Nanoflares and MHD turbulence in Coronal Loop: a Hybrid Shell Model

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Nanoflares and MHD turbulence in Coronal Loopa
Hybrid Shell Model

• Giuseppina Nigro,
• F.Malara, V.Carbone, P.Veltri

Dipartimento di Fisica
Università della Calabria
Chalkidiki, September 2003
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A Statistical approach to Solar Flares
Ratio of EIT full Sun images in Fe XII 195A to Fe
IX/X 171A Temperature distribution in the Sun's
corona - dark areas cooler regions - bright
areas hotter regions
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Power laws for statistics of events
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Parkers conjecture (1988)
Nanoflares correspond to dissipation of many
small current sheets, forming in the bipolar
regions as a consequence of the continous
shuffling and intermixing of the footpoints of
the field in the photospheric convection.
Current sheets tangential discontinuity which
become increasingly severe with the continuing
winding and interweaving eventually producing
intense magnetic dissipation in association with
magnetic reconnection.
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Waiting time distribution
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Parkers conjecture modified
Nanoflares correspond to dissipation of many
small current sheets, forming in the nonlinear
cascade occuring inside coronal magnetic
structure as consequence of the power input in
the form of Alfven waves due to footpoint
motiont.
Current sheets coherent intermittent small scale
structures of MHD turbulence
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MHD equations in the wave vector space
For s , -
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Solar Flares intermittent dissipative events
within MHD turbulence?
The time between two bursts is t, we calculate
the pdf p(t).
1) Total energy of bursts 2) Time duration 3)
Energy of peak
In all cases we found power laws.
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The Hybrid Shell Model
Limitations of classical Shell Model

• Associated with incompressible fluids (?gtgt1)
• Shell models do not give any information on
  spatial structure (the energy input from
  photospheric motions is
• 
  delocalized in space)

To take into account

• Corona cold plasma (?ltlt1)
• Geometry associated with coronal magnetic
  structures
• High magnetic field B0 along the loop

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MHD Turbulence in Coronal Loops

• Alfven wave propagation along background magnetic
  field
• Incompressible MHD in perpendicular direction
  were non linear couplings
• 
  
  take place

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A Hybrid Shell Model
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Space dependence along B0 allows to chose
boundary conditions
A random gaussian motion with autocorrelation
time tc 300 s is imposed at the lower boundary
only on the largest scales
The level of velocity fluctuations at lower
boundary is of the order of photospheric
motions dv 5 10-4 cA 1 Km/s
Model parameters L 3 104 Km, R 6, cA
2 103 Km/s
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• A Kolmogorov spectrum is formed mainly on kinetic
  energy
• Magnetic energy dominates with respect to kinetic
  energy ?forcinggtgt TACA/L
• The velocity fluctiation in the loop are larger
  two orders of magnitude with
• 
  respect to photospheric motions

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Energy balance
After a transient a statistical equilibrium is
reached between incoming flux, outcoming flux and
dissipation.
The level of fluctuations inside the loop is
considerably higher than that imposed at the
lower loop boundary.
Dissipated power displays a sequence of spikes.
About 60 of the energy which enter the sistem is
dissipated while about 35 propagate outside.
Averege flux and dissipation tend to cancel out.
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Power laws are recovered on Power peak, burst
duration, burst energy and waiting time
distributions
The obtained energy range correspond to nanoflare
energy range
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CONCLUSIONS
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