Injection of Magnetic Energy and Magnetic Helicity into Solar Atmosphere by Emerging Flux Tube


We performed a three-dimensional MHD simulation of an emerging twisted flux tube to investigate flow and magnetic structure involved in flux emergence, especially focusing on how emerging field lines and the associated flows contribute to injecting magnetic energy and relative magnetic helicity into a solar atmosphere. The flux emergence started with appearance of a simple bipolar region (a pair of main polarity regions) in a solar surface (photosphere), which was subsequently deformed and fragmented, leading to a quadrupolar region (one main polarity region accompanied by one satellite polarity region). The flux emergence produced not only a vertical flow but also horizontal flow (shear and/or rotational flow) in the photosphere, both of which contributed to injecting the magnetic energy and relative magnetic helicity. The emergence term related to the vertical flow was dominant at the early phase, while the shear term related to the horizontal flow became a dominant contributor at the late phase. We also investigated spatial distributions of force and flow along selected emerging field lines, explaining that emerging field lines may be classified into two types based on the aspect ratio of field line (ratio of height to footpoint distance).


References

Magara, T. & Longcope, D. W. 2003 ApJ, 586, 630
Magara, T. 2004 ASP, 325, 185




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).


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