A Global galactic dynamo with a corona constrained by relative helicity

Abstract

We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona that treats the parameters of turbulence driven by supernovae and by magneto-rotational instability under a common formalism. The nonlinear quenching of the dynamo is alleviated by the inclusion of small-scale advective and diffusive magnetic helicity fl uxes, which allow the gauge-invariant magnetic helicity to be transferred outside the disk and consequently to build up a corona during the course of dynamo action. The time-dependent dynamo equations are expressed in a separable form and solved through an eigenvector expansion constructed using the steady-state solutions of the dynamo equation. The parametric evolution of the dynamo solution allows us to estimate the fi nal structure of the global magnetic fi eld and the saturated value of the turbulence parameter α m , even before solving the dynamical equations for evolution of magnetic fi elds in the disk and the corona, along with α -quenching. We then solve these equations simultaneously to study the saturation of the large-scale magnetic fi eld, its dependence on the small-scale magnetic helicity fl uxes, and the corresponding evolution of the force-free fi eld in the corona. The quadrupolar large-scale magnetic fi eld in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic fi eld in the corona obtained is much weaker than the fi eld inside the disk and has only a weak impact on the dynamo operation.