Topological classification of global magnetic fields in the solar corona

ABSTRACT

Numerous magnetic fragments in the interior of the Sun give rise to many interesting energy processes in the solar corona, for example solar flares and prominences. Magnetic charge topology explains these phenomena by appearance and disappearance of heteroclinic trajectories (separators) — magnetic lines that belong to an intersection of stable and unstable invariant two-dimensional manifolds (fans) of different saddle singularities (nulls). Separators are the locations in the magnetic field configuration where the magnetic energy is transferred from one region (a connected component into which the fans divide the solar corona) to another. Many recent papers has gone into investigation of the configurations that arise in different concrete models. In the present paper, we solve the problem of interrelation between existence of separators of any given magnetic field in the Solar corona and the type and the number of saddle singularities and charges. Following the classical definition, we introduce the concept of equivalence of two magnetic fields and get a classification of such fields up to topological equivalence.

Keywords:

• Magnetic fields
• models corona
• photosphere magnetic reconnection
• dynamics prominences
• topological classification

Acknowledgments

This work was supported by the Russian Science Foundation (project 17-11-01041) in a mathematical part and the Basic Research Program at the HSE (project 90) in 2017 in a physical part.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Here cl A is the closure of A.

2. For saddle points from the set Ω₂ we can prove similar statements if we consider the flow f ^−t .

3. A 2-sphere S ² in a 3-manifold X is said to be cylindrical or cylindrically embedded into X if there is a homeomorphism to its image such that .

4. The three-dimensional 1-handle is the product of the interval and the 2-disc. The gluing is made along the top and bottom disks (see Section 3 in [17] ).

Additional information

Funding

Basic Research Program at the HSE [grant number 2017]; Russian Science Support Foundation [grant number 17-11-01041].