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A Dynamic, Data-Driven, A Dynamic, Data-Driven, Integrated Flare ModelIntegrated Flare ModelRelying on Self-Organized Relying on Self-Organized CriticalityCriticality

Michaila DimitropoulouMichaila Dimitropoulou

Kapodistrian University of AthensKapodistrian University of Athens

Nokia Siemens Networks SAENokia Siemens Networks SAE

Bern, CH, 15 - 19 Oct Bern, CH, 15 - 19 Oct 20122012SOC & TURBULENCESOC & TURBULENCE 1

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Loukas Vlahos, Loukas Vlahos, University of Thessaloniki, Department of Physics, Thessaloniki, University of Thessaloniki, Department of Physics, Thessaloniki, GreeceGreece

Manolis Georgoulis, Manolis Georgoulis, Research Center of Astronomy & Applied Mathematics, Research Center of Astronomy & Applied Mathematics, Academy of Athens, GreeceAcademy of Athens, Greece

Heinz Isliker, Heinz Isliker, University of Thessaloniki, Department of Physics, Thessaloniki, University of Thessaloniki, Department of Physics, Thessaloniki, GreeceGreece

PhD Supervisor:PhD Supervisor:Xenophon Moussas, Xenophon Moussas, University of Athens, Department of Physics, Athens, GreeceUniversity of Athens, Department of Physics, Athens, Greece

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

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Some “critical” introductory commentsSome “critical” introductory comments

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

• One apology and one request…One apology and one request…

• No “flying” slides… No “flying” slides…

SOC & TURBULENCESOC & TURBULENCE

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SCRUM: A Self-Organization example in SW SCRUM: A Self-Organization example in SW engineering industryengineering industry

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Bring them together despite of:

• character• experience• expertise

…and let them SCRUM !!!

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SOC: ID vs CVSOC: ID vs CV

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

PREREQUISITES:PREREQUISITES:

• ThresholdThreshold

• Long - term correlationsLong - term correlations

• Phase transitions: driving (Phase transitions: driving (ww (or (or w/o) time-scale separation) + w/o) time-scale separation) + relaxationrelaxation

• Stationary stateStationary state

SOC & TURBULENCESOC & TURBULENCE

WHEN AT WORK:WHEN AT WORK:

• Power - law - like PDFsPower - law - like PDFs

• FractalityFractality

• ……

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SOC system vs SOC stateSOC system vs SOC state

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC system: SOC system:

• One that eventually will One that eventually will reach the SOC state, if let to reach the SOC state, if let to operate long enoughoperate long enough

• Embedded SOC dynamics Embedded SOC dynamics (limited d.o.f)(limited d.o.f)

• A SOC system needs “time” A SOC system needs “time” to reach the SOC state (both to reach the SOC state (both in nature as well as in in nature as well as in simulations)simulations)

• One needs more than a One needs more than a snapshot to determine when snapshot to determine when a system has reached the a system has reached the SOC stateSOC state

SOC & TURBULENCESOC & TURBULENCE

SOC state:SOC state:

• Statistically stationary Statistically stationary state that SOC systems state that SOC systems finally reach and never exitfinally reach and never exit

• Reached when the critical Reached when the critical system’s quantity average system’s quantity average stabilizes slightly under stabilizes slightly under the critical thresholdthe critical threshold

• When reached, it provides When reached, it provides its “evidence” (power its “evidence” (power laws…)laws…)

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The motivation behind the “IFM”The motivation behind the “IFM”

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

• 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 regimeMHD regime

• Bursting/relaxation mechanism (coronal reconnection)Bursting/relaxation mechanism (coronal reconnection)

• Kinetic regimeKinetic regime

• Data driven (based on 2D photospheric vector magnetograms)Data driven (based on 2D photospheric vector magnetograms)

• 3D magnetic reconstruction through NLFF optimization 3D magnetic reconstruction through NLFF optimization extrapolationextrapolation

• Modular (“drawer” input-output concept)Modular (“drawer” input-output concept)

• Each module simulates one physical processEach module simulates one physical process

• Each module “is fed” by its predecessor module and “feeds” Each module “is fed” by its predecessor module and “feeds” its successor module with a limited number of variablesits successor module with a limited number of variables

SOC & TURBULENCESOC & TURBULENCE

SPATIAL RESOLUTION: 10^2 Kms - SPATIAL RESOLUTION: 10^2 Kms - Mms Mms

TEMPORAL RESOLUTION: HRS - DAYSTEMPORAL RESOLUTION: HRS - DAYS

SPATIAL RESOLUTION: > Kms SPATIAL RESOLUTION: > Kms

TEMPORAL RESOLUTION: msTEMPORAL RESOLUTION: ms

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The Static IFM (S-IFM)The Static IFM (S-IFM)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

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• Dataset: Dataset: 11 AR photospheric vector magnetograms from IVM11 AR photospheric vector magnetograms from IVM• spatial resolution of 0.55 arcsec/pixelspatial resolution of 0.55 arcsec/pixel• 180 azimuthal ambiguity removed (180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation)Non-Potential magnetic Field Calculation)• rebinned into a 32x32 gridrebinned into a 32x32 grid

Dimitropoulou et. al 2011Dimitropoulou et. al 2011Dimitropoulou et. al 2011Dimitropoulou et. al 2011

• Model:Model:

EXTRA:EXTRA: MAGNETIC FIELD EXTRAPOLATORMAGNETIC FIELD EXTRAPOLATORReconstructs the 3D configurationReconstructs the 3D configurationNLFF optimization (Wiegelmann NLFF optimization (Wiegelmann 2008):2008):Lorentz force + B divergence Lorentz force + B divergence minimizationminimizationHANDOVER to DISCOHANDOVER to DISCO

DISCO:DISCO: INSTABILITIES SCANNERINSTABILITIES SCANNERIdentifies an instability when one site Identifies an instability when one site exceeds a critical threshold in the exceeds a critical threshold in the magnetic field Laplacianmagnetic field LaplacianIf YES, HANDOVER to RELAXIf YES, HANDOVER to RELAXIf NO, HANDOVER to LOADIf NO, HANDOVER to LOAD

RELAX:RELAX: Magnetic Field Re-distributor Magnetic Field Re-distributor (reconnection)(reconnection) Redistributes the magnetic field Redistributes the magnetic field accordingaccording to predefined relaxation rules to predefined relaxation rules (Lu & Hamilton 1991)(Lu & Hamilton 1991)HANDOVER to DISCOHANDOVER to DISCO

LOAD:LOAD: Driver (photospheric convection / Driver (photospheric convection / plasma upflows)plasma upflows)Adds a magnetic field increment of Adds a magnetic field increment of random magnitude (though obeying random magnitude (though obeying to specific “physically” imposed rules) to specific “physically” imposed rules) to a random site of the grid, to a random site of the grid, HANDOVER to DISCOHANDOVER to DISCO

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The physics behind the “S-IFM” (1)The physics behind the “S-IFM” (1)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

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1. EXTRA: a nonlinear force-free extrapolation module 1. EXTRA: a nonlinear force-free extrapolation module

Lorentz force minimizationLorentz force minimization Magnetic field divergence minimizationMagnetic field divergence minimization

Wiegelmann 2008Wiegelmann 2008Wiegelmann 2008Wiegelmann 2008

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The physics behind the “S-IFM” (2)The physics behind the “S-IFM” (2)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

2. DISCO: a module to identify magnetic field instabilities 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 reconnectionWhy this? It favors reconnection Is there an underlying physical meaning behind this selection?Is there an underlying physical meaning behind this selection?

Induction Induction EquationEquation

central finite central finite differencedifference

(1(1))

(1(1))

Resistive term dominates,Resistive term dominates,in the presence of local in the presence of local currentscurrents

Threshold determination:Threshold determination:

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The physics behind the “S-IFM” (3)The physics behind the “S-IFM” (3)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

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3. RELAX: a redistribution module for the magnetic energy3. 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 Do these rules meet basic physical requirements, like magnetic field zero divergence?divergence?

NLFF NLFF extrapolationextrapolation

Magnetic field retains divergence Magnetic field retains divergence freedomfreedom

Lu & Hamilton 1991Lu & Hamilton 1991Lu & Hamilton 1991Lu & Hamilton 1991

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The physics behind the “S-IFM” (4)The physics behind the “S-IFM” (4)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

4. LOAD: the driver4. LOAD: the driver Selection of driving rules: Selection of driving rules:

1.1.Magnetic field increment perpendicular to existing site fieldMagnetic field increment perpendicular to existing site field - localized Alfvenic waves- localized Alfvenic waves - convective term of induction eq:- convective term of induction eq:

2.2.Slow drivingSlow driving

3. Divergent free magnetic field during the driving process3. Divergent free magnetic field during the driving process

- tolerate a 20% - tolerate a 20% departuredeparture

- the slower the driving, the longer the average the slower the driving, the longer the average waiting timewaiting time between 2 subsequent eventsbetween 2 subsequent events

- only a first degree approximation only a first degree approximation need to monitor need to monitor thethe departure from the divergence-free condition:departure from the divergence-free condition:

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““S-IFM” results (1)S-IFM” results (1)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Is SOC reached?Is SOC reached?

Is B retained nearly divergent-free?Is B retained nearly divergent-free?

NOAA AR NOAA AR 1024710247

NOAA AR NOAA AR 1057010570

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““S-IFM” results (2)S-IFM” results (2)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

DurationDuration

Total Total EnergyEnergy

Peak Peak EnergyEnergy

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““S-IFM” results (3)S-IFM” results (3)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

NOAA AR NOAA AR 1005010050

NOAA AR NOAA AR 94159415

16BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

NOAA AR 10247NOAA AR 102472003-01-13 18:26 UT2003-01-13 18:26 UT

Haleakala IVMHaleakala IVM

““S-IFM” results (4)S-IFM” results (4)NOAA AR NOAA AR 1024710247

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Is “S-IFM” a SOC model?Is “S-IFM” a SOC model?

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

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Critical ThresholdCritical Threshold Critical quantity stabilizes slightly below the critical Critical quantity stabilizes slightly below the critical thresholdthreshold Time-scale separation (MHD driving vs. kinetic Time-scale separation (MHD driving vs. kinetic relaxation)relaxation) Bursting/Avalanches-productiveBursting/Avalanches-productive PDFs following power-like lawsPDFs following power-like laws

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What else is it?What else is it?

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Data-drivenData-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 mechanismAlfvenic waves / plasma upflows through its driving mechanism Diffusion through its relaxation mechanismDiffusion through its relaxation mechanism

Attempts to fulfill principal physical requirements (zero B Attempts to fulfill principal physical requirements (zero B divergence)divergence)

What is it not?What is it not? Dynamic (arbitrary time units Dynamic (arbitrary time units model timesteps for all model timesteps for all time scales)time scales) Anisotropic (LH isotropic relaxation)Anisotropic (LH isotropic relaxation)

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The Dynamic IFM (D-IFM)The Dynamic IFM (D-IFM)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

• Dataset:Dataset: 7 subsequent photospheric vector magnetograms from IVM 7 subsequent photospheric vector magnetograms from IVM (NOAA AR 8210)(NOAA AR 8210)• spatial resolution of 0.55 arcsec/pixelspatial resolution of 0.55 arcsec/pixel• 180 azimuthal ambiguity removed (180 azimuthal ambiguity removed (Non-Potential magnetic Field Calculation)Non-Potential magnetic Field Calculation)• rebinned into a 32x32 gridrebinned into a 32x32 grid

Dimitropoulou et. al 2012Dimitropoulou et. al 2012accepted in A&Aaccepted in A&A

Dimitropoulou et. al 2012Dimitropoulou et. al 2012accepted in A&Aaccepted in A&A

• Getting going:Getting going:

EXTREXTRAA

DISCDISCOO

RELARELAXX

LOADLOAD

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The Dynamic IFM (D-IFM)The Dynamic IFM (D-IFM)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Dimitropoulou et. al 2012Dimitropoulou et. al 2012accepted in A&Aaccepted in A&A

Dimitropoulou et. al 2012Dimitropoulou et. al 2012accepted in A&Aaccepted in A&A

DISCO:DISCO: INSTABILITIES SCANNERINSTABILITIES SCANNERIdentifies an instability when one site Identifies an instability when one site exceeds a critical threshold in the exceeds a critical threshold in the magnetic field Laplacianmagnetic field LaplacianIf YES, HANDOVER to RELAXIf YES, HANDOVER to RELAXIf NO, HANDOVER to INTERIf NO, HANDOVER to INTER

RELAX:RELAX: Magnetic Field Re-distributor Magnetic Field Re-distributor (reconnection)(reconnection) Redistributes the magnetic field Redistributes the magnetic field accordingaccording to predefined relaxation rules to predefined relaxation rules (Lu & Hamilton 1991)(Lu & Hamilton 1991)HANDOVER to DISCOHANDOVER to DISCO

INTER:INTER: Driver (photospheric convection / Driver (photospheric convection / plasma upflows)plasma upflows)Adds magnetic increments in multiple Adds magnetic increments in multiple sites following a spline interpolation sites following a spline interpolation from one magnetic snapshot to the from one magnetic snapshot to the next next HANDOVER to DISCOHANDOVER to DISCO

50 additional S-IFM 50 additional S-IFM avalanchesavalanches

1623616236- 7- member SOC - 7- member SOC groupsgroups

i = 0,1,2,…,6i = 0,1,2,…,6 j = 0, 1,2,…16235j = 0, 1,2,…16235 90971 avalanches90971 avalanches

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The physics behind the “D-IFM” The physics behind the “D-IFM”

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

1. INTER: a magnetic field interpolator acting as driver 1. INTER: a magnetic field interpolator acting as driver

Cubic spline interpolation for all transitions SOC:i,j Cubic spline interpolation for all transitions SOC:i,j SOC:i+1,j of the same SOC:i+1,j of the same

sequence sequence jj Interval Interval ττ between 2 interpolation steps: between 2 interpolation steps:

32x32x32 grid dimensions32x32x32 grid dimensions IVM spatial resolution 0.55 arcsec/pixelIVM spatial resolution 0.55 arcsec/pixel pixel size = 8.8 arcsecpixel size = 8.8 arcsec grid site linear dimension = 6.4Mmgrid site linear dimension = 6.4Mm Alfven speed (1Alfven speed (1stst approximation, coronal height) = 1000km/s approximation, coronal height) = 1000km/s τ = 6.4 τ = 6.4 secsec

Multisite drivingMultisite driving No avalanche overlappingNo avalanche overlapping MHD timestamps (t) on the avalanche onsetMHD timestamps (t) on the avalanche onset Instant relaxation (MHD time t stops)Instant relaxation (MHD time t stops)

Monitoring of the magnetic field divergenceMonitoring of the magnetic field divergence

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““D-IFM” results (1)D-IFM” results (1)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Is B retained nearly divergent-free?Is B retained nearly divergent-free?

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““D-IFM” results (2)D-IFM” results (2)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

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““D-IFM” results (3)D-IFM” results (3)

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

How does the driver behave?How does the driver behave?

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Is “D-IFM” a SOC model?Is “D-IFM” a SOC model?

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Critical ThresholdCritical Threshold Critical quantity stabilizes slightly below the critical Critical quantity stabilizes slightly below the critical thresholdthreshold Time-scale separation (MHD driving (tag) vs. kinetic Time-scale separation (MHD driving (tag) vs. kinetic relaxation)relaxation) Bursting/Avalanches-productiveBursting/Avalanches-productive PDFs following power-like lawsPDFs following power-like laws

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What else is it?What else is it?

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

SOC & TURBULENCESOC & TURBULENCE

Data-drivenData-driven Physical units for energies (peak and total)Physical units for energies (peak and total) Physical units for the MHD time-scalePhysical units for the MHD time-scale DynamicDynamic Attempts to simulate physical processes:Attempts to simulate physical processes:

Alfvenic waves / plasma upflows through its driving mechanismAlfvenic waves / plasma upflows through its driving mechanism Diffusion through its relaxation mechanism\Diffusion through its relaxation mechanism\ Data-based driving mechanismData-based driving mechanism

Attempts to fulfill principal physical requirements (zero B Attempts to fulfill principal physical requirements (zero B divergence)divergence)

What is it not?What is it not? Anisotropic (LH isotropic relaxation)Anisotropic (LH isotropic relaxation)

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Some “critical” conclusive commentsSome “critical” conclusive comments

BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012

• If you fail to define, you fail to fully If you fail to define, you fail to fully comprehend…comprehend…

• ISSI Inter- disciplinatory policyISSI Inter- disciplinatory policy

• ““young scientists exposed to how young scientists exposed to how science is really done”…science is really done”…

SOC & TURBULENCESOC & TURBULENCE