are eruptive solar active regions in a self-organized criticality state?
DESCRIPTION
Are Eruptive Solar Active Regions in a Self-Organized Criticality state?. Michaila Dimitropoulou Kapodistrian University of Athens. Bern, 16 - 20 October 2013. SOC & TURBULENCE. 1. L. Vlahos, University of Thessaloniki, Department of Physics, Thessaloniki, Greece - PowerPoint PPT PresentationTRANSCRIPT
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
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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 ?