Analytic mean-field α²-dynamo with a force-free corona

¹ INAF-Osservatorio Astrofisico di Catania, 95125 Catania, Italy
e-mail: alfio.bonanno@oact.inaf.it
² Department of Geology & Geophysics, Yale University, New Haven, CT 06511, USA
³ Nordita, Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
e-mail: fabio@nordita.org

Received: 7 June 2017
Accepted: 24 July 2017

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.

Aims. We aim to analytically evaluate the effect of coronal currents and of an outer boundary condition on the efficiency of an α² dynamo. We intend to estimate the change in geometry and dynamo excitation numbers with respect to the current-free case.

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.

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.