Differential rotation

Galaxies and protostars usually show differential rotation; examples in the Solar System include the Sun, Jupiter and Saturn.

In 1630, Christoph Scheiner reported that the Sun had different rotational periods at the poles and at the equator, in good agreement with modern values.

It may be possible to measure the differential of stars that regularly emit flares of radio emission.

Using 7 years of observations of the M9 ultracool dwarf TVLM 513-46546, astronomers were able to measure subtle changes in the arrival times of the radio waves.

These measurements demonstrate that the radio waves can arrive 1–2 seconds sooner or later in a systematic fashion over a number of years.

The researchers concluded that this effect was best explained by active regions emerging and disappearing at different latitudes, such as occurs during the solar sunspot cycle.

The interface between these two regions is where angular rotation gradients are strongest and thus where dynamo processes are expected to be most efficient.

is the difference in angular velocity between pole and equator, called the strength of the rotational shear.

On the Sun, the study of oscillations revealed that rotation is roughly constant within the whole radiative interior and variable with radius and latitude within the convective envelope.

The highly turbulent nature of solar convection and anisotropies induced by rotation complicate the dynamics of modeling.

Molecular dissipation scales on the Sun are at least six orders of magnitude smaller than the depth of the convective envelope.

A direct numerical simulation of solar convection would have to resolve this entire range of scales in each of the three dimensions.

Consequently, all solar differential rotation models must involve some approximations regarding momentum and heat transport by turbulent motions that are not explicitly computed.