Sketch showing possible solutions (upper panel) to equation (8) with S = const = −1 in z < 0 and S = 0 in z > 0. The red (dashed) and black (solid) lines show solutions for which the magnetic helicity flux (, see lower panel) is negative in the exterior. This corresponds to the case observed in the Sun. The blue (dotted) line shows the case, where the magnetic helicity flux is zero above the surface and therefore does not reverse the sign of in the exterior.