Interpreting magnetic helicity flux in solar flux emergence

Magnetic helicity flux gives information about the topology of a magnetic field passing through a boundary. In solar physics applications, this boundary is the photosphere and magnetic helicity flux has become an important quantity in analysing magnetic fields emerging into the solar atmosphere. In this work we investigate the evolution of magnetic helicity flux in magnetohydrodynamic (MHD) simulations of solar flux emergence. We consider emerging magnetic fields with different topologies and investigate how the magnetic helicity flux patterns corresponds to the dynamics of emergence. To investigate how the helicity input is connected to the emergence process, we consider two forms of the helicity flux. The first is the standard form giving topological information weighted by magnetic flux. The second form represents the net winding and can be interpreted as the standard helicity flux less the magnetic flux. Both quantities provide important and distinct information about the structure of the emerging field and these quantities differ significantly for mixed sign helicity fields. A novel aspect of this study is that we account for the varying morphology of the photosphere due to the motion of the dense plasma lifted into the chromosphere. Our results will prove useful for the interpretation of magnetic helicity flux maps in solar observations.