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Laura F. Morales Canadian Space Agency / Agence Spatiale Canadienne

Anisotropic braiding avalanche model for solar flares: A new 2D application. Laura F. Morales Canadian Space Agency / Agence Spatiale Canadienne Paul Charbonneau Département de Physique, Université de Montréal Markus Aschwanden Lockheed Martin, Adv. Tec. Center ,

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Laura F. Morales Canadian Space Agency / Agence Spatiale Canadienne

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  1. Anisotropic braiding avalanche model for solar flares: A new 2D application Laura F. Morales Canadian Space Agency / AgenceSpatialeCanadienne Paul Charbonneau Départementde Physique, Université de Montréal Markus AschwandenLockheed Martin, Adv. Tec. Center, Solar and Astrophysics Lab.

  2. Outline Solar Flares : Observations + Classical Th. Models SOC paradigm: The sandpile model SOC & Solar Flares: Lu & Hamilton's classic model New SOC model for solar flares: * Cellular Automaton * Statistical results & Spreading exponents * Expanding the model capabilities: Temperature Density

  3. Sun's Atmosphere PHOTOSPHERE CHROMOSPHERE SOLAR CORONA Sunspots Granules Super-granules Spicules Filaments Active regions Loops Solar Flares Etc…. http://www-istp.gsfc.nasa.gov/istp/outreach/images/Solar/Educate/atmos.gif

  4. “...a solar flare is a process associated with a rapid temporary release of energy in the solar corona triggered by an instability of the underlying magnetic field configuration …” M-Class Flare - STEREO (March, 25 2008) – EUV http://stereo.gsfc.nasa.gov/img/stereoimages/movies/Mflare2008.mpg X-Class Flare - SOHO (November, 4 2003) http://sohowww.nascom.nasa.gov/gallery/Movies/EITX27/StormEIT195sm.mpg

  5. tonset ~ 1-2s - tthermalization ~ 100s tdiffusion~ 1016-18 s in the solar corona another mechanism Magnetic Reconnection http://www.sflorg.com/spacenews/images/imsn051906_01_04.gif

  6. Parker's Model for solar flares • SpontaneousCurrent Sheets in Magnetic Fields: With Applications to Stellar X-rays • (Oxford U. Press 1) – Figure 11.2 http://helio.cfa.harvard.edu/REU /images/TRACE171_991106_023044.gif High conductivity B0 uniform Photospheric motions shuffle the footpoints of magnetic coronal loops

  7. Solar Flares Energy Liberation Solar Corona Storage of Magnetic Energy Magnetic reconnection Very small Photosphere Injection of kinetic Energy

  8. Energy is released in a wide range of scales ~1024-1033 ergs Power law self similarbehavior (Dennis 1985, Solar Phys., 100, 465) TURBULENCE OR SELF ORGANIZED CRITICALITY?

  9. SOC + Solar Corona  instability threshold: Critical Angle Slowly driven open system Photospheric motions Intermitent release of energy: Magnetic Reconnection Statistically stationary state: thesolar corona is an statistically stationary state

  10. How can we obtain predictions by using this model? Integrate MHD aquations tflare ~ seconds LB ~ 1010 cm tphotosphere ~ hs Cellular automaton-like simulations

  11. Classic SOC Models • Each node is a measure of the B • B(0)=0 • Driving mechanism: add perturbations at some randomly selected interior nodes • Stability criterion: associated • to the curvature of B (Charbonneau et al. SolPhys, 203:321-353, 2001)

  12. soc Time series of lattice energy & energy released for the avalanches produced by 48 X 48 lattice (Charbonneau et al. SolPhys, 203:321-353, 2001)

  13. Probability Distributions

  14. Classic SOC Models: Ups Successfully reproduced statistical properties observed in solar flares:  pdf’s exhibiting power law form  good predictions for exponents: aE,aP, aT

  15. Classic SOC Models: Downs 1. No magnetic reconnection 2. Link between CA elements & MHD If Bk↔ B .B ≠ 0 If Bk↔ A .B ≠ 0 solved & A interpreted as a twist in the magnetic field Bk2 is no longer a measure of the lattice energy 3. No good predictions for A

  16. NEW MODEL (2008) Threshold  = 1 + 2 angle formed by 2 fieldlines 1 Lattice + perturbation 2 Lattice Energy ~ ∑ Li(t)2 i

  17. + @ (1,3) Reconnect One-step redistribution E=1.25E0 Elim/reduce angle E = 1.22 E0 Perturbation starts again

  18. Reconnect E = 1.32E0 (3,2) unstable Two-step redistribution  (3,1) Perturbation starts again E = 1.19E0 E=1.4E0 E=1.19E0

  19. The lattice in action 64 x 64 32 x 32

  20. T P T E Lattice Energy & Released Energy SOC Morales, L. & Charbonneau, P. ApJ. 682,(1), 654-666. 2008

  21. Observations Classic SOC New SOC E 1.63-1.71 P 1.73-1.84 Morales, L. & Charbonneau, P. ApJ. 682,(1), 654-666. 2008 1.40 1.54 1.79-2.11 1.7

  22. Observations Classic SOC New SOC T 1.79-1.95 Morales, L. & Charbonneau, P. ApJ. 682,(1), 654-666. 2008 1.15 – 2.93 1.70

  23. Area covered by an avalanche: a movie

  24. Area covered by Avalanches t0 +30 t0 +116 = tmax unstable (12,2) Peak Area t0 Time integrated Area unstable (10,1) t0 +150 tf = t0+332

  25. A A* EUV – TRACE 1.83 – 2.45 Classic SOC 1.02 ± 0.06 0.55 ± 0.02 New SOC 2.45 ± 0.11 1.93 ± 0.07 Geometric Properties Morales, L. & Charbonneau, P. GRL., 35, L04108

  26. Spreading Exponents Number of unstablenodesat time t Probability of existence att Size of an avalanche ‘death’ by t k Probability of an avalanche to reach a size S b

  27. Morales, L. & Charbonneau, P. GRL., 35, L04108 Just an example…

  28. fold From a 2D lattice to a loop bend

  29. Avalanching strands in the loop

  30. Projection

  31. Projections

  32. Geometrical properties for the projected areas *A = 1.84 ± 0.07 A = 2.39 ± 0.05

  33. N=32 N=64

  34. Another way of looking at the simulations Near vertical current sheet that extends from the coronal reconnection regions to the photospheric flare ribbons mapped into

  35. Temperature & Density Evolution The maximum loop temperature based on the maximum heating rate and the loop length for uniform heating case: k = 9.210-7 erg s-1 K7/2 (Spitzer conductivity) Emax Pressure Density

  36. Temperatures Avalanche duration: 106 it. Avalanche duration: 138 it. N=64 THR=2 51013 avalanches in 4e5 iterations Max duration ~ 700 it

  37. Density ] ]

  38. Coming up….. With the temperature T(t) and density evolution n(t) of each avalanche we can compute the resulting peak fluxes and time durations for a given wavelength filter in EUV or SXR, because for optically thin emission we just have: I(t) = ∫ n(t)2 w R(T) dT w is the loop width R(T) is the instrumental response function. We can plot the frequency distributions of energies: W =E_Hmax * duration peak fluxes (I_EUV, I_SXR)

  39. Conclusions The new cellular automaton we introduced and fully analyzed represents a major breakthrough in the field of self-organized critical models for solar flares since: • Every element in the model can be directly mapped to Parker's model for solar flares thus solving the major problems of interpretation posed by classical SOC models. • For the first time a SOC model for solar flares succeeded in reproducing observational results for all the typical magnitudes that characterize a SOC model: E, P, T, T & the time integrated A and the peak A*.

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