Stellar rotation is a well-known quantity for tens of thousands of stars. In contrast, differential rotation (DR) is only known for a handful of stars because DR cannot be measured directly. We present rotation periods for more than 24,000 active stars in the Kepler field. Thereof, more than 18,000 stars show a second period, which we attribute to surface differential rotation. Our rotation periods are consistent with previous measurements and the theory of magnetic braking. Our results on DR paint a rather different picture: The temperature dependence of the absolute shear δΩ is split into two groups separated around 6000 K. For the cooler stars δΩ only slightly increases with temperature, whereas stars hotter than 6000 K show large scatter. This is the first time that DR has been measured for such a large number of stars.

A-type stars have both a near-surface layer of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be probed with asteroseismology. Many A-type stars also exhibit large magnetic spots that are often attributed to surviving primordial fields of global scale in the intervening radiative zone. We have explored the potential for core convection in rotating A-type stars to build strong magnetic fields through dynamo action. These 3-D simulations using the ASH code provide guidance on the nature of differential rotation and magnetic fields that may be present in the deep interiors of these stars, thus informing the asteroseismic deductions now becoming feasible. Our models encompass the inner 30% by radius of a two solar mass A-type star, rotating at four times the solar rate and capturing the convective core and a portion of the overlying radiative envelope. Convection in these stars drives a strong retrograde differential rotation and yields a core that is prolate in shape. When dynamo action is admitted, the convection generates strong magnetic fields largely in equipartition with the dynamics. Remarkably, introducing a modest but large-scale external field threading the radiative envelope (which may be of primordial origin) can substantially alter the turbulent dynamics of the convective interior. The resulting convection involves a complex assembly of helical rolls that link distant portions of the core and stretch and advect magnetic field, ultimately yielding magnetic fields of super-equipartition strength.

The differential rotation of the compact elements of the large-scale magnetic fields is studied using Solar Synoptic Charts (1966–1986). It is revealed that compact magnetic elements with the similar polarity of the polar magnetic field of the Sun have a larger rotation rate than the elements with the opposite polarity at all stages in the cycle.

From the comparison of the experimental measuring data of the solar magnetic elements there are received the results: a) The differential rotations of the compact magnetic elements with negative and positive polarities have the similar behavior for the solar 20 and 21 cycles; b) It is established that in the rotation rate of compact magnetic elements there are present some variations at the time of polarity reversal of the Sun.

There is assumed that the physical understanding of the connections of differential rotation of compact magnetic elements and polarity reversal of the Sun depends upon establishing a connection between the temporal variability of spatially resolved solar magnetic elements and polar reversals.

we briefly describe historical development of the concept of solar dynamo mechanism that generates electric current and magnetic field by plasma flows inside the solar convection zone. The dynamo is the driver of the cyclically polarity reversing solar magnetic cycle. The reversal process can easily and visually be understood in terms of magnetic field line stretching and twisting and folding in three-dimensional space by plasma flows of differential rotation and global convection under influence of Coriolis force. This process gives rise to formation of a series of huge magnetic flux tubes that propagate along iso-rotation surfaces inside the convection zone. Each of these flux tubes produces one solar cycle. We discuss general characteristics of any plasma flows that can generate magnetic field and reverse the polarity of the magnetic field in a rotating body in the Universe. We also mention a list of problems which are currently being disputed concerning the solar dynamo mechanism together with observational evidences that are to be constraints as well as verifications of any solar cycle dynamo theories of short and long term behaviors of the Sun, particularly time variations of its magnetic field, plasma flows, and luminosity.