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
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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
SOC & TURBULENCE
BERN, 15 -19 OCT, 2012
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Some “critical” introductory comments
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One apology and one request…
No “flying” slides…
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BERN, 15 -19 OCT, 2012
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SCRUM: A Self-Organization example in SW
engineering industry
Bring them together despite of:
• character
• experience
• expertise
…and let them SCRUM !!!
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SOC: ID vs CV
PREREQUISITES:
WHEN AT WORK:
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Threshold
Long - term correlations
Phase transitions: driving (w (or w/o)
time-scale separation) + relaxation
Power - law - like PDFs
Fractality
…
Stationary state
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BERN, 15 -19 OCT, 2012
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SOC system vs SOC state
SOC system:
SOC state:
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•
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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
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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…)
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The motivation behind the “IFM”
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Integrating the basic processes behind a flare:
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Driving mechanism (photospheric convection, plasma upflows)
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Kinetic regime
SPATIAL RESOLUTION: > Kms
TEMPORAL RESOLUTION: ms
Data driven (based on 2D photospheric vector magnetograms)
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TEMPORAL RESOLUTION: HRS - DAYS
Bursting/relaxation mechanism (coronal reconnection)
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MHD regime
SPATIAL RESOLUTION: 10^2 Kms - Mms
3D magnetic reconstruction through NLFF optimization extrapolation
Modular (“drawer” input-output concept)
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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
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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 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:
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
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The physics behind the “S-IFM” (1)
1. EXTRA: a nonlinear force-free extrapolation module

Lorentz force minimization
 Magnetic field divergence minimization
Wiegelmann 2008
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BERN, 15 -19 OCT, 2012
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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
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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
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The physics behind the “S-IFM” (4)
4. LOAD: the driver

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
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“S-IFM” results (1)
 Is SOC reached?
NOAA AR 10570
 Is B retained nearly divergent-free?
NOAA AR 10247
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“S-IFM” results (2)
 Duration
 Total Energy
SOC & TURBULENCE
 Peak Energy
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“S-IFM” results (3)
NOAA AR 10050
NOAA AR 9415
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“S-IFM” results (4)
NOAA AR 10247
Haleakala IVM
NOAA AR 10247
2003-01-13 18:26 UT
SOC & TURBULENCE
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Is “S-IFM” a SOC model?
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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
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BERN, 15 -19 OCT, 2012
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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
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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
• Getting going:
DISCO
EXTRA
RELAX
LOAD
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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
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The physics behind the “D-IFM”
1. INTER: a magnetic field interpolator acting as driver
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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
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“D-IFM” results (1)
 Is B retained nearly divergent-free?
SOC & TURBULENCE
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“D-IFM” results (2)
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“D-IFM” results (3)
 How does the driver behave?
SOC & TURBULENCE
BERN, 15 -19 OCT, 2012
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Is “D-IFM” a SOC model?
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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
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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
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Some “critical” conclusive comments
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If you fail to define, you fail to fully
comprehend…
ISSI Inter- disciplinatory policy
“young scientists exposed to how science
is really done”…
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