1. A Topological Analysis of the Magnetic Breakout Model by Rhona Maclean University of St Andrews 10 th August 2004 Collaborators: Colin Beveridge, Dana Longcope, Dan Brown and Eric Priest

2. Magnetic Charge Topology (MCT) Simple yet powerful Based on three assumptions: 1) point magnetic sources 2) sources lie in z=0 plane, the photosphere 3) potential field Leads to explicit expression for magnetic field:

3. The Skeleton of the Field Important structural features: null points spines separatrices separators

4. Topological Bifurcations Changes from one topological state to another Two types: –local: change in number of nulls –global: change in structure of field; number of nulls unaffected

5. What is Magnetic Breakout? Explanation for onset of solar flare –central flux system initially enclosed by overlying arcade –shear applied near neutral line in photosphere –magnetic reconnection in vicinity of coronal null –overlying field weakens and allows originally enclosed flux to ‘break out’ explosively Simplest configuration is delta sunspot –new flux emerging inside pre-existing sunspot region

6. Delta Sunspot Model Six unbalanced sources Positive central source corresponds to emerging flux Two separatrix domes prevent flux from connecting to infinity

7. Experiment 1: Source Strength Before global spine-fan bifurcation: After bifurcation:

8. Experiment 2: Source Position

9. Experiment 3: Changing α linear force-free field central source fixed series of 3 global spine-fan bifurcations (α=-0.01, -0.028 and -0.197) 3 rd bifurcation causes breakout

10. Conclusions New flux domain created in process of breakout This can only be caused by global bifurcations Examples here are global spine-fan and global separator Breakout behaviour can occur due to change of: –source strength –source position –force-free parameter α