<p>In principle, differential rotation can refer to (at least) two different things:</p>
<ol>
<li><p>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.</p>
</li>
<li><p>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 &quot;<a href="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.84.25" rel="nofollow noreferrer">internal differential rotation</a>.&quot; 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.</p>
</li>
</ol>
<p>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 <a href="https://ui.adsabs.harvard.edu/abs/1998A&amp;A...334.1000M/abstract" rel="nofollow noreferrer">an open problem</a> in stellar evolution theory, however a lot has been done in recent decades in various regimes, for example <a href="https://ui.adsabs.harvard.edu/abs/2019ApJ...887..203T/abstract" rel="nofollow noreferrer">this</a> and <a href="https://arxiv.org/abs/1301.2487" rel="nofollow noreferrer">this</a>. For a population synthesis study that parameterizes the effect of this coupling on black-hole binary spins, see this work by <a href="https://arxiv.org/abs/1706.00369" rel="nofollow noreferrer">Postnov <span class="math-container">$\it{et~al.}$</span> (2018)</a>, specifically section 4.1 and references therein.</p>

CC BY-SA 4.0
2024-01-25T07:16:54.010Z
The outer layer of the Sun does not have differential rotation in the sense that you discuss. Convective zones tend to rotate as solid bodies. The Sun's outer layers have differential rotation with latitude.
ProfRob
CC BY-SA 4.0
2024-01-30T13:26:31.460Z
indeed, but the Sun isn't fully convective?
Daddy Kropotkin
CC BY-SA 4.0
2021-09-15T13:42:50.413Z
2021-09-16T01:12:04.067Z
2021-09-16T01:12:04.067Z
Daddy Kropotkin
<p>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.</p>

CC BY-SA 4.0
2020-12-19T13:48:01.410Z
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?
uhoh
CC BY-SA 4.0
2020-12-19T19:23:07.453Z
@uhoh I think the answer is useful because what it does is resolve the apparent contradiction.
Timothy
CC BY-SA 4.0
2021-09-15T14:38:48.877Z
@Timothy Did you ask the question and then answer it yourself?
Justin T
CC BY-SA 4.0
2021-09-15T21:14:06.107Z
@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)
uhoh
CC BY-SA 4.0
2020-12-19T04:15:49.187Z
2020-12-19T04:15:49.187Z
Timothy
<p>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 &quot;How is it possible?&quot; I am asking on behalf of others who might have that question what assumptions they are making and how to break them.</p>

CC BY-SA 4.0
2020-12-20T10:15:45.043Z
At least to those unaware of it or surprised by it the https://en.m.wikipedia.org/wiki/Differential_rotation page should suffice.
Alchimista
CC BY-SA 4.0
2024-01-25T07:12:58.190Z
Does this answer your question? [What is the exact reason for the Sun's differential rotation to occur?](https://astronomy.stackexchange.com/questions/45082/what-is-the-exact-reason-for-the-suns-differential-rotation-to-occur)
ProfRob
<the-sun>
Why does the outer layer of the sun have differential rotation?
Timothy
# Why does the outer layer of the sun have differential rotation?

(Asked by: username_0 on 2020-12-19)

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.

**Tags:** the-sun
> **Comments:**
> **username_1**: At least to those unaware of it or surprised by it the https://en.m.wikipedia.org/wiki/Differential_rotation page should suffice.  
> **username_2**: Does this answer your question? [What is the exact reason for the Sun's differential rotation to occur?](https://astronomy.stackexchange.com/questions/45082/what-is-the-exact-reason-for-the-suns-differential-rotation-to-occur)  

---

## 2 answers

### Answer by username_3 on 2021-09-15. Score: 3

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](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.84.25)." 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](https://ui.adsabs.harvard.edu/abs/1998A&A...334.1000M/abstract) in stellar evolution theory, however a lot has been done in recent decades in various regimes, for example [this](https://ui.adsabs.harvard.edu/abs/2019ApJ...887..203T/abstract) and [this](https://arxiv.org/abs/1301.2487). 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)](https://arxiv.org/abs/1706.00369), specifically section 4.1 and references therein.

> **Comments:**
> **username_2**: The outer layer of the Sun does not have differential rotation in the sense that you discuss. Convective zones tend to rotate as solid bodies. The Sun's outer layers have differential rotation with latitude.  
> **username_3**: indeed, but the Sun isn't fully convective?  

---

### Answer by username_0 on 2020-12-19. Score: 1

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.

> **Comments:**
> **username_4**: 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?  
> **username_0**: @uhoh I think the answer is useful because what it does is resolve the apparent contradiction.  
> **username_5**: @Timothy Did you ask the question and then answer it yourself?  
> **username_4**: @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)  

---

