Diagnostics of flare activity level from turbulence parameters of photospheric plasma

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Diagnostics of flare activity level from
turbulence parameters of photospheric plasma
RHESSI/SOHO/TRACE Workshop
Pre-event Physics
December 8-11, 2004,Sonoma, California

• Abramenko, Valentyna
• Big Bear Solar Observatory of NJIT
• avi_at_bbso.njit.edu
• www.bbso.njit.edu/avi

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Introduction
A solar flare may be triggered as a chain
reaction in a stressed coronal magnetic
configuration.
Flares occur as an unavoidable phase in evolution
of a complex non-linear dynamical system of
magnetized plasma (Parker 1988, a review by
Charbonneau et al. 2001)
The system extents from the convective zone to
the corona through layers of plasma of different
physical conditions.
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Introduction
Introduction
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Introduction
Essential properties of the photospheric plasma
Magnetized plasma in a turbulent state (Parker
1979),
very intermittent (or, in other words,
multifractal) medium (Lawrence et al. 1993,
Abramenko et al. 2002),
where the magnetic helicity may have an inverse
cascade (Biskamp 1993)
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Introduction
Situation in the photosphere flaring in the
corona
Magnetic helicity transport in the photosphere
(Rust LaBonte 2003 Georgoulis, Rust
LaBonte present meeting Chae 2001
Romano present meeting ).
Statistical properties of electric currents,
current helecity, magnetic flux, etc., derived
from vector-magnetograms (Leka Barnes
2004).
Fractal dimensions of the photospheric magnetic
fields (Tarbell et al. 1990 Balke et al.
1993 Meunier 1999 Ireland, Gallagher
McAteer 2003).
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Introduction
Situation in the photosphere flaring in the
corona we propose to analyze
1. Distribution functions of the magnetic flux
in elements of the magnetic field in active
regions present talk. (Abramenko
Longcope, ApJ, 2005)
2. Turbulence state of the photospheric magnetic
field as derived from magnetic power
spectrum present talk.

• Multifractality (intermittency) of the
  photospheric magnetic
• fields poster at the current meeting.
• (Abramenko, Yurchyshyn, Wang, Goode, ApJ
  577, 2002).

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Distribution functions of the magnetic flux
(Abramenko Longcope, ApJ, 2005)
Flare-quiet active region 0061 (C2)
Flaring active region 9077 (X5.7)
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Distribution functions of the magnetic flux
(Abramenko Longcope, ApJ, 2005)
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Magnetic Power Spectrum
Flare-quiet active region 0061
Flaring active region 9077

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Magnetic Power Spectrum
Flare-quiet active region 0061
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Magnetic Power Spectrum
Flare-quiet emerging active region NOAA 9851
No X-ray flares during the passage across the disk
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Magnetic Power Spectrum
Flaring emerging active region NOAA 0365
The most powerful flare during the passage across
the disk X3.6
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Multifractality vs. Turbulence
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Conclusions

• Parameters of the turbulence state (the power
  index ?) and of the structural organization (the
  distribution functions and the degree of
  multifractality, ?h) of the photospheric
  magnetic field correlate with flaring
  productivity of an active region.

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Conclusions

• The turbulence state of the magnetic field at the
  phase of emergence seems to determine the
  ongoing flare productivity of an active region.
• Further study on a large statistics is needed
  the catalog of active regions observed in a high
  resolution mode by SOHO/MDI will be used
• (Paolo Romano Vasyl Yurchyshyn,
  www.bbso.njit.edu/vayur/MDI_catalog.htm)

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Calculation of Multifractality
Structure functions were first introduced by
Kolmogorov (1941). They were defined as
statistical moments of the field increments
q is the order of a statistical moment, r is a
separation vector, x is the current point on a
magnetogram. ltgt denotes the averaging over a
magnetogram. ??q? is a slope within the inertial
range of scales.
Classical Kolmogorov theory
Refined Kolmogorov theory, multifractal structure
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Calculation of Multifractality
Historically accepted terminologyAnalysis of
Time series intermittencyAnalysis of
Spatial arrays multifractality

h(q) d?(q)/dq
D(h(q))2qh(q)- ?(q)
RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Examples of different multifractality
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Calculation the Power Spectrum

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California
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Calculation the Power Spectrum

RHESSI/SOHO/TRACE Workshop/ WG 1 Pre-event
Physics Dec 8-11, 2004, Sonoma, California