Measuring Differential Rotation
There are many ways to measure and calculate differential rotation in stars to see if different latitudes have different angular velocities. The most obvious being tracking spots on the stellar surface.
By doing helioseismological measurements of solar "p-modes" it is possible to deduce the differential rotation. The Sun has very many acoustic modes that oscillate in the interior simultaneously, and the inversion of their frequencies can yield the rotation of the solar interior. This varies with both depth and (especially) latitude.
The broadened shapes of absorption lines in the optical spectrum depend on vrotsin(i), where i is the angle between the line of sight and the rotation axis, permitting the study of the rotational velocity’s line-of-sight component vrot. This is calculated from Fourier transforms of the line shapes, using equation (2) below for vrot at the equator and poles. See also plot 2. Solar differential rotation is also seen in magnetograms, images showing the strength and location of solar magnetic fields.
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