A Dynamic, Data-Driven, Integrated Flare Model Relying on Self-Organized Criticality

1. A Dynamic, Data-Driven, Integrated Flare ModelRelying on Self-Organized Criticality • Michaila Dimitropoulou • Kapodistrian University of Athens • Nokia Siemens Networks SAE Bern, CH, 15 - 19 Oct 2012 SOC & TURBULENCE 1

2. SOC & TURBULENCE BERN, 15 -19 OCT, 2012 Loukas Vlahos, University of Thessaloniki, Department of Physics, Thessaloniki, Greece Manolis Georgoulis, Research Center of Astronomy & Applied Mathematics, Academy of Athens, Greece Heinz Isliker, University of Thessaloniki, Department of Physics, Thessaloniki, Greece PhD Supervisor: Xenophon Moussas, University of Athens, Department of Physics, Athens, Greece

3. Some “critical” introductory comments • One apology and one request… • No “flying” slides… SOC & TURBULENCE BERN, 15 -19 OCT, 2012

4. SCRUM: A Self-Organization example in SW engineering industry • Bring them together despite of: • character • experience • expertise …and let them SCRUM !!! SOC & TURBULENCE BERN, 15 -19 OCT, 2012

5. SOC: ID vs CV • WHEN AT WORK: • Power - law - like PDFs • Fractality • … • PREREQUISITES: • Threshold • Long - term correlations • Phase transitions: driving (w (or w/o) time-scale separation) + relaxation • Stationary state SOC & TURBULENCE BERN, 15 -19 OCT, 2012

6. SOC system vs SOC state • SOC system: • One that eventually will reach the SOC state, if let to operate long enough • Embedded SOC dynamics (limited d.o.f) • A SOC system needs “time” to reach the SOC state (both in nature as well as in simulations) • One needs more than a snapshot to determine when a system has reached the SOC state • SOC state: • Statistically stationary state that SOC systems finally reach and never exit • Reached when the critical system’s quantity average stabilizes slightly under the critical threshold • When reached, it provides its “evidence” (power laws…) SOC & TURBULENCE BERN, 15 -19 OCT, 2012

7. The motivation behind the “IFM” • Integrating the basic processes behind a flare: • Driving mechanism (photospheric convection, plasma upflows) • MHD regime • Bursting/relaxation mechanism (coronal reconnection) • Kinetic regime • Data driven (based on 2D photospheric vector magnetograms) • 3D magnetic reconstruction through NLFF optimization extrapolation • Modular (“drawer” input-output concept) • Each module simulates one physical process • Each module “is fed” by its predecessor module and “feeds” its successor module with a limited number of variables SPATIAL RESOLUTION: > Kms SPATIAL RESOLUTION: 10^2 Kms - Mms TEMPORAL RESOLUTION: ms TEMPORAL RESOLUTION: HRS - DAYS SOC & TURBULENCE BERN, 15 -19 OCT, 2012

8. Dimitropoulou et. al 2011 The Static IFM (S-IFM) • Dataset: 11 AR photospheric vector magnetograms from IVM • spatial resolution of 0.55 arcsec/pixel • 180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation) • rebinned into a 32x32 grid • Model: DISCO: INSTABILITIES SCANNER Identifies an instability when one site exceeds a critical threshold in the magnetic field Laplacian If YES, HANDOVER to RELAX If NO, HANDOVER to LOAD EXTRA: MAGNETIC FIELD EXTRAPOLATOR Reconstructs the 3D configuration NLFF optimization (Wiegelmann 2008): Lorentz force + B divergence minimization HANDOVER to DISCO LOAD: Driver (photospheric convection / plasma upflows) Adds a magnetic field increment of random magnitude (though obeying to specific “physically” imposed rules) to a random site of the grid, HANDOVER to DISCO RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according to predefined relaxation rules (Lu & Hamilton 1991) HANDOVER to DISCO SOC & TURBULENCE BERN, 15 -19 OCT, 2012

9. The physics behind the “S-IFM” (1) • 1. EXTRA: a nonlinear force-free extrapolation module • Lorentz force minimization • Magnetic field divergence minimization Wiegelmann 2008 SOC & TURBULENCE BERN, 15 -19 OCT, 2012

10. The physics behind the “S-IFM” (2) • 2. DISCO: a module to identify magnetic field instabilities • Selection of critical quantity (magnetic field stress): • where: (1) • Why this? It favors reconnection • Is there an underlying physical meaning behind this selection? Induction Equation central finite difference • Threshold determination: (1) Resistive term dominates, in the presence of local currents SOC & TURBULENCE BERN, 15 -19 OCT, 2012

11. The physics behind the “S-IFM” (3) • 3. RELAX: a redistribution module for the magnetic energy • Selection of redistribution rules: • and Lu & Hamilton 1991 • Do these rules meet basic physical requirements, like magnetic field zero divergence? NLFF extrapolation Magnetic field retains divergence freedom SOC & TURBULENCE BERN, 15 -19 OCT, 2012

12. The physics behind the “S-IFM” (4) • 4. LOAD: the driver • Selection of driving rules: • Magnetic field increment perpendicular to existing site field • - localized Alfvenic waves • - convective term of induction eq: • Slow driving • 3. Divergent free magnetic field during the driving process • the slower the driving, the longer the average waiting time • between 2 subsequent events • only a first degree approximation  need to monitor the • departure from the divergence-free condition: - tolerate a 20% departure SOC & TURBULENCE BERN, 15 -19 OCT, 2012

13. “S-IFM” results (1) • Is SOC reached? NOAA AR 10570 • Is B retained nearly divergent-free? NOAA AR 10247 SOC & TURBULENCE BERN, 15 -19 OCT, 2012

14. “S-IFM” results (2) • Duration • Total Energy • Peak Energy SOC & TURBULENCE BERN, 15 -19 OCT, 2012

15. “S-IFM” results (3) NOAA AR 10050 NOAA AR 9415 SOC & TURBULENCE BERN, 15 -19 OCT, 2012

16. Haleakala IVM SOC & TURBULENCE BERN, 15 -19 OCT, 2012 NOAA AR 10247 2003-01-13 18:26 UT “S-IFM” results (4) NOAA AR 10247

17. Is “S-IFM” a SOC model? • Critical Threshold • Critical quantity stabilizes slightly below the critical threshold • Time-scale separation (MHD driving vs. kinetic relaxation) • Bursting/Avalanches-productive • PDFs following power-like laws SOC & TURBULENCE BERN, 15 -19 OCT, 2012

18. What else is it? • Data-driven • Physical units for energies (peak and total) • Attempts to simulate physical processes: • Alfvenic waves / plasma upflows through its driving mechanism • Diffusion through its relaxation mechanism • Attempts to fulfill principal physical requirements (zero B divergence) What is it not? • Dynamic (arbitrary time units  model timesteps for all time scales) • Anisotropic (LH isotropic relaxation) SOC & TURBULENCE BERN, 15 -19 OCT, 2012

19. The Dynamic IFM (D-IFM) • Dataset:7 subsequent photospheric vector magnetograms from IVM (NOAA AR 8210) • spatial resolution of 0.55 arcsec/pixel • 180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation) • rebinned into a 32x32 grid Dimitropoulou et. al 2012 accepted in A&A DISCO EXTRA • Getting going: RELAX LOAD SOC & TURBULENCE BERN, 15 -19 OCT, 2012

20. The Dynamic IFM (D-IFM) Dimitropoulou et. al 2012 accepted in A&A 50 additional S-IFM avalanches DISCO: INSTABILITIES SCANNER Identifies an instability when one site exceeds a critical threshold in the magnetic field Laplacian If YES, HANDOVER to RELAX If NO, HANDOVER to INTER INTER: Driver (photospheric convection / plasma upflows) Adds magnetic increments in multiple sites following a spline interpolation from one magnetic snapshot to the next HANDOVER to DISCO RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according to predefined relaxation rules (Lu & Hamilton 1991) HANDOVER to DISCO • - 7- member SOC groups • i = 0,1,2,…,6 • j = 0, 1,2,…16235 • 90971 avalanches SOC & TURBULENCE BERN, 15 -19 OCT, 2012

21. The physics behind the “D-IFM” • 1. INTER: a magnetic field interpolator acting as driver • Cubic spline interpolation for all transitions SOC:i,j SOC:i+1,j of the same sequence j • Interval τ between 2 interpolation steps: • 32x32x32 grid dimensions • IVM spatial resolution 0.55 arcsec/pixel • pixel size = 8.8 arcsec • grid site linear dimension = 6.4Mm • Alfven speed (1st approximation, coronal height) = 1000km/s • τ = 6.4 sec • Multisite driving • No avalanche overlapping • MHD timestamps (t) on the avalanche onset • Instant relaxation (MHD time t stops) • Monitoring of the magnetic field divergence SOC & TURBULENCE BERN, 15 -19 OCT, 2012

22. “D-IFM” results (1) • Is B retained nearly divergent-free? SOC & TURBULENCE BERN, 15 -19 OCT, 2012

23. “D-IFM” results (2) SOC & TURBULENCE BERN, 15 -19 OCT, 2012

24. “D-IFM” results (3) • How does the driver behave? SOC & TURBULENCE BERN, 15 -19 OCT, 2012

25. Is “D-IFM” a SOC model? • Critical Threshold • Critical quantity stabilizes slightly below the critical threshold • Time-scale separation (MHD driving (tag) vs. kinetic relaxation) • Bursting/Avalanches-productive • PDFs following power-like laws SOC & TURBULENCE BERN, 15 -19 OCT, 2012

26. What else is it? • Data-driven • Physical units for energies (peak and total) • Physical units for the MHD time-scale • Dynamic • Attempts to simulate physical processes: • Alfvenic waves / plasma upflows through its driving mechanism • Diffusion through its relaxation mechanism\ • Data-based driving mechanism • Attempts to fulfill principal physical requirements (zero B divergence) What is it not? • Anisotropic (LH isotropic relaxation) SOC & TURBULENCE BERN, 15 -19 OCT, 2012

27. Some “critical” conclusive comments • If you fail to define, you fail to fully comprehend… • ISSI Inter- disciplinatory policy • “young scientists exposed to how science is really done”… SOC & TURBULENCE BERN, 15 -19 OCT, 2012