A global galactic dynamo with a corona constrained by relative helicity

We present a model for a global axisymmetric turbulent dynamo operating in a galaxy with a corona which treats the supernovae (SNe) and magneto-rotational instability (MRI) driven turbulence parameters under a common formalism. The nonlinear quenching of the dynamo is alleviated by inclusion of small-scale advective and diffusive magnetic helicity fluxes, which allow the gauge invariant magnetic helicity to be transferred outside the disk and consequently 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 final structure of the global magnetic field and the saturated value of the turbulence parameter $\alpha_m$, even before solving the dynamical equations for evolution of magnetic fields in the disk and the corona, along with $\alpha$-quenching. We then solve these equations simultaneously to study the saturation of large-scale magnetic field, its dependence on the small-scale magnetic helicity fluxes and corresponding evolution of the force-free field in the corona. The quadrupolar large-scale magnetic field in the disk is found to reach equipartition strength within a timescale of 1 Gyr. The large-scale magnetic field in the corona obtained is much weaker in strength compared to the field inside the disk and has only a weak impact on the dynamo operation.