Nouvelle mod

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Anisotropic braiding avalanche model for solar
flares A new 2D application
Laura F. Morales Canadian Space Agency /
Agence Spatiale Canadienne Paul Charbonneau
Département de Physique, Université de
Montréal Markus Aschwanden
Lockheed Martin, Adv. Tec. Center,
Solar and Astrophysics
Lab.
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Outline
Solar Flares Observations Classical Th.
Models SOC paradigm The sandpile model SOC
Solar Flares Lu Hamilton's classic
model New SOC model for solar flares
Cellular Automaton Statistical results
Spreading exponents Expanding the model
capabilities Temperature
Density
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Sun's Atmosphere
PHOTOSPHERE CHROMOSPHERE SOLAR CORONA
Sunspots Granules Super-granules Spicules
Filaments Active regions Loops Solar
Flares Etc.
http//www-istp.gsfc.nasa.gov/istp/outreach/images
/Solar/Educate/atmos.gif
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...a solar flare is a process associated with a
rapid temporary release of energy in the solar
corona triggered by an instability of the
underlying magnetic field configuration
M-Class Flare - STEREO (March, 25 2008)
EUV http//stereo.gsfc.nasa.gov/img/stereoimages/m
ovies/Mflare2008.mpg
X-Class Flare - SOHO (November, 4 2003)
http//sohowww.nascom.nasa.gov/gallery/Movies/EIT
X27/StormEIT195sm.mpg
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tonset 1-2s - tthermalization 100s
tdiffusion 1016-18 s in the solar corona
another mechanism
Magnetic Reconnection
http//www.sflorg.com/spacenews/images/imsn051906_
01_04.gif
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Parker's Model for solar flares

• Spontaneous Current Sheets in Magnetic Fields
  With Applications to Stellar X-rays
• (Oxford U. Press 1) Figure 11.2

http//helio.cfa.harvard.edu/REU /images/TRACE171_
991106_023044.gif
High conductivity
B0 uniform
Photospheric motions shuffle the footpoints of
magnetic coronal loops
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Solar Flares Energy Liberation
Solar Corona Storage of Magnetic Energy
Magnetic reconnection
Very small ?
Photosphere Injection of kinetic Energy
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Energy is released in a wide range of
scales 1024-1033 ergs
Power law ? self similar behavior
(Dennis 1985, Solar Phys., 100, 465)
TURBULENCE OR SELF ORGANIZED CRITICALITY?
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SOC Solar Corona
? instability threshold Critical Angle
Slowly driven open system Photospheric motions
Intermitent release of energy Magnetic
Reconnection Statistically stationary state the
solar corona is an statistically
stationary state
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How can we obtain predictions by using this model?
Integrate MHD aquations
tflare seconds LB 1010 cm tphotosphere hs
Cellular automaton-like simulations
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Classic SOC Models

• Each node is a measure of the B
• B(0)0
• Driving mechanism add perturbations at some
  randomly selected interior nodes
• Stability criterion associated
• to the curvature of B

(Charbonneau et al. SolPhys, 203321-353, 2001)
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soc
Time series of lattice energy energy
released for the avalanches produced by 48 X 48
lattice (Charbonneau et al. SolPhys,
203321-353, 2001)
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Probability Distributions
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Classic SOC Models Ups
Successfully reproduced statistical properties
observed in solar flares ? pdfs
exhibiting power law form ? good
predictions for exponents aE, aP, aT
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Classic SOC Models Downs

• 1. No magnetic reconnection
• 2. Link between CA elements MHD
• If Bk ? B ? ?.B ? 0
• If Bk ? A ? ?.B ? 0 solved
• ?A interpreted as a twist in the magnetic
  field
• ?Bk2 is no longer a measure of the
  lattice energy
• 3. No good predictions for ?A

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NEW MODEL (2008)
Threshold ? ? ?1 ?2 angle formed by 2
fieldlines
Lattice perturbation
Lattice Energy ? Li(t)2
i
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Reconnect
_at_ (1,3)
One-step redistribution
E1.25E0
Elim/reduce angle
E 1.22 E0
Perturbation starts again
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Reconnect
E 1.32E0
(3,2) unstable
Two-step redistribution
? (3,1)
Perturbation starts again
E 1.19E0
E1.4E0
E1.19E0
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The lattice in action
64 x 64
32 x 32
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Lattice Energy Released Energy
SOC
Morales, L. Charbonneau, P. ApJ. 682,(1),
654-666. 2008
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Morales, L. Charbonneau, P. ApJ. 682,(1),
654-666. 2008
1.54
1.40
1.79-2.11
1.7
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Morales, L. Charbonneau, P. ApJ. 682,(1),
654-666. 2008
1.15 2.93
1.70
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Area covered by an avalanche a movie
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Area covered by Avalanches
t0 30
t0 116 tmax
unstable (12,2)
Peak Area
t0
Time integrated Area
unstable (10,1)
t0 150
tf t0 332
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Geometric Properties
Morales, L. Charbonneau, P. GRL., 35, L04108
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Spreading Exponents
Number of unstable nodes at time t
Probability of existence at t
Size of an avalanche death by t
k
Probability of an avalanche to reach a size S
b
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Morales, L. Charbonneau, P. GRL., 35, L04108
Just an example
128 x 128 ?c2.5
? 0.090.02
? 1.1 0.1
? 1.830.25
? 1.700.2
?th1 ? ? 2.190.1
?th(1 ?2 ?)/ ?th 1.48 0.01
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fold
From a 2D lattice to a loop
bend
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Avalanching strands in the loop
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Projection
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Projections
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Geometrical properties for the projected areas
?A 2.39 0.05
?A 1.84 0.07
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N32

N64
N D (stretch1) D (stretch10)
32 1.26 0.04 1.21 0.04
64 1.21 0.04 1.23 0.04
128 1.20 0.03 1.25 0.05
Observations
1 1.93
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Another way of looking at the simulations
Near vertical current sheet that extends from
the coronal reconnection regions to the
photospheric flare ribbons
mapped into
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Temperature Density Evolution

• The maximum loop temperature based on the maximum
  heating rate and the loop length for uniform
  heating case

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Temperatures
Avalanche duration 106 it.
Avalanche duration 138 it.
N64 THR2 51013 avalanches in 4e5 iterations
Max duration 700 it
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Density


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Coming up..
With the temperature T(t) and density evolution
n(t) of each avalanche we can compute the
resulting peak fluxes and time durations for a
given wavelength filter in EUV or SXR, because
for optically thin emission we just have I(t)
? n(t)2 w R(T) dT w is the loop width R(T) is
the instrumental response function. We can plot
the frequency distributions of energies W
E_Hmax duration peak fluxes (I_EUV, I_SXR)
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Conclusions
The new cellular automaton we introduced and
fully analyzed represents a major breakthrough in
the field of self-organized critical models for
solar flares since

• Every element in the model can be directly mapped
  to Parker's model for solar flares thus solving
  the major problems of interpretation posed by
  classical SOC models.
• For the first time a SOC model for solar flares
  succeeded in reproducing observational results
  for all the typical magnitudes that characterize
  a SOC model E, P, T, ?T the time integrated A
  and the peak A.