Helicity and alpha effect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth ra
tes but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the alpha effect by the most rapidly growing mode has the same sign as the current helicity of the background field. The alpha effect is found as too small to drive an alpha^{2} dynamo but the excitation conditions for an alphaOmega dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own alpha effect by the magnetic instability then problems with its sign do not arise. For all cases, however, the alpha effect shows an extremely strong concentration to the poles so that a possible alphaOmega dynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in stellar radiation zones on the basis of the current-driven instability of toroidal fields.
In this work the latitude dependent stellar spot rotation is investigated based on dynamo models. The maps of the magnetic pressure at the surface from the dynamo calculations are treated similarly to the temperature maps obtained using Doppler imagi
ng techniques. A series of snapshots from the dynamo models are cross-correlated to obtain the shift of the magnetic patterns at each latitude and time point. The surface differential rotation patterns obtained from the snapshots of the dynamo calculations show in all studied cases variability over the activity cycle. In the models using only the large scale dynamo field the measured rotation patterns are only at times similar to the input rotation law. This is due to the spot motion being mainly determined by the geometric properties of the large scale dynamo field. In the models with additional small scale magnetic field the surface differential rotation measured from the model follows well the input rotation law. The results imply that the stellar spots caused by the large scale dynamo field are not necessarily tracing the stellar differential rotation, whereas the spots formed from small scale fields trace well the surface flow patterns. It can be questioned whether the large spots observed in active stars could be caused by small scale fields. Therefore, it is not clear that the true stellar surface rotation can be recovered using measurements of large starspots, which are currently the only ones that can be observed.
To find out whether toroidal field can stably exist in galaxies the current-driven instability of toroidal magnetic fields is considered under the influence of an axial magnetic field component and under the influence of both rigid and differential r
otation. The MHD equations are solved in a simplified model with cylindric geometry. We assume the axial field as uniform and the fluid as incompressible. The stability of a toroidal magnetic field is strongly influenced by uniform axial magnetic fields. If both field components are of the same order of magnitude then the instability is slightly supported and modes with m>1 dominate. If the axial field even dominates the most unstable modes have again m>1 but the field is strongly stabilized. All modes are suppressed by a fast rigid rotation where the m=1 mode maximally resists. Just this mode becomes best re-animated for Omega > Omega^A (Omega^A the Alfven frequency) if the rotation has a negative shear. -- Strong indication has been found for a stabilization of the nonaxisymmetric modes for fluids with small magnetic Prandtl number if they are unstable for Pm=1. For rotating fluids the higher modes with m>1 do not play an important role in the linear theory. In the light of our results galactic fields should be marginally unstable against perturbations with m<= 1. The corresponding growth rates are of the order of the rotation period of the inner part of the galaxy.
Differential rotation plays a crucial role in the alpha-omega dynamo, and thus also in creation of magnetic fields in stars with convective outer envelopes. Still, measuring the radial differential rotation on stars is impossible with the current tec
hniques, and even the measurement of surface differential rotation is difficult. In this work we investigate the surface differential rotation obtained from dynamo models using similar techniques as are used on observations, and compare the results with the known radial differential rotation used when creating the Dynamo model.
We investigate in isothermal MHD simulations the instability of toroidal magnetic fields resulting by the action of z-dependent differential rotation on a given axial field B^0 in a cylindrical enclosure where in particular the helicity of the result
ing nonaxisymmetric flow is of interest. The idea is probed that helicity H is related to the external field and the differential rotation as H ~ B^0_i B^0_j Omega_i,j. The observed instability leads to a nonaxisymmetric solution with dominating mode m=1. With the onset of instability both kinematic and current helicity are produced which fulfill the suggested relation. Obviously, differential rotation dOmega/dz only needs an external axial field B^0_z to produce remarkable amounts of the helicities. Any regular time-dependency of the helicity could not be found. The resulting axial alpha-effect is mainly due to the current helicity, the characteristic time scale between both the values is of order of the rotation time. If the axial field is switched off then the helicity and the alpha-effect disappear.
