A Dynamic DataDriven Integrated Flare Model Relying on

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

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 Ph. D Supervisor: Xenophon Moussas, University of Athens, Department of Physics, Athens, Greece SOC & TURBULENCE BERN, 15 -19 OCT, 2012 2

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

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 4

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

SOC system vs SOC state SOC system: SOC state: • • • 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 & TURBULENCE • • 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…) BERN, 15 -19 OCT, 2012 6

• The motivation behind the “IFM” Integrating the basic processes behind a flare: • Driving mechanism (photospheric convection, plasma upflows) • • Bursting/relaxation mechanism (coronal reconnection) • • Kinetic regime SPATIAL RESOLUTION: > Kms TEMPORAL RESOLUTION: ms Data driven (based on 2 D photospheric vector magnetograms) • • MHD regime SPATIAL RESOLUTION: 10^2 Kms Mms TEMPORAL RESOLUTION: HRS - DAYS 3 D 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 SOC & TURBULENCE BERN, 15 -19 OCT, 2012 7

The Static IFM (S-IFM) Dimitropoulou et. al 2011 • 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 32 x 32 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 3 D configuration NLFF optimization (Wiegelmann 2008): Lorentz force + B divergence minimization HANDOVER to DISCO LOAD: RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according to predefined relaxation rules (Lu & Hamilton 1991) HANDOVER to DISCO SOC & TURBULENCE 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 BERN, 15 -19 OCT, 2012 8

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

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

The physics behind the “S-IFM” (3) 3. RELAX: a redistribution module for the magnetic energy ü Selection of redistribution rules: and Lu & Hamilton 1991 ü 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 11

The physics behind the “S-IFM” (4) 4. LOAD: the driver ü Selection of driving rules: 1. Magnetic field increment perpendicular to existing site field - localized Alfvenic waves - convective term of induction eq: 2. Slow driving - the slower the driving, the longer the average waiting time between 2 subsequent events 3. Divergent free magnetic field during the driving process - 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 12

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

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

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

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

Is “S-IFM” a SOC model? ü ü ü 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 17

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

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 32 x 32 grid Dimitropoulou et. al 2012 accepted in A&A • Getting going: DISCO EXTRA RELAX LOAD SOC & TURBULENCE BERN, 15 -19 OCT, 2012 19

The Dynamic IFM (D-IFM) Dimitropoulou et. al 2012 accepted in A&A 50 additional S-IFM avalanches DISCO: INTER: 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 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 SOC & TURBULENCE 16236 - 7 - member SOC groups i = 0, 1, 2, …, 6 j = 0, 1, 2, … 16235 90971 avalanches BERN, 15 -19 OCT, 2012 20

The physics behind the “D-IFM” 1. INTER: a magnetic field interpolator acting as driver ü ü ü Cubic spline interpolation for all transitions SOC: i, j SOC: i+1, j of the same sequence j Interval τ between 2 interpolation steps: ü 32 x 32 grid dimensions ü IVM spatial resolution 0. 55 arcsec/pixel ü pixel size = 8. 8 arcsec ü grid site linear dimension = 6. 4 Mm ü Alfven speed (1 st approximation, coronal height) = 1000 km/s ü τ = 6. 4 sec Multisite driving No avalanche overlapping MHD timestamps (t) on the avalanche onset Instant relaxation (MHD time t stops) ü Monitoring of the magnetic field divergence SOC & TURBULENCE BERN, 15 -19 OCT, 2012 21

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

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

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

Is “D-IFM” a SOC model? ü ü ü 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 25

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

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 27