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The Search for Units: A Gradient Distribution route to Multifractality in Solar Magnetic Fields R.T. James McAteer New Mexico State University 1
The Search for Units: A Gradient Distribution route to Multifractality in
Solar Magnetic Fields
R.T. James McAteerNew Mexico State University
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Maybe SOC?Scale free, maybe SOC
Fractals, maybe SOC
Units, in SOC
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The Why and The How
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Connection to SOCallows for energy build up over timescales much longer than energy release
allows for a system to approach SOC
requires a threshold in ‘energy’ which must be followed by a release of energy
dictates energy output sizescales much less than spatial scale of system. 5
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Scale free, maybe SOC?
Abramenko 2002, 2005, 2006Hewett, McAeer et al., 2008
E(k) ~ k-a
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Scale free, maybe SOC
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Scale free, maybe SOC
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Scale free, maybe SOC
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Scale free, maybe SOC
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Fractals, maybe SOCMcAteer et al., 2005
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Fractals, maybe SOCMcAteer et al., 2005
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Fractals, maybe SOCMcAteer et al., 2005
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Fractals, maybe SOCMcAteer et al., 2005
2700 days9300 images
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Units, in SOC
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gradients, gradients, gradients,...
Sammis et al, ApJ, 2000, 540, 587Schrijver, ApJ, 2007, 655, L117Falconer et al., ApJ, 2008, 689, 1433Al-Ghraibai, Boucheron, McAteer, ApJ, 201316
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gradients, gradients, gradients
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dB/dx, dB/dy
Jz
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Size of gradientSize of gradient at each scale
0 0.5 1.0
#or
D(h)
h
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Wavelet Transform Modulus Maxima
(1) Take a *multiscale* gradient(2) At the smallest spatial, detect a strong gradient.(3) Track this gradient up through each size scale. (4) Calculate partition function
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The quiet Sun
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Wavelet Transform Modulus Maxima
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New flux arises near to ‘strong’ gradientsNew gradients arise near ‘strong’ gradients
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Maybe SOC?
Scale free, maybe SOC
Fractals, maybe SOC
Units, in SOC
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ProblemsWe’re measuring the wrong part of the active region?
Energy build up in transverse component of magnetic field.
Magnetic field in corona is where the flare occurs.
We only measure the driver of the build up of energy.
What is the appropriate time scale?Sun doesn’t care what is happening on 24 hour timescale.
Is there a strong solar cycle dependence?
Flaring is non-Poisson - events are not independent.
What is a big flare?What is the total energy in an event? How is this distributed between radiation, particle, coronal mass ejection, etc..?
Careful not to succumb to big-flare syndrome
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Looking forwardDetection of energy release mechanism.
how much energy is available?
how much energy is released?
how much energy is needed to maintain a stable active region?
Predictions over appropriate timescales.
How do we combine the maximum predictive timescale of each measure and flare size?
ConclusionsThe multifractal spectrum is a number distribution of gradient persistence to high spatial scales
higher h, higher D, more energy build up
pointer to further flux emergence and gradient build up
this may the connection to resulting flares.
Is there a maximum predictive timescale of each measure?
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Accuracy depends: predict X class / fast CME (HSS 0.7) 12 hourspredict C class (HSS 0.65) over 72 hours.
Bloomfield et al, ApJ, 2012Also Poster Session 6.1
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Questions
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What about some Units?Multifractal spectrum is directly related to the distribution of gradients
Magnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm)
StrengthStrengthMagnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm) 300 25
#5 D=1.2 D=1.0
#25 D=1.45 D=1.2
Magnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm)
StrengthStrengthMagnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm) 300 25
#4 D=1.3 D=1.0
#20 D=1.45 D=1.1
Magnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm)
StrengthStrengthMagnetic Gradients(G / Mm)
Magnetic Gradients(G / Mm) 300 25
#2 D=1.4 D=1.0
#10 D=1.45 D=1.05
2 pixels
16 pixels4 pixels
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Where are the gradients? Abramenko, 2005, ApJ
Hewett, Gallagher, McAteer, et al., 2008, Solar Physics, 248, 311
Size Scaling index related to structure function
Ireland, Young, McAteer, et al., 2008, Solar Physics, 252, 121
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Outline
The promise of flare prediction
The premise of flare prediction
The problems of flare prediction
The promise of flare prediction
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The promise of flare prediction
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“Big and Ugly’
Prediction requires understanding
The promise of flare prediction
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Outline
The promise of flare prediction
The premise of flare prediction
The problems of flare prediction
The premise of flare prediction
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The premise of flare prediction
Big and Ugly?
Global properties are useful
Local properties are key
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The premise of flare predictionAbramenko, ApJ, 2005Conlon, McAteer et al., ApJ, 2010
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The premise of flare prediction
What flare size?
What timescale?
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The premise of flare prediction
Paul Higgins 2009
Leka & Barnes ApJ, 2003Higgins et al, ASR, 2010
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The premise of flare prediction
Paul Higgins 2009
What flare size?
What timescale?
What parameters matter?
What is accurate flare prediction?
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Outline
The promise of flare prediction
The premise of flare prediction
The problems of flare predictionThe problems of flare prediction
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Conclusions
Progress is significant
solar cycle of synoptic data
Combination of local and global properties works at HSS score of 0.8
Looking forward to full disk vector data.
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