The source of Flare energy
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Transcript The source of Flare energy
COMPLEXITY IN SOLAR
ACTIVE REGIONS
Loukas Vlahos
Department of Physics
University of Thessaloniki, Greece
Active regions are open, non-linear
dynamical systems
Energy enters and escape from all
boundaries but the most important
boundary is the photosphere...
The statistical properties of the
formation and evolution of active
regions at the photosphere are of
importance for the flare energy
release
SMALL SCALE VS LARGE SCALE
ORGANIZATION
AR are formed and developed gradually till
they disappear
Follow well defined statistical laws
Size distribution of AR, fractal dimension
have been studied
AR made by N-mutually interacting loops,
which are never stable and represent the
eddy patterns of turbulence in the
convection zone
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.
THE CORONAL PART OF ACTIVE REGIONS RESPOND TO
THE EVOLUTION OF THEIR PHOTOSPHERIC BOUNDARY
Active region formation
Key observations to constrain the models
Size distribution of active regions
N ( A) ~ A k
1.9<k<2.1 (see Howard 1996)
Active regions form fractal structures
The geometrical characteristics of the
active regions can be represented with a
single characteristic correlation
dimension
1.3 DF 1.7
See Meunier 1999 and references sited in
this article
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)
a
N (E) ~ E
1.5 a 2.5
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 New York”
apply to all solar phenomena.
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 circle 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
Statistics of sub-photospheric evolution of
magnetic fields
See Bogdan and Lerche (1985)
N 1
N
[ru (r , , t ) N ] [ (r , , t ) N ] Coll
t r r
T
There is considerable
work published on the
filamentary MHD
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)
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.
A Cellular Automaton Model based on percolation
(models 2/3)
See Wentzel and Seiden (1992), Seiden and
Wenrzel (1996)
The basic rules for Model-4
(Vlahos, et al, ApJ Letters, 2002)
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 nonactive.
Spontaneous generation of new flux E: (its value is not
important) To keep the process going
The basic rules for Model-4
(Vlahos, et al., ApJ Letters, 2002)
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)]
Results
The evolution of active points
Are the values of P,D,E unique?
A basic portrait
Size distribution
k=2.05
Fractal correlation dimension
See also Meunier 1999 for similar results
using a variant of Wentzel and Seiden
model.
Energy release
Cancellation of flux due to collisions
2
of opposite flux releases energy
E~B
Peak flux frequency distribution
a=2.24
N (E) ~ E
a
Waiting Time Distribution
P(t ) ~ (t )
2.14
D
exp
Dmax
Is the statistics of the size distribution correlated to the
energy release statistics?
A movie on the active region evolution and
magnetic field cancellation
The standard SOC model for flares
Loading phase-very important
Rule-1: Instability threshold
(criticality)
Rule-2: Redistribution and energy
release
Reloading - Either continuous or
after relaxation
Magnetic field evolution in the corona(A 3-D MHD
simulation)
Ake Nordlund and Klaus Galsgaard
(1996)
Similar results from the SOC theory
Vlahos, Georgoulis, Isliker, Anastasiadis see also
review by Charbonneau et al. (2001)
Connection of CA to MHD
Equations used
B A
4
J B
c
1
E J u B
c
B
(u B ) 2 B Si 2 B
t
A movie from the SOC and TRACE
..\..\..\movie_flare.mpg
A TRACE movie
Fractal properties of the unstable current regions
McIntosh et al (2002) (DF1.8-2.0)
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
“Old” paradigm
Let us leave behind these nice historic cartoons
and search for a new one to replace them…
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 subphotospheric/photospheric evolution are
imprinted on the evolving and changing current
sheet in all levels of the corona
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)
Levy flights in velocity
an anomalous diffusion in velocity space
Combine magnetic turbulence and E-field
Magnetic
turbulence are
trapping the particles for
Energies E<Ec
Electric fields heat the
particles up to Ec and freely
accelerate them above Ec
Velocity Distribution above cut off
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 dynamical evolution
There is strong correlation between the evolution
of photosphere patterns and
chromospheric/coronal effects (this is indicated
by my k-a dependence)
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…