Abstract Using the Chebyshev-tau method, the generation of oscillatory non-axisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and -dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (i) when the angular factor of α-profile is sinnθ cos θ(n = 1,2,4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the non-axisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
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