Are Eruptive Solar Active Regions in a Self-Organized Criticality state?

1

Michaila Dimitropoulou

Kapodistrian University of Athens

Bern, 16 - 20 October 2013

SOC & TURBULENCE 1

L. Vlahos, University of Thessaloniki, Department of Physics, Thessaloniki, Greece

M. Georgoulis, Research Center of Astronomy & Applied Mathematics, Academy of Athens, Greece

H. Isliker, University of Thessaloniki, Department of Physics, Thessaloniki, Greece

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

2Bern, 16 - 20 October 2013

SOC & TURBULENCE 2

From the sandpile to the Sun…The BTW model

Bak, Tang & Wiesenfield (1987)

Control parameter

Transition rules

Instability criterion

Relaxation rules

The LH model

Lu, Hamilton (1991)

Frette et al., 1996

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SOC: Concept & misconceptionsSelf-Organized Criticality: open systems self-organize in a statistical stationary state in which a phase transition far from equilibrium is undergone; by means of:

• slow-driving, • critical threshold, • time scale separation, • metastability, and • boundary dissipation

the dynamics of the system leads it to a critical state in which scale invariance is present in all the observables.

SOC Diagnostics:

• “control parameter”: stabilization of mean value just below the critical threshold

• avalanches: well defined mean number in equal time intervals

• long-term/extensive temporal/spatial two-point-correlations scale invariance/self-similarity

long-term memory

fractality

power-law scaling

SOC

5

SOC in Solar Flares?

Crosby et al, 1993(HXRBS/SMM)

Georgoulis et al, 2001 (WATCH/GRANAT)

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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

Dimitropoulou et al., 2011

• Model:

EXTRA: MAGNETIC FIELD EXTRAPOLATORReconstructs the 3D configurationNLFF optimization (Wiegelmann 2008):Lorentz force + B divergence minimizationHANDOVER to DISCO

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

RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according 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

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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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The physics behind the “S-IFM” (2)

2. DISCO: a module to identify magnetic field instabilities Selection of critical quantity (magnetic field stress = magnetic field

Laplacian):

where:

Why this? It favors reconnection 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:

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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

Do these rules meet basic physical requirements, like magnetic field zero divergence?

NLFF extrapolation

Magnetic field retains divergence freedom

Lu & Hamilton 2001

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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

3. Divergent free magnetic field during the driving process

- tolerate a 20% departure

- the slower the driving, the longer the average waiting time

- only a first degree approximation need to monitor the

departure from the divergence-free condition:

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“S-IFM” results (1)

SOC reached

NOAA AR 10247

NOAA AR 10570

B nearly divergent-free

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“S-IFM” results (3)NOAA AR 10050

NOAA AR 9415

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NOAA AR 102472003-01-13 18:26 UT

Haleakala IVM

“S-IFM” results (4)NOAA AR 10247

Static! (a

rbitrary tim

e

units model ti

mesteps

for all t

ime scales)

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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., 2013

• Getting going:

EXTRA

DISCO

RELAX

LOAD

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The Dynamic IFM (D-IFM)

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

RELAX: Magnetic Field Re-distributor (reconnection) Redistributes the magnetic field according 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

16236- 7- member SOC groups

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

Dimitropoulou et al., 2013

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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

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“D-IFM” results (1)

Is B retained nearly divergent-free?

How does the driver behave?

S-IFM

D-IFM

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“D-IFM” results (2)

SOC & TURBULENCE

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Are Eruptive Solar ARs in SOC?

SOC & TURBULENCE

AR11158, HMI/SDO13/02/2011, 15:58:12

rebin

S-IFM

EXTRA D-IFM

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Critical Quantity: Behaviour

SOC & TURBULENCE

S-IFM

D-IFM

Gcr = 488 Gauss (max( |Gav| ) = 487.7 Gauss)

iterations

Mean

( |G

av| )

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Avalanche numbers: Behaviour

SOC & TURBULENCE

S-IFM

D-IFM

Gcr = 488 Gauss (max( |Gav| ) = 487.7 Gauss)

iterations

avala

nch

es

avala

nch

es

iterations

S-IFM

D-IFM

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WNDB: Behaviour

SOC & TURBULENCE

Gcr = 488 Gauss (max( |Gav| ) = 487.7 Gauss)

iterations

WN

DB

S-IFM

D-IFM

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Some additional experiments

SOC & TURBULENCE

S-IFM

D-IFM

Gcr = 488 Gauss (max( |Gav| ) = 487.7 Gauss)

iterations

Mean

( |G

av| )

S-IFM

D -

IFM

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Some additional experiments

SOC & TURBULENCE

S-IFM

Gcr = 488 Gauss (max( |Gav| ) = 487.7 Gauss)

iterations

Mean

( |G

av| )

D -

IFM

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Conclusions(1/2)

Why IFM? Data-driven Physical units for energies (peak and

total) Physical units for the MHD time-scale (D-

IFM)Attempts to simulate physical processes:

Alfvenic waves / plasma upflows Diffusion Data-based driving mechanism (D-

IFM) Attempts to fulfill principal physical

requirements (zero B divergence)

SOC CA models complement the MHD approach, by reproducing the global statistics of the physical processes at play

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Conclusions (2/2)

Are Eruptive Solar ARs in SOC? They may be !

Is the “external” driver embedded in the internal dynamics of the system ?

Critical quantity ????? Critical threshold ?????

+ Can a simple smooth interpolation in a magnetogram sequence reproduce nature?

+ Hopefully not: Discontinuities !+ Can this test get us closer to our critical quantity+ …and to the definition of our critical thresholdin terms of reproducing real “big” events?

What about the (quiet) Sun ?