After a time tQ, there remains only an axisymmetric poloidal field in the differentially rotating star. The magnetic coupling by this poloidal field keeps a constant rotation Q on the magnetic surface (the magnetic coupling is achieved by the phase t mixing of different Alfven waves, which damps out the differential motions on a magnetic surface, thus imposing Q = const).

On the contrary, if the initial field B(0) is larger than B1 (13.59), the rotational smoothing does not happen and the field remains non-axisymmetric. The magnetic torque is able to suppress the differential rotation, leading to a state of uniform rotation. This is achieved by Alfven waves traveling on the non-axisymmetric magnetic surfaces and by phase mixing. The differential motions on these surfaces are damped out and as they are non-axisymmetric, the only solution is a state of uniform rotation.

In conclusion, there are schematically two possibilities for the evolution of the field in rotating stars [545]:

- For initial fields smaller than B1: the star tends toward a state of differential rotation with an axisymmetric poloidal field, Q being constant on magnetic surfaces.

- For initial fields larger than B1: the star tends toward solid body rotation with a non-axisymmetric field.

These are the main evolutionary scenarios for radiative stellar regions and they are confirmed by many numerical models [431, 432]. The further evolution of the field and rotation may also be influenced by magnetic instabilities.

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