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The following is an excerpt from the Wikipedia article for "Differential Rotation":

Differential rotation is seen when different parts of a rotating object move with different angular velocities (rates of rotation) at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as accretion disks, this leads to shearing. Galaxies and protostars usually show differential rotation; examples in the Solar System include the Sun, Jupiter and Saturn.

The cause of differential rotation

Stars and planets rotate in the first place because conservation of angular momentum turns random drifting of parts of the molecular cloud that they form from into rotating motion as they coalesce. Given this average rotation of the whole body, internal differential rotation is caused by convection in stars which is a movement of mass, due to steep temperature gradients from the core outwards. This mass carries a portion of the star's angular momentum, thus redistributing the angular velocity, possibly even far enough out for the star to lose angular velocity in stellar winds. Differential rotation thus depends on temperature differences in adjacent regions.

Can you please explain the cause of differential rotation described above in a very simple way?

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    $\begingroup$ Are you referring to the differential rotation between the sun's equator and poles, or the differential rotation between the sun's core and envelope? $\endgroup$
    – Daddy Kropotkin
    Aug 2, 2021 at 1:03
  • $\begingroup$ @DaddyKropotkin I am referring to the differential rotation between the sun's equator and poles. $\endgroup$
    – user41291
    Aug 2, 2021 at 8:20
  • $\begingroup$ Duplicate: astronomy.stackexchange.com/questions/40494/… $\endgroup$
    – Nilay Ghosh
    Sep 16, 2021 at 2:29

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The short answer is that the differential rotation is the result of combining convection, viscosity and a global rotation.

A ball of honey

Imagine you were on the ISS and you had a jar of honey (do not actually try this ;). You take out the honey and make a floating ball of honey. Then you gently star to spin it. You would notice that if at the start you gave the ball some amount of differential rotation, in some time the viscosity of the honey smears the rotation and if you wait a bit you will see that the ball is now rotating uniformly, with no differential rotation.

A rotating ball of viscous fluid tends to rotate uniformly, like a rigid body, because if two layers rotate at a different speed, friction tends to slow the faster layer and drag the slower one until they move at the same speed.

A star

A star is different from a ball of honey, because it generates heat in its core, due to nuclear fusion. This heat propagates from the center outwards. In most stars the heat flow is so intense that some part of the plasma starts to boil, just like water in a pot (the scientific term is convection). Hot bubbles of plasma form deep inside the star and rise towards the surface.

If the star is rotating, as the plasma bubble moves radially outwards it is also pushed sideways, just like when you throw a ball while standing on a merry-go-round. (It is called Coriolis effect). The sideways push will be stronger for plasma bubbles on the equatorial plane, because their velocity is orthogonal to the axis of rotation. The effect will be less intense for bubbles that move towards higher latitudes and negligible for bubbles that move from the centre to the poles.

The equatorial bubbles will develop a greater sideways velocity and will drag with them the plasma in the equatorial region. As a consequence, we see that the plasma at the equator of the Sun rotates faster than at higher latitudes.

This explanation is extremely simplifying, and leaves out lots of details. For a rigorous mathematical model of differential rotation in stars see the review in reference.

Reference

Kitchatinov, L. L., “REVIEWS OF TOPICAL PROBLEMS: The differential rotation of stars”, Physics Uspekhi, vol. 48, no. 5, pp. 449–467, 2005. doi:10.1070/PU2005v048n05ABEH002099.

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  • $\begingroup$ Great explanation, thank you! I am studying more and more and i am happy to learn and understand new things. Again, thank you and good luck! $\endgroup$
    – user41291
    Aug 3, 2021 at 9:58
  • $\begingroup$ You are welcome, I learned a lot too by answering your question $\endgroup$
    – Prallax
    Aug 3, 2021 at 10:30
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In a rotating solid body, regions that are adjacent at one point in time will remain adjacent as the body rotates. This means that points further from the rotation centre will travel at greater speeds than those closer in. If the rotating body is not solid, however, regions that are adjacent at one point in time do not necessarily maintain that configuration. This is known as ‘differential rotation’.

Examples of differential rotation are found throughout astronomy. In stars (including the Sun) and the gas giant planets, the equatorial regions rotate faster than regions closer to the poles, meaning that equatorial sunspots and cloud formations will move across the face of the object faster than their polar ones.

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In the disks of spiral galaxies, all of the material orbits at roughly the same speed. However, the outer stars have further to travel in their orbit around the galactic centre than the inner stars. The result is that the outer stars lag behind the stars in the inner reaches of the galaxy.All objects in the disk of a spiral galaxy are moving at roughly the same orbital speed. Since the outer objects have further to travel in their orbits than the inner ones, they lag behind.

Source: https://astronomy.swin.edu.au/cosmos/d/Differential+Rotation

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