We study the effect of photospheric motions on the braiding and tangling of coronal magnetic fields. For that we make use of horizontal velocity data that was extracted from magnetograms using the local correlation tracking technique. By tracing trajectories we are able to compute the injected field line winding and finite time topological entropy. Both are quantitative measures of tangling that can be compared to the blinking vortex motion as a benchmark. Here we show that through photospheric motions there can indeed be substantial injection of winding into the system that can potentially be transfered into magnetic loops. This can potentially lead to thin magnetic structures that are potential sites of magnetic energy loss.

1. Rate of field line braiding
in the solar corona
Simon Candelaresi, David Pontin,
Anthony Yeates, Gunnar Hornig

2. Coronal Magnetic Fields
2
NASA
(Thiffeault et al. 2006)
Field line tangling in solar magnetic fields.
Study the tangling of solar magnetic field lines.

3. Blinking Vortex Benchmark
Repeated applications of the blinking vortex motion.
World lines correspond to 3d braided magnetic field
(pig tail, E3).
3
twisting region

4. Blinking Vortex Benchmark
4

5. Magneto-Convection Simulations
periodic
periodic
closed,
stress free
full MHD
Helmholtz-Hodge Decomposition:
(Bushby et al. 2012)
5

6. Magneto-Convection Simulations
6

7. Active Region 10930
7
Consider this region.
FLCT
Helmholtz-Hodge Decomposition
12th of December 2006, 14:04 UT,
(Tsuneta et al. 2008, Fisher & Welsch 2008)

8. Winding Number
8
(Prior & Yeates 2014)
normalised averaged winding number:

9. Winding Number
9
blinking vortex simulation

10. Winding Number
10

11. Winding Number
11
observations
High winding for simulations.
Low winding for observations.

12. Finite Time Topological Entropy
12
material line
advected material line
FTTE:

13. Finite Time Topological Entropy
13
High tangling for simulations and observations.
It takes 3.95h for the photosphere to get as tangled as
during for one cycle of the blinking vortex motion.

14. Conclusions
●
High degree of winding possible.
●
High degree of entanglement
●
Tangled magnetic field stores free energy to be released in
reconnection events.
simon.candelaresi@gmail.com

15. Winding Number
normalisation:
Compressional part does not
significantly contribute to the
winding.

16. Passive Scalar
initial profile:
High mixing of passive scalar.
No clear scale due to turbulent motions.