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Peter Meadows gave us a great talk yesterday at the BAA meeting in London on this topic and I would recommend people watch the video if they didn’t see it. Peter showed us how he has used sunspots on the surface of the sun to measure how fast the surface layers are rotating at different solar latitudes. It turns out that sun does not rotate like a solid body; in fact it rotates faster at the equator than it does at the poles. A few questions were asked at the end about how this occurs and how deep it goes in the sun and how the model for the differential rotation was arrived at. I have been digging around on the internet and have learnt that the differential rotation is limited to the convection zone inside the sun. Below the convection zone is the radiative zone and, apparently, this region does rotate like a solid body (I think). There has been some recent advances in understanding how this differential rotation in the convective zone arises and I would point people to this article Long-period oscillations control the Sun’s differential rotation. People also asked how the model for differential rotation came about (it is an equation which depends on the Sun’s latitude) and I think this paper in the Monthly Notices of the RAS may explain it (though I haven’t read it thoroughly) Global model of differential rotation in the Sun.. Forgive me Peter if there are better references or I have made errors in my reading – I don’t want to confuse the situation!
I also like the fact that the differential rotation drives the creation of sunspots! If you imagine a line drawn on the surface of the Sun from pole to pole and this marked points on its surface, as the rotation progresses, the points on the equator move faster round the sun than those at the poles – this drags the line into a curve and eventually into a shape that twists back on itself. Now imagine what this does to the magnetic field emanating from the sun – lines of the field get dragged along by the plasma at different rates and this twists up the magnetic field and strengthens it into tight knots and these cause the sunspots that we see. So neat!
Thanks for your comments Duncan and for your additional information and links. If anyone is interested in the workings of the Sun, including the role of the magnetic field, I would recommend a 2019 Springer book ‘The Sun Today’ by Claudio Vita-Finzi. It is very readable without any equations and it appears to be still available on Amazon and Ebay at around £10.
I have been giving some more thought to how the form of the equation that Peter used in his talk to describe solar differential rotation was arrived at. I think Peter used the equation ω = A + B sin²θ + C sin⁴θ where ω is angular velocity of the sun at the observable surface in degrees per day, θ is the solar latitude, A is the angular velocity at the equator and B and C are constants that control how the velocity decreases with increasing latitude (see this reference in wikipedia).
What I think is that the physics tells us that ω is a function of sin²θ, that is w = f(sin²θ). If that is the case then writing x = sin²θ we can expand w = f(x) using a Taylor series about x = 0, namely
f(x) = f(0) + f'(0)x + (f”(0)/2)x² + …
where f'(0) and f”(0) are the first and second derivatives of f with respect to x at x = 0. Replacing x by sin²θ we get
f(θ) = f(0) + f'(0)sin²θ + (f”(0)/2)sin⁴θ + …
Now x = 0 when θ = 0, so f(0) = A, the angular velocity at the equator. Also if x is small, which is true if θ is small then we can neglect higher order terms (those involving powers of x greater than 2) in the expansion. Equating constants B and C with constants f'(0) and (f”(0)/2) we get
w = f(θ) = A + B sin²θ + C sin⁴θ
as Peter quoted. I hope this makes sense.
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