
Three-dimensional evolution of selected emerging field lines (purple and orange => outer (envelope) field lines, red => inner (axis) field line). Contours and colors indicate vertical magnetic flux density and vertical flow velocity in solar surface (photosphere).


Formula for magnetic energy flux (Eq. 22) and relative magnetic helicity flux (Eq. 23) in photosphere. In both formulae, the first term (shear term) represents contribution by horizontal flow (vx, vy), while the second term (emergence term) contribution by vertical flow (vz).

Flux emergence produces not only vertical flow but also horizontal flow in photosphere, both of which contribute to injecting magnetic energy and relative magnetic helicity. The emergence term related to the vertical flow is dominant at an early phase of the emergence, while the shear term related to the horizontal flow (shear and/or rotational flow) becomes a dominant contributor at the late phase.

The emergence term related to the vertical flow is dominant at the early phase.

The shear term related to the horizontl flow is dominant at the late phase.


Evolution of main polarity region and associated flow (relative velocity field around the center of the polarity region).

If one of the legs of emerging twisted flux tube is completely vertical to photosphere, only main polarity region is formed (left panel). On the other hand, when the leg is inclined, satellite polarity region is also formed in addition to the main polarity region (right panel; Magara 2004).