." Our sun is an example of such a star. But it is complicated, because the amount of internal differential rotation depends on the amount of coupling between the angular momenta of the various layers. This coupling is physically due to chemical mixing across the layers due to turbulent and viscous convective processes, and magnetic fields can play a role.

For simplicity, consider a star with a core and an envelope that was born with some nonzero amount of angular momentum (spin). As the star ages, it can lose some spin due to wind mass loss. By the end of its life, it will lose its envelope (to strong wind mass loss if in isolation or to mass transfer if bounded with a companion). The process of losing its envelope can deplete the core of spin if the coupling between the core and the envelope is strong, i.e., angular momentum will be transported out of the core by the envelope, resulting in a slowly spinning core (which becomes a late stage star, i.e. a Wolf-Rayet star). On the other hand, if the spin coupling between the core and envelope is weak, then the spin of the core is essentially independent of the spin of the envelope (and consequently of the initial spin of the star!). Thus, these two extremes can be thought of as two extremes for differential rotation: strong coupling implies the same spin between the core and envelope, i.e., no differential rotation; whereas weak coupling implies uncorrelated spins of the core and the envelope, i.e., yes differential rotation. The physical mechanisms/processes that cause the spin coupling between stellar layers is complicated and an open problem in stellar evolution theory, however a lot has been done in recent decades in various regimes, for example this and this. For a population synthesis study that parameterizes the effect of this coupling on black-hole binary spins, see this work by Postnov $\it{et~al.}$ (2018), specifically section 4.1 and references therein.

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I think they're not taking into account the Coriolis force in the frame of reference of the part of the outer layer of the sun at each latitude. I can't quite think of a proof that the outer layer of the sun would be predicted to have differential rotation. However, when you realize about the Coriolis force acting on the convection currents, you see that it does not give you a proof that there shouldn't be differential rotation. Maybe the part at one latitude then exerts a force on the part at an adjacent latitude until the rates of the two layers satisfy a certain equation.

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    $\begingroup$ I think that answers should not begin with "I think" followed by "I can't quite think of..." This should be part of your question, not the answer to it. Answer posts need to really strive to be proper answers, not speculation. Why not move this back into the question and wait for an answer with some more certainty? $\endgroup$
    – uhoh
    Dec 19 '20 at 13:48
  • $\begingroup$ @uhoh I think the answer is useful because what it does is resolve the apparent contradiction. $\endgroup$
    – Timothy
    Dec 19 '20 at 19:23
  • $\begingroup$ @Timothy Did you ask the question and then answer it yourself? $\endgroup$ Sep 15 at 14:38
  • $\begingroup$ @Timothy it is always okay to post an answer to your own question in Stack Exchange, as long as it's a good answer. It's just that in this particular case the post as currently written is not yet a stand-alone answer, so "I think" it should still be part of the question. (You can verify this by clicking "Ask a Question" and checking the bottom of the edit box, there's even a check box with an explicit invitation to answer your own question at the time of asking) $\endgroup$
    – uhoh
    Sep 15 at 21:14

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