On the Availability of Sufficient Twist in Solar Active Regions to Trigger the Kink Instability 

K. D. Leka Submitted: 20041213 09:45
The question of whether there is sufficient magnetic twist in solar active
regions for the onset of the kink instability is examined using a ``blind
test'' of analysis methods commonly used to interpret observational data.
``Photospheric magnetograms'' are constructed from a recentlydeveloped
numerical simulation of a kinkunstable emerging fluxrope with nearly
constant (negative) wind. The calculation of the bestfit linear
forcefree parameter α _{
m best} is applied, with the goal of
recovering the model input helicity. It is shown that for this simple
magnetic structure, three effects combine to produce an underestimation
of the known helicity: (1) the influence of horizontal fields with lower
local α values within the fluxrope, (2) an assumed simple relation
between α _{
m best} and the winding rate q does not apply to
nonaxis fields in a fluxrope which is not thin, and (3) the difficulty
in interpreting the forcefree twist parameter measured for a field which
is {it forced}. A different method to evaluate the magnetic twist in
active region fluxropes is presented which is based on evaluating the
peak α value at the fluxrope axis. When applied to data from
the numerical simulation, the twist component of the magnetic helicity
is essentially recovered. Both the α _{
m best} and the new
α _{
m peak} methods are then applied to observational photospheric
vector magnetic field data of NOAA~AR,7201. The α _{
m best}
approach is then confounded further in AR,7201 by (4) a distribution of
α which contains both signs, as is generally observed in active
regions. The result from the proposed α _{
m peak} approach
suggests that a larger magnetic twist is present in this active region's
deltaspot than would have been inferred from α _{
m best},
by at least a factor of three. It is argued that the magnetic fields in
localized active region fluxropes may indeed carry greater than 2pi
winds, and thus the kink instability is a possible trigger mechanism
for solar flares and Coronal Mass Ejections.
Authors: K.D. Leka, Y. Fan, G. Barnes
Projects:

Publication Status: ApJ, accepted
Last Modified: 20050308 16:07



Photospheric Magnetic Field Properties of Flaring vs. FlareQuietActive Regions. II. Discriminant Analysis 

K. D. Leka Submitted: 20030624 10:59
We apply statistical tests based upon discriminant analysis to the
wide range of photospheric magnetic parameters described in Paper~I (Leka & Barnes 2003), with the goal of identifying those properties which are
important for the production of energetic events such as solar flares.
The photospheric vector magnetic field data from the U.~Hawai`i Imaging
Vector Magnetograph are wellsampled both temporally and spatially, and
we include here data covering 24 flareevent and flarequiet epochs taken
from seven active regions. The mean value and rate of change of each
magnetic parameter are treated as separate variables, thus evaluating both
the parameter's state and its evolution, to determine which properties are
associated with flaring. Considering single variables first, Hotelling's
T^2tests show small statistical differences between flareproducing and
flarequiet epochs. Even pairs of variables considered simultaneously,
which do show statistical difference for a number of properties, have
high error rates, implying a large degree of overlap of the samples.
To better distinguish between flareproducing and flarequiet populations,
larger numbers of variables are simultaneously considered; lower error
rates result, but no unique combination of variables is clearly the
best discriminator. The sample size is too small to directly compare the
predictive power of large numbers of variables simultaneously. Instead,
we rank all possible fourvariable permutations based on Hotelling's
T^2test, and look for the most frequently appearing variables in the
best permutations, with the interpretation that they are most likely
to be associated with flaring. These variables include: an increasing
kurtosis of the twist parameter, a larger standard deviation of the twist
parameter, but a smaller standard deviation of the distribution of the
horizontal shear angle and of the distribution of the horizontal magnetic
field, but a larger kurtosis of that horizontal field. To support the
``sorting all permutations'' method of selecting the most frequently
occurring variables, we show that the results of a single tenvariable
discriminant analysis are consistent with the ranking. We demonstrate
that individually, the variables considered here have little ability
to differentiate between flaring and flarequiet populations, but with
multivariable combinations, the populations may be distinguished.
Authors: K. D. Leka and G. Barnes
Projects:

Publication Status: ApJ (accepted)
Last Modified: 20030624 11:00



Photospheric Magnetic Field Properties of Flaring vs. FlareQuiet Active Regions I: Data, General Approach, and Sample Results 

K. D. Leka Submitted: 20030624 10:56
Photospheric vector magnetic field data from the U. Hawai`i Imaging Vector
Magnetograph with good spatial and temporal sampling, are used to study
the question of identifying a preflare signature unique to flare events
in parameters derived from BB. In this first of a series of papers,
we present the data analysis procedure and sample results
focusing only on three active regions (NOAA Active Regions #8636,
#8771, and #0030), three flares (two Mclass and one Xclass), and
(most importantly) a flarequiet epoch in a comparable flareproducing
region.
Quantities such as the distribution of the field morphology, horizontal
spatial gradients of the field, vertical current, current helicity,
``twist'' parameter α and magnetic shear angles are parameterized
using their moments and appropriate summations. The time series of the
resulting parameterizations are examined one at
a time for systematic differences in overall magnitude and evolution
between the flare and flarequiet examples.
The variations expected
due to atmospheric seeing changes are explicitly included. In this
qualitative approach we find (1) no obvious flareimminent signatures
from the plain magnetic field vector and higher moments of its horizontal
gradient, or from most parameterizations of the vertical current density;
(2) counterintuitive but distinct flarequiet implications from the
inclination angle, and higher moments of the photospheric excess magnetic
energy; (3) flarespecific or flareproductivity signatures, sometimes
weak, from the lower moments of the field gradients, kurtosis of
the vertical current density, magnetic twist, current
helicity density and magnetic shear angle. The strongest results are,
however, that (4) in ensuring a flareunique signature, numerous candidate
parameters (considering both their variation and overall magnitude) are
nullified on account of similar behavior in a flarequiet region, and
hence (5) considering single parameters at a time in this qualitative
manner is inadequate. To address these limitations, a quantitative
statistical approach is presented in Paper II (Leka and Barnes 2003).
Authors: K. D. Leka and G. Barnes
Projects: None

Publication Status: ApJ (accepted)
Last Modified: 20030624 10:56




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