Non-current-free coronal closure of subphotospheric MHD models

We propose a method that allows the matching of two classes of models that have been well developed so far, but largely independently from each other: (1) convection zone (CZ) models, which generally either end up below the photosphere or are matched with an external potential field, and (2) coronal models of eruptive processes and heating, which usually consider the evolution of current-carrying magnetic fields driven by given photospheric changes. In our approach, the thin turbulent photospheric layer between the two large regions is modeled as a resistive layer across which the physical quantities suffer stiff variations. We show that this layer enables the transport of an electric current into the corona through the tangential component of the electric field (continuous across the various interfaces), as well as good conservation of the global magnetic helicity. To illustrate our general approach, we present in detail a model problem in which the rising of an initially twisted flux rope through the CZ is described kinematically while the physics inside the corona is described by a full magneto-hydrodynamic model. We show that the evolution leads to the emergence of magnetic flux and electric current into the corona, with the creation of a flux rope that eventually suffers a dynamical transition toward fast expansion.