Analytic mean-field α^2-dynamo with a force-free corona

Abstract

Context. Stellar dynamos are affected by boundary conditions imposed by stellar coronae. Under some approximations, it is possible to find analytical solutions. Interior dynamo models often consider a current-free corona without taking into account the constraints imposed by the presence of currents in the corona. <BR /> Aims: We aim to analytically evaluate the effect of coronal currents and of an outer boundary condition on the efficiency of an α<SUP>2</SUP> dynamo. We intend to estimate the change in geometry and dynamo excitation numbers with respect to the current-free case. <BR /> Methods: We analytically solved the turbulent dynamo induction equation for a homogeneous, non-mirror symmetric turbulence in a spherical domain surrounded by a linear force-free corona with the mean magnetic field B satisfying ∇ × B = βB. <BR /> Results: The dynamo number is a decreasing function of β. Moreover, if the current is parallel to the field (β > 0), the dynamo number is smaller than in the force-free case. In contrast, for (β < 0), the dynamo number is greater than in the force-free case. Conclusions: Currents in the corona need to be taken into account because they affect the condition for excitation of a dynamo.