Distribution of the magnetic flux in elements of the magnetic field in an active region

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Distribution of the magnetic flux in elements of
the magnetic field in an active region

• Valentyna Abramenko
• Big Bear Solar Observatory, NJIT

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INTRODUCTION
Turbulent flows in the photospheric plasma
Braiding and intertwining of magnetic flux tubes
Heating of the corona (Parker, 1996)
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INTRODUCTION
Magnetic coupling between the photosphere and the
corona
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INTRODUCTION
The distribution function of the magnetic flux
content in flux concentrations in the
photosphere Previous studies - Wang, J.X.,
Wang H., Tang, Lee, Zirin 1995, Sol. Phys 160 the
flux range (0.01-10)1018 Mx quiet sun
areas Power Law with the index 1.67
(intranetwork) and 1.27(network) Schrijver,
Title, van Ballegooijen, Hagenaar, Shine 1997 the
flux range(0.7-5)1018 Mx quiet sun
areas Exponential approximation Schrijver,
Title, Hagenaar, Shine 1997, Sol.Phys.175 ( the
flux range (0.7-150)1018 Mx quiet sun plage
areas outside sunspots Exponential approximation
with the varying index Abramenko present
study the flux range (0.2-250)1018 Mx active
region Lognormal Power Law
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Observational data
248 high resolution SOHO/MDI magnetograms of
active region NOAA 9077 obtained on July 14, 2000
between 0626UT and 1100UT. The entire area of
the active region (145x145 arcsec or 250x250
pixels) was analyzed.
Processing - A 3-point running mean procedure -
An absolute value of the magnetic field density,
i.e. an unsigned flux.
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Two codes to determine flux concentrations
The Circle code
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Probability Distribution Function
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Probability Distribution Function
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Probability Distribution Function
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Probability Distribution Function
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Probability Distribution Function
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Probability Distribution Function
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Lognormal Distribution Function
m and s2 are the mean and the variance of the
Gaussian distribution of log(?)
The expected value
The variance
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Probability Distribution Function
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Discussion

• I. Longcope, Mc Leish Fisher (2003, ApJ 599)
  
• a viscoelastic theory of interaction
  between turbulent flows and fibril magnetic
  fields. The theory is based on an assumption of a
  back-reaction of fibrils on the plasma flow. All
  aspects of the viscous back-reaction depend on
  the distribution function of the magnetic flux in
  fibrils.
• An ensemble of log-normally-distributed flux
  tubes will provide viscous back-reaction larger
  than predictions based on exponential
  distributions.

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Discussion

• What does the lognormal distribution imply?
• When a random variable u is a product of a large
  number of independent random variables
• uu1 u2 u3
  un ,
• then log(u) is a sum of a large number of
  independent variables
• log(u)log(u1 ) log(u2 )log(u3
  ) log( un )
• And log(u) produces a normal (Gaussian)
  distribution. Then it is said that u has a
  lognormal distribution.
• This kind of random variables arises , in
  particular, through the fragmentation process.

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Discussion
III In the solar photosphere and convective
zone - fragmentation through the turbulent
diffusion - concentration at convergence
points of the flows. PetrovayMoreno-Insertis(1997
) in inhomogeneous and/or non-stationary
situation, turbulent diffusion dominates over
concentration causing a turbulent erosion of
magnetic flux tubes. Simon Leighton (1964)
observations of a gradual disintegration of
sunspots due to erosion of penumbral
boundaries. Bogdan, Gilmar, Lerche, Howard
(1988) observed lognormal distribution
of areas of sunspot umbra. Fragmentation of
magnetic elements may be the essential process in
the formation of an observed magnetic structure.
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