ar X iv : a st ro - p h / 05 03 09 5 v 1 4 M ar 2 00 5 The α effect and current helicity for fast sheared rotators : some applications to the solar dynamo

The α effect and current helicity for fast sheared rotators: some applications to the solar dynamo. Abstract We explore the α-effect and the small-scale current helicity, hc = h ′ · rot h ′ , for the case of weakly compressible magnetically driven turbulence that is subjected to the differential rotation. No restriction is applied to the amplitude of angular velocity, i.e., the derivations presented are valid for an arbitrary Coriolis number, Ω * = 2Ωτcor, though the differential rotation itself is assumed to be weak. The expressions obtained are used to explore the possible distributions of α effect and hc in convection zones (CZ) of the solar-type stars. Generally, our theory gives α φφ > 0 in the northern hemisphere of the Sun and the opposite case in the southern hemisphere. In most cases the hc has the opposite sign to α φφ. However, we show that in the depth of CZ where the influence of rotation upon turbulence (associated with Ω *) and the radial shear of angular velocity are strong, the distribution of α φφ might be drastically different from a classical cos θ-dependence, where θ is colatitude. It is shown that α φφ has a negative sign at the bottom and below of CZ at mid latitudes. There, the distribution of hc is also different from cos θ, but it does not change its sign with the depth. Further, we briefly consider these quantities in the disk geometry. The application of the developed theory to dynamos in the accretion disk is more restrictive because they usually have a strong differential rotation, ∂ log Ω/∂ log r > 1.