Statistical studies of the evolution of magnetic fields in the sun

1
Statistical studies of the evolution of magnetic
fields in the sun

• Loukas Vlahos
• Department of Physics,
• University of Thessaloniki, Greece
• (vlahos_at_astro.auth.gr)

2
Outline

• Introductory remarks
• Key observations
• Sub-photospheric evolution of magnetic fields
• Formation and evolution of active regions
  (photosphere)
• Coronal evolution of magnetic fields
• Summary

3
Introduction(a few well accepted facts)

• Active regions are diagnostics of
  sub-photospheric activity
• Active regions reflect (heating and flaring) the
  dynamic interaction of magnetic fields with the
  turbulent convection zone
• Flux tubes generated initially at the base of the
  convection zone rise to the surface by buoyant
  forces.

4
Introduction(a few well accepted facts)

• The flux tubes during their buoyant rise to the
  surface are influenced by several physical
  effects e.g. Coriolis force, magnetic tension,
  drag and most importantly the convection motion.

5
A working hypotheses
6
Key observations to constrain the models

• Size distribution of active regions
• 1.9ltklt2.1 (see Howard 1996)

7
Active regions form fractal structures

• The geometrical characteristics of the active
  regions can be represented with a single
  characteristic correlation dimension
• See Meunier 1999 and references sited in this
  article

8
Statistics of the explosive events

• Peak intensity distribution of explosive events
  in the low chromosphere follow also a power law
  with index (see for example Ellerman bombs,
  Georgoulis et al. 2002)

9
Question?

• Are the sub-photospheric / photospheric /
  chromospheric/coronal characteristics of the
  magnetic field evolution independent?
• Basic working assumption The Complexity of the
  magnetic field in active region suggest that all
  solar phenomena are interdependent and the well
  known say for the evolution of non-linear systems
  (attributed to Lorentz) the sensitivity to the
  initial conditions in non-liner systems is such
  that the flopping of the winds of a butterfly in
  Brazil will influence the weather in Santorini
  apply to all solar phenomena.

10
Sub-photospheric evolution

• Let us assume that the convection zone is
  penetrated with flux tubes (fibrils) with
  different size and magnetic strength all moving
  with different speeds towards the surface.
• Can we cut the 3-D box with a surface and
  consider that each magnetic tube is represented
  with a sphere with diameter R.
• Almost 20 years ago Tom Bogdan in his Ph.D pose
  this question and try to develop the statistical
  evolution of the dilute gas consisted of 2-D
  fibrils

11
Statistics of sub-photospheric evolution of
magnetic fields

• See Bogdan and Lerche (1985)
• There is considerable
• work published on the
• filamentary MHD
  

12
Vortex attraction and formation of active regions

• The magnetic field emerging through the surface
  of the sun are individually encircled by one or
  more subsurface vortex rings, providing an
  important part of the observed clustering of
  magnetic fibrils.. Parker (1992)

13
A model based on transport on fractal support and
percolation(Model-1)

• Carl Schrijver and collaborators (1992/1997)
  presented a model were magnetic field robes are
  filling a point in this lattice with probability
  p and then executing random walks on a
  structured lattice. The flux robe diffuse on a
  network already structured.

14
A Cellular Automaton Model based on
percolation(models 2/3)

• See Wentzel and Seiden (1992), Seiden and Wenrzel
  (1996)

15
The basic rules for Model-4(Vlahos,
Frangos,Isliker,Georgoulis)

• We use a 200x1000 square grid with no magnetic
  flux (0)
• We star by filling 0.5 (1)positive magnetic
  flux a 0.5 (-1) negative.
• Stimulation probability P Any active point for
  one time step stimulate the emergence of new flux
  in the neighborhood. Newly emerged flux appear in
  dipoles.
• Diffusion due to unrestricted random walk
  Dm(mobility) free motion on the grid.
• Diffusion due to submergence Dd (submergence of
  flux) Fast disappearance if the neighboring
  points are non-active.
• Spontaneous generation of new flux E (its value
  is not important) To keep the process going

16
Results

• The evolution of active points
• Are the values of P,D,E unique?

17
A basic portrait
18
Size distribution

• k2.05

19
Fractal correlation dimension

• See also Meunier 1999 for similar results using a
  variant of Wentzel and Seiden model.

20
Energy release

• Cancellation of flux due to collisions of
  opposite flux releases energy

21
Peak flux frequency distribution

• a2.24

22
Waiting Time Distribution
23
Is the statistics of the size distribution
correlated to the energy release statistics?
24
A movie on the active region evolution and
magnetic field cancellation
25
The basic rules for Model-4(Vlahos,
Fragos,Isliker,Georgoulis)

• Comment These models are based on two universal
  principals on the development of complex systems.
  (A) The continuous fight tendencies Emergence
  vs diffusion and (B) Percolation
• The results are generic and independent on the
  exact values of the free parameters but the
  observations constrain their values to a subset
  of the available 3-D space (PxDmxDd
  (0-1)X(0-1)x(0-1)

26
Magnetic field evolution in the corona(A 3-D MHD
simulation)

• Ake Nordlund and Klaus Galsgaard (1996)

27
Similar results from the SOC theory

• Vlahos, Georgoulis, Isliker, Anastasiadis see
  also review by Charbonneau et al. (2001)

28
A movie from the SOC and TRACE

• ..\..\..\movie_flare.mpg
• A TRACE movie

29
Fractal properties of the unstable current regions

• McIntosh et al (2002) (DF?1.8-2.0)

30
Wave propagation in a structured active region
(filled with intermittent current sheets sitting
on a fractal in 3-D space)

• Wave propagation reinforces the current sheet and
  the absorption coefficient of the waves is
  enhanced by several orders of magnitude

31
The new paradigm

• A new model for the energy release seems to be
  suggested
• This model has different characteristics from the
  old cartoons
• The current sheets are driven from the evolution
  of magnetic fields at the convection
  zone/photosphere level.
• Many characteristics of this sub-photospheric/phot
  ospheric evolution are imprinted on the evolving
  and changing current sheet in all levels of the
  corona

32
Old paradigm

• Let us leave behind these nice historic cartoons
  and search for a new one to replace them

33
Photos from Skylab/SMM/Yohkoh seem to agree so
well with this cartoon?Pictures some times may
lead you to the wrong conclusions so be careful
how far you push the connection of the visual
impression with the energy release when you form
cartoons
34
My favorite cartoon(it is time for change of
paradigm) although here we must be careful on the
same problems I have just mention.

• Vlahos(1992/1993), Vlahos and Anastasiadis
  (1991-92)

35
Summary

• The turbulent convection zone, through the
  magnetic fields drives the entire solar
  atmosphere.
• The complexity of our system (convection
  zone/photosphere/chromosphere/corona) is such
  that only statistical analysis and statistical
  models can capture its dynamic evolution
• There is strong correlation between the evolution
  of photosphere patterns and chromospheric/coronal
  effects (this is indicated by my k-a dependence)

36
Summary

• We need a series of 3-D MHD studies to understand
  deeper the physical meaning of the free
  parameters of our CA models and restrict the
  rules further
• I believe that we need to start building global
  solar models using more techniques borrowed from
  complexity theory.
• We will make considerable progress only if we
  understand deeper the interconnection of the
  elements of our system, this new global
  understanding has to be reflected even on the
  drawing of new cartoons