1 Self-Organized Criticality in the Solar Atmosphere: Universal Property of Solar Magnetism, Or...

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Self-Organized Criticality in Self-Organized Criticality in the Solar the Solar

Atmosphere:Atmosphere:Universal Property of Solar Universal Property of Solar

Magnetism, Magnetism, Or Merely One of Eruptive Active Or Merely One of Eruptive Active

Regions?Regions?

Manolis K. Georgoulis*Manolis K. Georgoulis*

RCAAM of the Academy of AthensRCAAM of the Academy of Athens

RCAAM of the Academy of AthensRCAAM of the Academy of Athens

* Marie Curie Fellow* Marie Curie Fellow

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

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OUTLINEOUTLINE

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

OUTLINEOUTLINE

• Observational facts in the solar Observational facts in the solar active-region atmosphere active-region atmosphere

• Where do observables and Where do observables and ““momentsmoments”” stem from? stem from?

• SOC models of solar active regionsSOC models of solar active regions

• X-CA approaches: revisions and X-CA approaches: revisions and enhancements of SOC modelsenhancements of SOC models

• Open questions: how can we Open questions: how can we rigorously determine SOC in solar rigorously determine SOC in solar active regions?active regions?

• If SOC is at work, what can we gain If SOC is at work, what can we gain from its application?from its application?

• ConclusionsConclusions

SOC & TURBULENCESOC & TURBULENCE

What is the extent of SOC validity in solar magnetic What is the extent of SOC validity in solar magnetic

structures?structures? Courtesy: TRACECourtesy: TRACE

Falling grains of sand Falling grains of sand

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SOLAR MAGNETIC FIELDS: COMPLEXITY AT SOLAR MAGNETIC FIELDS: COMPLEXITY AT WORKWORK

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SOLAR MAGNETIC FIELDS: COMPLEXITYSOLAR MAGNETIC FIELDS: COMPLEXITY


Source: Hinode SOT/SP Source: Hinode SOT/SP

NOAA AR 10930NOAA AR 1093012/12/06, 20:30 UT 12/12/06, 20:30 UT

Ever-increasing spatial resolution leads to ever-Ever-increasing spatial resolution leads to ever-increasing intermittency in the observed spatial increasing intermittency in the observed spatial

structuresstructures

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SOLAR MAGNETIC FIELDS: COMPLEXITY AT SOLAR MAGNETIC FIELDS: COMPLEXITY AT WORKWORK

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SOLAR MAGNETIC FIELDS: COMPLEXITYSOLAR MAGNETIC FIELDS: COMPLEXITY


Ever-increasing temporal resolution leads to ever-Ever-increasing temporal resolution leads to ever-increasing intermittency in the observed dynamical increasing intermittency in the observed dynamical

responseresponse

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OBSERVATIONAL FACTS: FRACTALITY, OBSERVATIONAL FACTS: FRACTALITY, MULTIFRACTALITY, TURBULENCEMULTIFRACTALITY, TURBULENCE

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SOLAE MAGNETIC FIELDS: MULTISCALINGSOLAE MAGNETIC FIELDS: MULTISCALING


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OBSERVATIONAL FACTS: OBSERVATIONAL FACTS: HIGHER-ORDER MULTISCALINGHIGHER-ORDER MULTISCALING

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SOLAR MAGNETIC FIELDS: MULTISCALINGSOLAR MAGNETIC FIELDS: MULTISCALING


Conlon et al. (2010)Conlon et al. (2010)

Wavelet transform Wavelet transform modulus maxima modulus maxima (WTMM) method(WTMM) method

h, D(h) --> multifractal h, D(h) --> multifractal scaling scaling spectra spectra

Solar magnetic fields Solar magnetic fields ““tested positivetested positive”” to to any mono- or multi-any mono- or multi-scaling method one scaling method one might devisemight devise

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OBSERVED BEHAVIOR OF POTENTIALLY OBSERVED BEHAVIOR OF POTENTIALLY FLARING VOLUMESFLARING VOLUMES

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SCALING OF FLARING VOLUMES: OBSERVATIONSSCALING OF FLARING VOLUMES: OBSERVATIONS


Fractality and power laws in the volume and Fractality and power laws in the volume and free energy of gradient-identified potentially free energy of gradient-identified potentially unstable structures unstable structures (Vlahos & Georgoulis 2004) (Vlahos & Georgoulis 2004)

Dimitropoulou et al. (2009)Dimitropoulou et al. (2009)

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MODELED BEHAVIOR OF FLARING VOLUMESMODELED BEHAVIOR OF FLARING VOLUMES

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SCALING OF FLARING VOLUMES: MODELSSCALING OF FLARING VOLUMES: MODELS


MacIntosh & Charbonneau (2001)MacIntosh & Charbonneau (2001)

Aschwanden & Aschwanden (2008)Aschwanden & Aschwanden (2008)

Clearly fractal flaring volumes in 3DClearly fractal flaring volumes in 3D

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STATISTICS OF SOLAR SUB-FLARES & FLARESSTATISTICS OF SOLAR SUB-FLARES & FLARES

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SOLAR FLARE STATISTICSSOLAR FLARE STATISTICS


Compilation of various statistical studies Compilation of various statistical studies ((Hannah et al. 2011Hannah et al. 2011))

Power-law statistics of events Power-law statistics of events

Well-defined, extended power-law Well-defined, extended power-law statistics reported for total flare statistics reported for total flare energy, peak luminosity, and energy, peak luminosity, and duration since the 1970duration since the 1970’’ss

Hannah et al. Hannah et al. (2011)(2011)

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WHAT LIES BEHIND THESE OBSERVABLES?WHAT LIES BEHIND THESE OBSERVABLES?-- -- ObservablesObservables::

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RECAP & INTERPRETATIONSRECAP & INTERPRETATIONS


-- -- InterpretationInterpretations:s:

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SELF-SIMILAR FLARE MODELSSELF-SIMILAR FLARE MODELS

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HISTORICAL, SELF-SIMILAR FLARE MODELSHISTORICAL, SELF-SIMILAR FLARE MODELS


• From a Poissonian flare-occurrence From a Poissonian flare-occurrence probability:probability:

Rosner & Vaiana Rosner & Vaiana (1978)(1978)

• To a power-law probability of flares To a power-law probability of flares with with energy between E and E+dE, if E >> energy between E and E+dE, if E >> EE0 0 ::

• Dependence of the PDF index on mean flaring rate and the systemDependence of the PDF index on mean flaring rate and the system’’s s stress rate αstress rate α• Criticism raised by future works, e.g. Lu & Hamilton - indeed, model was Criticism raised by future works, e.g. Lu & Hamilton - indeed, model was rather abstract rather abstract • Further works of the 1990Further works of the 1990’’s (e.g., RCS - Litvinenko 1994; 1996; master s (e.g., RCS - Litvinenko 1994; 1996; master equation - equation - Wheatland & Glukhov 1998; logistic equation - Aschwanden et al. 1998, etc.), Wheatland & Glukhov 1998; logistic equation - Aschwanden et al. 1998, etc.), all had all had pros and conspros and consClearly, more is needed than a simple, Clearly, more is needed than a simple, ““magicalmagical””

equation!equation!

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SELF ORGANIZATIONSELF ORGANIZATION

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SELF ORGANIZATIONSELF ORGANIZATION


Self-Organization: Reduction of the many degrees of freedom Self-Organization: Reduction of the many degrees of freedom exhibited by a complex system to a small number of exhibited by a complex system to a small number of significantsignificant degrees of freedom dictating the systemdegrees of freedom dictating the system’’s evolution (e.g. s evolution (e.g. Nicolis & Prigogine 1989)Nicolis & Prigogine 1989)

Flock of birds (Source: Youtube)Flock of birds (Source: Youtube)

• Competition between at least two parameters, or Competition between at least two parameters, or probabilitiesprobabilities

• System unstable, should any of these probabilities dominate System unstable, should any of these probabilities dominate

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PERCOLATION MODELS OF SOLAR PERCOLATION MODELS OF SOLAR ACTIVE-REGION EMERGENCE & EVOLUTIONACTIVE-REGION EMERGENCE & EVOLUTION

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PERCOLATION MODELSPERCOLATION MODELS


Seiden & Wentzel Seiden & Wentzel (1996)(1996)

-- Two -- Two primaryprimary competing probabilities: competing probabilities:

• PPstst : stimulation probability : stimulation probability• D : diffusion probabilityD : diffusion probability

-- Two secondary probabilities:-- Two secondary probabilities:

• PPspsp : probability of spontaneous emergence : probability of spontaneous emergence• PPmm : moving probability : moving probability

Simulated magnetic flux emergence and Simulated magnetic flux emergence and active-region formation in solar active-region formation in solar atmosphere - atmosphere - Implementation on cellular Implementation on cellular automata (CA) modelsautomata (CA) models

Wentzel & Seiden Wentzel & Seiden (1992)(1992)

Third-decimal digit changes in Third-decimal digit changes in stimulation and/or diffusion stimulation and/or diffusion

probability enough for the system to probability enough for the system to collapse (either die out or fill the collapse (either die out or fill the entire grid with magnetized cells)entire grid with magnetized cells)

(follow-up percolation models by MacKinnon, (follow-up percolation models by MacKinnon, MacPherson, Vlahos, etc.)MacPherson, Vlahos, etc.)

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PERCOLATION MODELSPERCOLATION MODELS


FLARE STATISTICS BY PERCOLATION MODELS?FLARE STATISTICS BY PERCOLATION MODELS?

Lower-boundary formed by Lower-boundary formed by percolation and LFF percolation and LFF extrapolation model defining extrapolation model defining the overlaying field the overlaying field (Fragos (Fragos et al. 2004)et al. 2004)

Energy Energy ““releaserelease”” episodes episodes due to lower-boundary due to lower-boundary dissipation and subsequent dissipation and subsequent extrapolation changes extrapolation changes (Fragos et al. 2004)(Fragos et al. 2004)

Power-law PDFs Power-law PDFs in event energy in event energy with index ~ -with index ~ -1.551.55

Plausible Plausible timeseries of timeseries of magnetic magnetic energy releaseenergy release

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SELF-ORGANIZED CRITICALITY (SOC) MODELSSELF-ORGANIZED CRITICALITY (SOC) MODELS

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SOC MODELSSOC MODELS


• Introducing criticality via a critical threshold, one alleviates the need Introducing criticality via a critical threshold, one alleviates the need for fine tuning for fine tuning • The system is The system is notnot followed from initial formation, but it is allowed to followed from initial formation, but it is allowed to evolve to the evolve to the SOC state.SOC state.• SOC is a robust state of statistical stationarity exhibited by systems SOC is a robust state of statistical stationarity exhibited by systems that are that are ““far far from equilibriumfrom equilibrium”” By definition, SOC applies to By definition, SOC applies to

randomly triggered instabilities for randomly triggered instabilities for which, however, there are which, however, there are

deterministic relaxation rulesdeterministic relaxation rules

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ORIGINAL SOC SOLAR-FLARE MODELS ORIGINAL SOC SOLAR-FLARE MODELS

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SOC FLARE MODELSSOC FLARE MODELS


-- Characteristics:-- Characteristics:

A state in which the system A state in which the system enters, but has no way of enters, but has no way of exiting. If external forcing exiting. If external forcing ceases, the system remains ceases, the system remains static.static.

-- The first model -- The first model (Lu & Hamilton 1991; Lu (Lu & Hamilton 1991; Lu et et al. 1993; Lu 1995)al. 1993; Lu 1995), in accordance with , in accordance with BTWBTW• Constant driver δConstant driver δΒ Β << critical threshold |<< critical threshold |BBcc||

• Randomly chosen point i perturbedRandomly chosen point i perturbed

• Local gradient calculated & compared to |Local gradient calculated & compared to |BBcc| |

• Isotropic redistribution rules if |dIsotropic redistribution rules if |dBBii| > || > |BBcc| |

• Elementary energy release per instability: Elementary energy release per instability:

• Flux conservation, avalanches, and a Flux conservation, avalanches, and a spectral spectral power of the form S(f) ~ fpower of the form S(f) ~ f-2 -2

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REVISED SOC SOLAR-FLARE MODELS REVISED SOC SOLAR-FLARE MODELS

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-- The second -- The second ““Statistical FlareStatistical Flare”” model model (Vlahos, (Vlahos, Georgoulis, et al.)Georgoulis, et al.)

• Constant driver δΒConstant driver δΒ << critical threshold B<< critical threshold Bcc

• Randomly chosen point i perturbedRandomly chosen point i perturbed

• Local gradient calculated & compared to BLocal gradient calculated & compared to Bc, c, both isotropically, and both isotropically, and anisotropically anisotropically

• Isotropic redistribution rules if dBIsotropic redistribution rules if dB i (isotropic)i (isotropic) > B > Bcc and anisotropic rules in case dB and anisotropic rules in case dB i i

(anisotropic)(anisotropic) > B > Bcc

• Elementary energy release per instability: Elementary energy release per instability:

SOC survived in this SOC survived in this ““unorthodoxunorthodox”” model, model, too!too!

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DIFFERENT FACES OF SOC DIFFERENT FACES OF SOC

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Vlahos et al. (1995)Vlahos et al. (1995)

--> Different avalanche attributes--> Different avalanche attributes

--> Single power-law PDF--> Single power-law PDF (Lu et al. 1993)(Lu et al. 1993)--> Double power-law PDF--> Double power-law PDF (Georgoulis & (Georgoulis & Vlahos Vlahos 1996)1996)

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FURTHER SOC CA REVISIONS: VARIABLE DRIVER FURTHER SOC CA REVISIONS: VARIABLE DRIVER

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• Constant Constant VariableVariable driver δΒ with PDF driver δΒ with PDF

with α --> free parameterwith α --> free parameter•For α ∈ [1.0, 2.5], SOC manages to For α ∈ [1.0, 2.5], SOC manages to

survivesurvive

Output power-law indices variable, and controlled by α!Output power-law indices variable, and controlled by α!

Georgoulis & Vlahos Georgoulis & Vlahos (1998)(1998)

Event PDFs for α=1.6Event PDFs for α=1.6

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EXTENDED CELLULAR AUTOMATA (X-CA) FLARE EXTENDED CELLULAR AUTOMATA (X-CA) FLARE MODELSMODELS

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X-CA SOC FLARE MODELSX-CA SOC FLARE MODELS


--> First effort to discretize the resistive term of the MHD induction --> First effort to discretize the resistive term of the MHD induction equation equation (Vassiliadis et al. 1998)(Vassiliadis et al. 1998)

Model setupModel setup

Inferred resistivity of Inferred resistivity of isotropic SOC models isotropic SOC models (Lu & Hamilton 1991 (Lu & Hamilton 1991 [LH91]; Lu et al. 1993 [LH91]; Lu et al. 1993 [L93], Georgoulis & [L93], Georgoulis & Vlahos (iGV)Vlahos (iGV)

Inferred resistivity of the Inferred resistivity of the anisotropic anisotropic anisotropic anisotropic SOC model of SOC model of Georgoulis & Vlahos Georgoulis & Vlahos (aVG)(aVG)

Isotropic SOC CA Isotropic SOC CA models resemble models resemble hyper-resistivity hyper-resistivity

conditions (η ∇conditions (η ∇22J), J), while nonlinear while nonlinear

resistivity (η J) is resistivity (η J) is exhibited by exhibited by

anisotropic SOC CA anisotropic SOC CA modelsmodels

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--> Solar-like magnetic field --> Solar-like magnetic field BB introduced, complete with knowledge of introduced, complete with knowledge of vector vector potential potential AA, where ∇ x , where ∇ x AA = = BB (Isliker et al. 2000; 2001)(Isliker et al. 2000; 2001)

--> Resistivity calculated, giving rise to current sheets and Ohmic --> Resistivity calculated, giving rise to current sheets and Ohmic dissipationdissipation

Envisioned (top) Envisioned (top) and achieved and achieved (bottom) (bottom) magnetic field magnetic field configurationconfiguration

Isliker et al. (2001)Isliker et al. (2001)

Distribution of (sub-critical) electric Distribution of (sub-critical) electric current density in the simulation current density in the simulation boxbox

Both isotropic and anisotropic SOC Both isotropic and anisotropic SOC rules were implemented, and SOC rules were implemented, and SOC managed to survivemanaged to survive

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--> SOC in a 2D loop geometry --> SOC in a 2D loop geometry (Morales & Charbonneau 2008; 2009)(Morales & Charbonneau 2008; 2009)

Basic model Basic model setup and setup and drivingdriving

The modelThe model’’s dynamical s dynamical responseresponse

Morales & Charbonneau (2008)Morales & Charbonneau (2008)

SOC manages to survive and, moreover, SOC manages to survive and, moreover, assigning typical coronal-loop values, assigning typical coronal-loop values, physical energy units appear for the first physical energy units appear for the first time. Inferred avalanche energies range time. Inferred avalanche energies range between 10between 102323 and 10 and 102929 erg. erg.

Other successful SOC X-CA approaches: Other successful SOC X-CA approaches: -- Using helicity and its conservation -- Using helicity and its conservation (Chou 1999)(Chou 1999)-- Using separator reconnection -- Using separator reconnection (Longcope & Noonan 2000)(Longcope & Noonan 2000) -- Using a statistical fractal-diffusive model -- Using a statistical fractal-diffusive model (Aschwanden 2012)(Aschwanden 2012)

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DATA-DRIVEN CA FLARE MODELS DATA-DRIVEN CA FLARE MODELS

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DATA-DRIVEN SOC FLARE MODELSDATA-DRIVEN SOC FLARE MODELS


--> SOC --> SOC achievedachieved using a single vector magnetogram of an observed using a single vector magnetogram of an observed solar active region - solar active region - ““StaticStatic”” integrated flare model (S-IFM) integrated flare model (S-IFM)

Avalanche relaxation in NOAA AR 10247Avalanche relaxation in NOAA AR 10247

Dimitropoulou et al. (2011)Dimitropoulou et al. (2011)

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

Haleakala IVMHaleakala IVM

--> NLFF field solution as an initial condition--> NLFF field solution as an initial condition--> LH driving and isotropic instability --> LH driving and isotropic instability criterioncriterion--> Critical threshold on the local field --> Critical threshold on the local field LaplacianLaplacian--> Physical units of energy released achieved --> Physical units of energy released achieved

Any initial valid field solution can Any initial valid field solution can be brought into the SOC statebe brought into the SOC state

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DATA-DRIVEN CA FLARE MODELS DATA-DRIVEN CA FLARE MODELS

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DATA-DRIVEN SOC FLARE MODELSDATA-DRIVEN SOC FLARE MODELS


--> SOC --> SOC survivedsurvived evolving via a timeseries of SOC-state magnetic field evolving via a timeseries of SOC-state magnetic field solutions - solutions - ““DynamicDynamic”” integrated flare model (D-IFM) integrated flare model (D-IFM) Dimitropoulou et al. (2012), A&A, submittedDimitropoulou et al. (2012), A&A, submitted

--> S-IFM applied to each magnetogram--> S-IFM applied to each magnetogram--> Discrete, Alfvén-timescale of spline---> Discrete, Alfvén-timescale of spline-interpolated interpolated evolution from one magnetogram to the other evolution from one magnetogram to the other --> Real time units for events--> Real time units for events ’’ onset onsetSingle-point driving abandoned in Single-point driving abandoned in

D-IFM. The entire grid receives D-IFM. The entire grid receives perturbations, perturbations,

yet SOC survivesyet SOC survives

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SUMMARY AND OVERARCHING QUESTIONS SUMMARY AND OVERARCHING QUESTIONS

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TOP-LEVEL SUMMARYTOP-LEVEL SUMMARY


Therefore, is SOC at work in solar active Therefore, is SOC at work in solar active regions?regions?

To find out, we should consider the following fundamental questions: To find out, we should consider the following fundamental questions: 1. 1. Critical thresholdCritical threshold: what is/are the critical threshold(s) for solar : what is/are the critical threshold(s) for solar flare flare occurrence? Does the system (i.e., an active region) reach occurrence? Does the system (i.e., an active region) reach minimal stability minimal stability with respect to that/those thresholds?with respect to that/those thresholds?

2. 2. Turbulence and SOCTurbulence and SOC: can a turbulent system exhibit avalanche : can a turbulent system exhibit avalanche behavior? behavior? Is active-region evolution reminiscent of this behavior?Is active-region evolution reminiscent of this behavior?

3. 3. Waiting-time distributionsWaiting-time distributions: what distribution form(s) should be : what distribution form(s) should be expected expected from a SOC system? Are observed distributions reminiscent of from a SOC system? Are observed distributions reminiscent of this? this?

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CRITICAL THRESHOLD: HOW ARE FLARES CRITICAL THRESHOLD: HOW ARE FLARES TRIGGERED? TRIGGERED?

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CRITICAL QUESTIONS FOR SOC APPLICABILITYCRITICAL QUESTIONS FOR SOC APPLICABILITY


Georgoulis, PhD Thesis (2000)Georgoulis, PhD Thesis (2000)

• Mean gradient or slope in SOC models Mean gradient or slope in SOC models manages to stabilize in SOC state manages to stabilize in SOC state • In real solar active regions we do not In real solar active regions we do not yet yet know (i) which parameter exhibits this know (i) which parameter exhibits this property, if any, and (ii) whether this property, if any, and (ii) whether this parameter can be calculatedparameter can be calculated

• Well-defined mean event (all sizes) Well-defined mean event (all sizes) frequency frequency in SOC statein SOC state• In real solar active regions we do not In real solar active regions we do not yet yet know (i) whether this feature exists, know (i) whether this feature exists, and and (ii) at what timescale (<< 11-year (ii) at what timescale (<< 11-year solar cycle) solar cycle) we should look for a well-defined mean we should look for a well-defined mean flare flare numbernumber

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TURBULENCE & SOC: TURBULENCE & SOC: COMPATIBLE OR CONFLICTING CONCEPTS? COMPATIBLE OR CONFLICTING CONCEPTS?

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Georgoulis, Velli, & Einaudi (1998)Georgoulis, Velli, & Einaudi (1998)

Event scaling lawsEvent scaling laws

Timeseries of mean Joule Timeseries of mean Joule dissipation rate dissipation rate 2.5D reduced MHD 2.5D reduced MHD

(RMHD - (RMHD - incompressible) systemincompressible) system

--> Some evidence of avalanching in a --> Some evidence of avalanching in a reduced reduced MHD (RMHD), incompressible turbulent MHD (RMHD), incompressible turbulent systemsystem--> However, incompressibility implies lack --> However, incompressibility implies lack of of magnetic energy storagemagnetic energy storage

Can we achieve avalanches in a Can we achieve avalanches in a fully compressible turbulent fully compressible turbulent

system? system?

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DOES CORONA EXHIBIT TURBULENCE AND SOC? DOES CORONA EXHIBIT TURBULENCE AND SOC?

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Threshold-dependent EUV coronal emissionThreshold-dependent EUV coronal emission

Uritsky et al. (2007)Uritsky et al. (2007)

and evidence for avalanching reminiscent and evidence for avalanching reminiscent of SOC behaviorof SOC behavior

--> However, this type of behavior is also exhibited by a well-known --> However, this type of behavior is also exhibited by a well-known intermittent intermittent turbulent model, even in 1D turbulent model, even in 1D (Watkins et al. 2009)(Watkins et al. 2009)

Question remains: Can turbulent systems also exhibit SOC? Question remains: Can turbulent systems also exhibit SOC?

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FLARE WAITING-TIME DISTRIBUTIONS: FLARE WAITING-TIME DISTRIBUTIONS: WHAT IS THEIR FORM AND WHAT IS EXPECTED? WHAT IS THEIR FORM AND WHAT IS EXPECTED?

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Flares are essentially random eventsFlares are essentially random events(Crosby et al. 1998)(Crosby et al. 1998)

Power-law PDF of waiting timesPower-law PDF of waiting times(Boffetta et al. 1999; Lepreti et (Boffetta et al. 1999; Lepreti et al. 2001)al. 2001)

Flare occurrence a non-Flare occurrence a non-stationary Poisson process stationary Poisson process (Wheatland 2000; 2001) (Wheatland 2000; 2001)

--> Isotropic LH and the Statistical Flare models favor --> Isotropic LH and the Statistical Flare models favor exponentialexponential waiting-times waiting-times distributions, distributions, indicating lack of memory and random flare occurrenceindicating lack of memory and random flare occurrence

--> --> However, there are indications that different driving mechanisms can give However, there are indications that different driving mechanisms can give rise to rise to different waiting-time distributions in a SOC system different waiting-time distributions in a SOC system (e.g., (e.g., Charbonneau et al. Charbonneau et al. 20012001)) Perhaps the specifics of waiting-time distributions is not Perhaps the specifics of waiting-time distributions is not

universal - generalized SOC models may account for universal - generalized SOC models may account for multiple cases!multiple cases!

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IF SOC IS AT WORK IN THE SOLAR ATMOSPHERE, IF SOC IS AT WORK IN THE SOLAR ATMOSPHERE, WHAT IS THE GAIN FROM ITS APPLICATION? WHAT IS THE GAIN FROM ITS APPLICATION?

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POTENTIAL BENEFITS FROM SOC APPLICATIONPOTENTIAL BENEFITS FROM SOC APPLICATION


What are the implications, or ramifications, of SOC What are the implications, or ramifications, of SOC validity?validity?• Deeper physical insight: how can cellular automata be Deeper physical insight: how can cellular automata be

further refined or generalized to account for more further refined or generalized to account for more observed properties?observed properties?

• Implications for coronal heating: a Implications for coronal heating: a ““softsoft”” nanoflare nanoflare population? population?

• Loss-of-equilibrium models of solar eruptions: a tell-Loss-of-equilibrium models of solar eruptions: a tell-tale SOC sign?tale SOC sign?

• SOC ramifications for solar flare forecasting: can flares SOC ramifications for solar flare forecasting: can flares be truly predicted?be truly predicted?

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GENERALIZATION OF CELLULAR AUTOMATA MODELS GENERALIZATION OF CELLULAR AUTOMATA MODELS

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--> What would be the optimal course of action in terms of cellular --> What would be the optimal course of action in terms of cellular automata? automata? • More physics-based, concept-oriented CAs (free energy, helicity, More physics-based, concept-oriented CAs (free energy, helicity,

stress, stress, tension, shear, twist, etc? - tension, shear, twist, etc? - Morales & Charbonneau, Chou, Longope & Morales & Charbonneau, Chou, Longope & NoonanNoonan

• Discrete, MHD-coupled cellular automata? - Discrete, MHD-coupled cellular automata? - Vassiliadis, Isliker, et al. Vassiliadis, Isliker, et al.

• Data-driven cellular automata? - Data-driven cellular automata? - Dimitropoulou et al. Dimitropoulou et al. Can the emphasis of cellular automata be shifted from statistics Can the emphasis of cellular automata be shifted from statistics to physics, to physics,

with physical units and even predictive power, with the with physical units and even predictive power, with the computational computational

convenience that automata traditionally have compared to MHD convenience that automata traditionally have compared to MHD models?models?

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A A ““SOFTSOFT”” NANOFLARE POPULATION? NANOFLARE POPULATION?

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GRANAT/WATCH flare GRANAT/WATCH flare PDFsPDFs

Statistical Flare Statistical Flare model reproductionmodel reproduction

Georgoulis et al. Georgoulis et al. (2001)(2001)

Besides the reproduced Besides the reproduced sizable flares, SOC sizable flares, SOC anisotropic relaxation criteria anisotropic relaxation criteria predict a soft small-event predict a soft small-event population. Does it really population. Does it really exist?exist?

Recent statistical studies Recent statistical studies have yet to identify this have yet to identify this population for population for ““smallsmall”” flares, flares, ““microflaresmicroflares””, or , or ““subflaressubflares””

• However, how small is However, how small is ““smallsmall””??• Can the soft population be Can the soft population be hidden underneath the big hidden underneath the big events?events?

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A HIDDEN A HIDDEN ““SOFTSOFT”” NANOFLARE POPULATION? NANOFLARE POPULATION?

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Shorter events in the WATCH/GRANAT Shorter events in the WATCH/GRANAT database obey steeper power lawsdatabase obey steeper power laws

And this is also reproduced by the And this is also reproduced by the Statistical Flare model, albeit more Statistical Flare model, albeit more pronounced pronounced

Georgoulis et al. (2001)Georgoulis et al. (2001)

It is possible that It is possible that ““nanoflaresnanoflares””, or even , or even ““picoflarespicoflares””, , are there, partially hidden and/or unobserved, with are there, partially hidden and/or unobserved, with

scaling indices steeper than -2 to sustain a significant scaling indices steeper than -2 to sustain a significant thermal heating hypothesisthermal heating hypothesis

(Hudson 2001)(Hudson 2001)

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LOSS-OF-EQUILIBRIUM SOLAR ERUPTION MODELS LOSS-OF-EQUILIBRIUM SOLAR ERUPTION MODELS

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If the loss-of-equilibrium, or If the loss-of-equilibrium, or ““catastrophecatastrophe”” models of solar flares models of solar flares (Forbes & Isenberg (Forbes & Isenberg 1991)1991) are of any validity, can this be a are of any validity, can this be a tell-tale signature of a SOC system? tell-tale signature of a SOC system?

Hinode/SOT Ca 3968.5 A

Lin & Forbes (2000)Lin & Forbes (2000)

--> Loss of equilibrium reminds us of marginal stability--> Loss of equilibrium reminds us of marginal stability--> If so, what is the critical parameter?--> If so, what is the critical parameter?--> Can we justify and record the course of an eruptive active region --> Can we justify and record the course of an eruptive active region to marginal to marginal stability?stability?--> Many candidates: electric currents, resistivity, non-potential --> Many candidates: electric currents, resistivity, non-potential magnetic energy, magnetic energy, magnetic (or current) helicity, etc.magnetic (or current) helicity, etc.

35BERN, 15 -19 OCT, BERN, 15 -19 OCT, 20122012



IN SUPPORT OF THE MARGINAL STABILITY CONCEPT IN SUPPORT OF THE MARGINAL STABILITY CONCEPT

The free magnetic The free magnetic energy - relative energy - relative magnetic helicity magnetic helicity diagram of solar diagram of solar active regionsactive regions

Tziotziou et al. (2012)Tziotziou et al. (2012)

--> Eruptive active regions tend to exceed well-defined thresholds in both free --> Eruptive active regions tend to exceed well-defined thresholds in both free magnetic magnetic energy and relative magnetic helicityenergy and relative magnetic helicity--> Can these thresholds be shown to bring the system into marginal stability --> Can these thresholds be shown to bring the system into marginal stability under SOC?under SOC?--> If so, what is the driver? - FYI, --> If so, what is the driver? - FYI, Georgoulis, Titov, & Mikic, 2012, ApJ, in pressGeorgoulis, Titov, & Mikic, 2012, ApJ, in press

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SOC RAMIFICATIONS FOR SOLAR FLARE SOC RAMIFICATIONS FOR SOLAR FLARE FORECASTING FORECASTING

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--> The classical SOC concept implies spontaneity in the system--> The classical SOC concept implies spontaneity in the system ’’s s dynamical dynamical responseresponse--> Therefore, if solar active regions, manifesting multiscaling --> Therefore, if solar active regions, manifesting multiscaling behavior, are in a behavior, are in a SOC state, can flares/eruptions be predicted? SOC state, can flares/eruptions be predicted?

• In a recent work (Georgoulis, 2012) it has been shown that flaring and non-flaring active regions show similar measures of fractality / multifractality

• As a result, multiscale methods cannot be used for flare prediction

•This conclusion, however, is subject to the outcome of the debate on waiting time distributions - notice also the work of Dimitropoulou et al. (2009) showing lack of correlation between photospheric and coronal fractal properties Flare prediction may remain inherently probabilistic!

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• 17733 SoHO/MDI magnetograms• 370 AR timeseries BERN, 15 -19 OCT, BERN, 15 -19 OCT,

20122012



PREDICTIVE ABILITY OF MULTISCALE METHODS PREDICTIVE ABILITY OF MULTISCALE METHODS

Georgoulis (2012)Georgoulis (2012)

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PREDICTIVE ABILITY OF MULTISCALE METHODS PREDICTIVE ABILITY OF MULTISCALE METHODS

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•The unsigned magnetic flux, a conventional predictor used as reference, works better than multiscale parameters - these parameters, therefore, cannot be used for flare prediction

•Multiscaling behavior is widespread in flaring and non-flaring ARs alike

Georgoulis (2012)Georgoulis (2012)

Does this mean that Does this mean that flaring and non-flaring flaring and non-flaring active regions might be active regions might be in a similar - in a similar - indistinguishable - SOC indistinguishable - SOC state (state (Vlahos & Vlahos & Georgoulis 2004Georgoulis 2004) ?) ?

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CONCLUSIONS CONCLUSIONS

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CONCLUSIONCONCLUSION


Overarching question / food for thought: Overarching question / food for thought: at what extent, if any, is SOC valid in solar active-region at what extent, if any, is SOC valid in solar active-region

magnetic fields? magnetic fields?

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How do we know that the creations of worlds are How do we know that the creations of worlds are not determined by falling grains of sand? Who can not determined by falling grains of sand? Who can

understand the reciprocal ebb and flow of the understand the reciprocal ebb and flow of the infinitely great and the infinitely small, the infinitely great and the infinitely small, the

echoing of causes in the abyss of being and the echoing of causes in the abyss of being and the avalanches of creation? avalanches of creation?

Victor Hugo, Victor Hugo, Les MisérablesLes Misérables

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BACKUP SLIDESBACKUP SLIDESBACKUP SLIDESBACKUP SLIDES

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STATISTICS OF OTHER SOLAR DYNAMICAL STATISTICS OF OTHER SOLAR DYNAMICAL PHENOMENAPHENOMENA

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SOLAR FLARE STATISTICSSOLAR FLARE STATISTICS


-- Active-region sizes-- Active-region sizes-- Quiet Sun fields-- Quiet Sun fields-- Ellerman bombs -- Ellerman bombs -- ARTBs-- ARTBs-- etc.-- etc.

1 Self-Organized Criticality in the Solar Atmosphere: Universal Property of Solar Magnetism, Or...

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