Auroral Complexity

1
Auroral Complexity

• Mervyn Freeman
• Thanks toNick Watkins, Steve Morley, and many
  others

2
Auroral Complexity

• Traditional reductionist view - the auroral zoo
• New holistic view based on complexity theory
• fractal aurora
• breakdown of fractality at system scale
• Physical models
• self-organised criticality, turbulence,
  percolation
• Comparative auroras open questions?
• Conclusions

3
Reductionist view

• Over the years, certain auroral structures have
  been identified at different spatial and temporal
  scales
• curl
• spiral
• omega band
• trans-polar arc
• westward travelling surge
• poleward boundary intensifications
• substorm bulge
• etc

4
Complicated aurora

• However, if we look at aurora as a whole (over
  all time and space) we get another picture
• many unidentified structures
• dynamic
• wide range of scales
• interaction between scales
• How can we study such behaviour?
• Does it have simplifying descriptions and
  explanations?

Movie of aurora above the northern
hemisphere Taken by Ultra-Violet Imager on NASA
Polar satellite, 1001-2302 UT, 10 January
1997 Courtesy G. Parks, UC Berkeley
5
Complexity
Periodic

• Behaviour of systems with many interacting parts
• non-equilibrium
• non-linear
• Lies between the steady-state, periodic and
  random ideals that most scientists like to
  explain!
• Involves behaviour of the whole, not just one
  part or limited set of parts
• holistic, not reductionist
• whole greater than sum of parts

Complex
Random
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A Hope

• The simplicity of nature is not to be measured
  by that of our conceptions. Infinitely varied in
  its effects, nature is simple only in its causes,
  and its economy consists in producing a great
  number of phenomena, often very complicated, by
  means of a small number of general laws
• Pierre Laplace (1749-1827)

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Methodology

• Complex systems may have universal properties and
  models
• how the many parts interact, not what those parts
  actually are
• Universal properties
• non-Gaussian, long-range correlated, self-similar
  (scale-free)
• Universal models
• random walks, fractals, networks, Self-Organised
  Criticality

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Complex aurora

• Structure can be studied using methods of
  statistical physics
• Track bright patches in the aurora in time and
  space
• Spacecraft imager Uritsky et al., 2002
• All-sky imagerKozelov et al., 2004
• Aurora is fractal
• no characteristic duration or size
• for any given duration there are
• 5 times fewer patches that last twice as long and
  
• 5 times more patches that last half as long
• similarly for area

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Complex Auroral Currents

• Similar structure previously observed in Auroral
  Electrojet (AE) indices
• Track magnetic disturbance from peak auroral
  currents
• AU eastward current
• AL westward current
• Measure durations of bright patches in auroral
  currents
• when AU or AL above arbitrary fixed threshold

auroral patch motion

• AE stations

Locations of AE index stations relative to
possible moving auroral patch
Example of thresholding data to find bright
patch duration
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Complex auroral currents

• Probability density function (PDF) comprises two
  componentsFreeman et al, Geophys Res Lett,
  2000
• Fractal aurora
• power law (exponential truncation)
• driven by solar wind?
• Substorm
• lognormal centred on 1-2 h
• dominant in nightside AL index
• Substorm component not reported in auroral imager
  analysis
• short, non-continuous observation

PDF of durations above threshold for AU and -AL
index Using thresholds at median of cumulative
distribution function Dashed curves are a power
law with exponential cut-off and a lognormal.
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Emergent substorm

• Substorm is not part of fractal aurora
• has characteristic scale
• global-scale energy release event
• May allow deterministic description
• Minimal substorm modelFreeman and Morley, GRL,
  2004
• simple integrate-and-fire model
• explains waiting time between substorms
• Also explains substorm occurrence at
  JupiterKronberg et al, in preparation, 2006
• and neuron activity in flys brain!

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Complex auroral convection

• Structure function analysis of auroral convection
  measured by SuperDARNAbel and Freeman, 2006
• Non-Gaussian distribution of velocity
  fluctuations at different spatial separations
• Can be re-scaled by power-law transformation
• Velocity fluctuations are fractal in space and
  time

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Fractals Wheres the physics?Kadanoff, 1986

• Shown fractal structure of auroral intensity,
  currents and convection
• Physical mechanisms for spatio-temporal
  fractality include
• Self-Organised CriticalityChang, IEEE Trans.
  Plasma Sci., 1992
• non-linear diffusion
• TurbulenceDungey, Phys. Rev. Lett, 1961
  Coleman, Astrophys. J., 1968
• non-linear advection
• PercolationMilovanov et al., J. Geophys. Res.,
  2001
• critical branching (paths through randomly
  defected media)

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Comparative auroras questions

• Are all planetary auroras fractal up to the
  system scale?
• Do they belong to the same universality class?
• Does minimal substorm model explain substorm
  occurrence at Saturn, mini-magnetospheres, etc

• Please help me to find out!
• Planetary science community has exciting data to
  provide answers

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Conclusions

• New holistic view of aurora based on complexity
  theory
• complementary to traditional reductionist
  approach
• Auroral intensity, current and convection are
  fractal in time and space
• self-similar from seconds to hours, 1 km to
  global scale (1000 km)
• Possible models SOC, turbulence, percolation
• Breakdown in fractality at global scale
  substorm
• Mimimal substorm model explains substorm waiting
  times
• Complexity gives new ideas for familiar earth
  system problems
• Can these be helpful for understanding planetary
  aurora too?
• MSM explains substorm occurrence at Jupiter