Signatures of Intermittent Turbulence in Hinode Quiet Sun Photosphere

1
Signatures of Intermittent Turbulence in Hinode
Quiet Sun Photosphere
Valentina Abramenko, Big Bear Solar Observatory,
USA, www.bbso.njit.edu/avi
Plasma turbulence is ubiquitous in astrophysics
in general and in the solar photosphere, in
particular. It is a fundamental physical process
that plays an important role in the near-surface
turbulent dynamo and plasma heating through
dissipation. Turbulence acquires intermittent
nature when extremely high fluctuations (in both
temporal and spatial domains) become not rare and
they thus determine the energy release dynamics
significant contribution to the traditional
turbulent energy cascade appears in the
intermittent medium. We estimated signatures of
intermittent turbulence in the quiet sun
photosphere utilizing Hinode/SOT data. We found
that at scales below 1 Mm the QS structures are
highly intermittent, which open possibilities for
enhanced energy release dynamics at small scales.
What is the Intermittency
How to measure the degree of intermittency
Intermittency of the magnetic field from SOHO/MDI
high resolution data
Structure functions were first introduced by
Kolmogorov (1941).
The ratio of the squared second structure
function, S2( r ) (red), over the forth
structure function, S4( r ) (blue), gives us
the Filling Factor, f(r ) . The Filling Factor
does not depend on the scale, r, For
non-intermittent (or, monofractal) structures
and time series. For intermittent structures,
the filling factor decreases as the scale
decreases. For non-intermittent structures (like
a Gaussian process) the filling factor does not
depend on scale. The steeper the slope of
decrease, the more intermittent the structure
is. In the multifractal terminology, the steeper
the filling factor means the more complex
multifractal, which is a superposition of a set
of monofractals. For example, in the solar wind
turbulence, the presence of interminnency
implies the presence of magnetic field
discontinuities, shocks and current sheets of
various scales. All these phenomena contribute
significantly into the energy release dynamics,
along with the usual turbulent cascade.
A turbulent medium can display a property of
intermittency a tendency to concentrate into
strong blobs (sometimes in a shape of sheets , or
tubes) of all scales intermittent with vast areas
of low intensity, a presence of extremely
strong fluctuations and a burst-like behavior in
time evolution. Intermittent structure is a
multufractal. Generally, intermittency and
multifractality are two different terms for the
same phenomenon. Historically, the former term
(intermittency) is usually applied to time series
Analysis, whereas the later one (multifractality)
is used for spatial objects (Takayasu, 1989
Frisch, 1995). In scale intervals, where
intermittency presence, it can reinforce the
energy release dynamics.
We first applied the filling factor technique to
magnetograms from SOHO/MDI obtained in the high
resolution mode. Areas of three types we
analyzed Active Region (AR) area ( red), Plage
area (green) and two areas in the quiet sun,
which were mostly located inside small coronal
holes (blue and turquoise). Middle figure the
filling factor function (linear axes) for the AR
data. The interval of decreasing filling factor
is well pronounced 5 30 Mm. Below 5 Mm the
filling factor increases, which is caused by the
noise influence and poor resolution of the
magnetogram. Right figure the filling factor as
a function of a spatial scale (double logarithmic
plot) for three types of magnetic structures. For
all of then, the filling factor function starts
to increase at small scales as a result of
insufficient data resolution. Note that while
both the AR and the plage data display an
intermittent nature of the magnetic field at
scales above 2 Mm, the quiet sun data seems to
display no intermittency at these scales. If we
ignore the noise-related hooks and contunuously
extend the AR and plage curves (dotted curve with
the arrow) below the base lane of the quiet sun
plateu, we may conclude that at scales below 1000
km one may expect the decreasing behavior of the
filling factor in the quiet sun areas, i.e., the
intermittent property of the QS magnetic field.
Note, that here a special type of the filling
factor formula was used f( r ) S6( r ) /( S3 (
r ) )2 , which is more sensitive to intermittency.
2
Hinode SOT/SP Intermittency in magnetic
structures
Hinode SOT/FG Intermittency in G-band and Ca II
images
SOT/SP Bz-component/ fast mode/ HAO calibration
2008 Nov 30
Active Region
SOT/SP Bz-component/ fast mode/ HAO calibration
2006 Dec 11
Weak Plage
Quiet Sun
G-band
Sot/SP data for the coronal hole area (blue
curve) indicates that at scales larger than 2 Mm,
the magnetic field structure seems to be
non-intermittent (monofractal). Only a very
slight slope (0.024) of the lower-law linear fit
is observed. For comparison, we plotted the
filling factor for an AR (red) and a plage area
(green). Data for the AR and plage show a
steeper slope of the power-law linear fit with
indice 0.18 and 0.09, which implies
intermittency at scales gt 2 Mm. What is
interesting is that Hinode data do not show the
behavior similar to that observed from MDI
magnetograms at scales less than 3 Mm. Instead,
the Hinode SOT/SP filling factor displays a rapid
decrease with scale for all data types, which
means enhanced intermittency in the magnetic
structures at small scales.
Ca II
At scales of 1 Mm and smaller the decrease of the
filling factor is observed for both the G-band
and Ca II images. Intermittent nature of the
solar granulation and low-chromosphere structures
is proved from the Hinode observations.
References Abramenko, V. 2005, Solar Phys.
288.29 Abramenko,V., Yurchyshyn, V., Watanabe, H.
2009, Solar Phys., 260, 43. Balke, A.C. et. Al.,
1993, Solar Phys. 143, 215 Berger, T.E., et al.,
1995, ApJ,454,531 Frisch, U. 1995, Turbulence,
The legacy of A.N. Kolmogorov, Cambridge Univ.
Press, Cambridge, 296. Takayasu, 1989,
Fractals in the Physical Science, Manchester
Univ. Press, Manchester and New York.
In monofractals, large fluctuations of the
parameters (say, energy release events) are rare
and do not determine mean values. In other words,
time profiles are non-intermittent and evolution
proceeds without catastrophes. On the contrary,
in multifractals, the time profiles are highly
intermittent, large fluctuations are not rare,
and they determine mean values. The temporal
energy release process is burst-like. If so,
the monofractal property of QS structures
explains their quiet temporal behavior at scales
above 2 Mm. The bulk of energy release dynamics
(needed, in particular, for the solar wind
acceleration) occurs at smaller scales, where the
magnetic field structure is entirely different.
In a way, one might say that below 1 Mm the
complexity and structural organization of the QS
magnetic field is similar to what we observe in
active regions at scales of 10-100 Mm same shear
motions, energy built-up and release through
explosions, but 2-3 order of magnitude weaker.
Many new phenomena will be discovered now, when
the spatial scales less than 1 Mm are available
from Hinode instruments.