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

2 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 BERN, OCT, 2012 SOC & TURBULENCE

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

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

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

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

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

8 The Static IFM (S-IFM) BERN, OCT, 2012 SOC & TURBULENCE Dataset: 11 AR photospheric vector magnetograms from IVM Dataset: 11 AR photospheric vector magnetograms from IVM spatial resolution of 0.55 arcsec/pixel spatial resolution of 0.55 arcsec/pixel 180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation) 180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation) rebinned into a 32x32 grid rebinned into a 32x32 grid Dimitropoulou et. al 2011 Model: Model: EXTRA: MAGNETIC FIELD EXTRAPOLATOR Reconstructs the 3D configuration NLFF optimization (Wiegelmann 2008): Lorentz force + B divergence minimization HANDOVER to DISCO 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 RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according Redistributes the magnetic field according to predefined relaxation rules to predefined relaxation rules (Lu & Hamilton 1991) 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

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

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

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

12 The physics behind the “S-IFM” (4) BERN, OCT, 2012 SOC & TURBULENCE 4. LOAD: the driver Selection of driving rules: Selection of driving rules: 1.Magnetic field increment perpendicular to existing site field - localized Alfvenic waves - localized Alfvenic waves - convective term of induction eq: - convective term of induction eq: 2.Slow driving 3. Divergent free magnetic field during the driving process 3. Divergent free magnetic field during the driving process - tolerate a 20% departure - the slower the driving, the longer the average waiting time between 2 subsequent events between 2 subsequent events - only a first degree approximation  need to monitor the departure from the divergence-free condition: departure from the divergence-free condition:

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

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

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

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

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

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

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

20 The Dynamic IFM (D-IFM) BERN, OCT, 2012 SOC & TURBULENCE Dimitropoulou et. al 2012 accepted in A&A Dimitropoulou et. al 2012 accepted in A&A 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 RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according Redistributes the magnetic field according to predefined relaxation rules to predefined relaxation rules (Lu & Hamilton 1991) HANDOVER to DISCO 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 50 additional S-IFM avalanches member SOC groups i = 0,1,2,…,6 i = 0,1,2,…,6 j = 0, 1,2,…16235 j = 0, 1,2,… avalanches avalanches

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

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

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

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

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

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

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