Analytic mean-fieldα²-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 coronae without taking into account the constraints imposed by the presence of currents in the corona. Aims. We aim to analytically evaluate the effect of coronal currents and of an outer boundary condition on the efficiency of an α 2 dynamo. We intend to estimate the change in geometry and dinamo excitation numbers with respect to the current-free case. Methods. We analytically solve the turbulent dynamo induction equation for a homogeneous, non-mirror symmetric turbulence, in a spherical domain surrounded by a linear force-free corona with mean magnetic field B satisfying ∇ × B = βB. 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. On the contrary (β < 0) the dynamo number is greater than in the force-free case. Conclusions. The presence of currents in the corona needs to be taken into account because it affects the condition for excitation of a dynamo.

Solar and Galactic Magnetic Halo Structure: Force-Free Dynamos?

“…In an earlier extensive Section 2 we have studied the axially symmetric non-linear force-free magnetic field by itself, because of possible solar corona applications [22,36] or galactic halo applications (e.g., [5]). The solutions in arbitrary geometry are notoriously difficult to find, but Equation (5) gives a simple formulation for the axially symmetric force-free field.…”