Linear astrophysical dynamos in rotating spheres Differential rotation, anisotropic turbulent magnetic diffusivity, and solar-stellar cycle magnetic parity

Differential rotation dependence of the selection mechanism for magnetic parity of solar and stellar cycles is studied by assuming various differential rotation profiles in the dynamo equation. The parity selection depends on propagation direction of oscillating magnetic fields in the form of dynamo waves which propagate along isorotation surfaces. When there is any radial gradient in the differential rotation, dynamo waves propagate either equatorward or poleward. In the former case, field systems of the two hemispheres approach each other and collide at the equator. Then, odd parity is selected. In the latter case, field systems of the two hemispheres recede from each other and do not collide at the equator, and even parity is selected. Thus the equatorial migration of wings of the butterfly diagram of the solar cycle and its odd parity are intrinsically related. In the case of purely latitudinal differential rotation, dynamo waves propagate purely radially and growth rates of odd and even modes are nearly the same even when dynamo strength is weak when the parity selection mechanism should work most efficiently. In this case, anisotropy of turbulent diffusivity is a decisive factor to separate odd and even modes. Unlike in the case of radial-gradient-dominated differential rotation in which any difference between diffusivities for poloidal and toroidal fields enhances the parity selection without changing the parity, the parity selection in the case of latitudinal-gradient-dominated differential rotation depends on the difference of diffusivities for poloidal and toroidal fields. When diffusivity for poloidal fields is larger than that for toroidal fields, odd parity is selected; and when diffusivity for toroidal fields is larger, even parity is selected. This suggests that diffusivity for poloidal fields is larger than that for toroidal fields in the solar convection zone where magnetic parity is odd and where radial gradient influence on the parity selection seems to play a minor role. Diffusivity that is smaller in the radial direction than in the latitudinal direction enhances the parity selection, whether radial or latitudinal gradient dominates the differential rotation.