Observations of Anisotropic Compressive Turbulence Near
The Sun
W. A. Coles1, A. P. Rao2 and S. Ananthakrishnan2
1
2
Electrical and Computer Engineering, University of California at San Diego
National Center for Radio Astrophysics,Tata Institute of Fundamental Research, Pune, India
Abstract. Small-scale density-fluctuations cause angular-broadening of distant radio sources observed through the solar
wind. Observations of angular broadening near the Sun show that the compressive microstructure is highly field aligned.
Recent work strongly suggests that the density fluctuations are caused by obliquely propagating MHD waves. With this
in mind we have made a new series of angular scattering observations using the Giant Meter Wavelength Radio
Telescope (GMRT) located near Pune. We selected radio sources passing over the solar poles at distances near 10 Rs.
By comparing these observations with simultaneous white light scattering from the LASCO C3 instrument, we hoped to
learn how the waves are related to the large scale coronal structures, i.e. coronal holes, polar plumes, and streamers.
INTRODUCTION
space-craft spectra show a Kolmogorov power-law
form at frequencies above the inverse of the transit
time.
Observations of angular broadening have three
distinctive characteristics, which suggest the presence
of obliquely propagating MHD waves. The scales of
the density fluctuations range upwards several decades
from the proton inertial scale. The spatial spectrum of
the density fluctuations in this range is flatter than
“Kolmogorov”, and most of the energy is transverse to
the local magnetic field1. Observations also indicate
that the velocity of the fluctuations is faster than the
flow speed by approximately the local Alfven speed.
Such waves may carry enough energy to contribute
significantly to the acceleration of the solar wind, so
their distribution with respect to coronal structures is
of interest.
Radio observations of phase scintillation made
using dual-frequency transponders on spacecraft
provide a measure of the mid-scale structure
overlapping with the direct observations3,4. These
observations match the space-craft spectra at low
frequencies and have approximately Kolmogorov
behavior. However they tend to flatten somewhat at
higher frequencies. Spectral broadening measurements
can be made using the same space craft transponder5.
These extend the spectral estimates to smaller scales,
past the ion-inertial scale in fact. The spectra become
considerably flatter than Kolmogorov as the ioninertial scale is approached.
PREVIOUS OBSERVATIONS
2. Anisotropy of spatial spectrum
1. The Spatial Spectrum of Ne
Two-dimensional measurements of the electric
field correlation can be made at scales of: (1) 100010,000 km using the VLBA; (2) at scales of 1-30 km
by the VLA or GMRT. The VLBA measurements are
nearly isotropic, whereas the VLA/GMRT
observations are very anisotropic7.
Spacecraft observations provide a measure of the
low frequency (large scale) structure. The spectrum of
Ulysses observations over the north pole shows a clear
break at an "outer scale" which is related to the transit
time. This spectrum agrees well with estimates made
from Helios observations by Tu and Marsch2. The
The observed axial ratio of the microstructure
decreases with increasing solar distance. However it is
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
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significantly reduced by the line of sight integration,
so the intrinsic axial ratio AR must be recovered by
model fitting. An empirical model has the form8
(AR-1) ≈ 160/R1.5
where R is in Rs .
FIGURE 2. The observed distribution of parallel velocity in
the polar wind. A model is fit to the data in which it is
assumed that the velocity transverse to the line of sight is
distributed over a range. The vertical bars show this range.
THE NEW OBSERVATIONS
FIGURE 1. The observed axial ratio vs solar distance. The
upper dashed line is a model of the intrinsic axial ratio of the
medium. The lower dashed line shows the effect of the line
of sight averaging.
The objective of these observations was to learn
how the characteristics of these MHD waves which are
presumed to cause the radio scattering are related to
plasma conditions and large scale structures in the
corona. This requires correlating some measure of the
MHD waves with another measure of the corona. The
most obvious measures of coronal structure are the
LASCO white light coronagraphs on SOHO. They
have the sensitivity to detect fine structure and they
have a field of view that includes the regions
accessible to radio scattering.
3. The spectral cutoff
The spectra show a distinct cutoff at high
frequencies, which we interpret as a dissipation or
"inner" scale. This is visible in VLA/GMRT angular
broadening, spectral broadening, and intensity
scintillation measurements, which are sensitive to the
smallest scales. It changes with radial distance roughly
as Si (km) ≈ R (Rs). This is very close to the behavior
of the ion inertial scale5.
It is difficult to make continuous radio
measurements of the velocity because the
measurements require long radial-aligned baselines,
which only persist for a short time because of the
Earth's rotation. However angular scattering measured
with arrays such as the VLA or GMRT can be made
anytime a suitable source is present. As a result
angular scattering measurements can be compared
with other solar measurements more readily. The level
of turbulence and the axial ratio of the angular
scattering, which indicates the "obliqueness" of the
wave spectrum, are particularly robust
4. The velocity distribution
The apparent velocity distribution of the density
fluctuations is characterized by a high mean and a very
wide spread in radial velocity8,9. Other measurements
and theoretical values tend to cluster around the lower
envelope of the radio scattering observations.
The radio observations can be explained under the
assumption that the scattering is caused by waves.
which are traveling out-wards with respect to the flow.
Very good model fits can be obtained assuming that
the waves are obliquely propagating Alfven waves or
if they include a 50% admixture of the slow magnetoacoustic mode. A wide range of apparent speeds is
observed because the line of sight includes a very wide
range of wave speeds.
. The spectral exponent and the inner scale can
also be determined but they are more dependent on
accurate calibration.
The GMRT operates at 150, 233, 327, 610, and
1420 MHz. It has a range of baselines up to 35 km.
The system is under development and has just been
opened to outside use. At this time the two higher
frequency bands are better developed. We found that
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good observations could be made around 10 Rs at 600
MHz and most of our observations are at that
frequency.
However these variations did not appear to be
correlated in any simple way.
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The GMRT gain calibration is not as precise as that
of the VLA, because the instrument is not as mature.
At present the GMRT data requires an additional "selfcalibration" step. This has little effect on the
determination of the anisotropy, but it can slightly bias
the shape of the spatial spectrum. Thus the spectral
exponent and inner scale estimates are not reliable but
the axial ratio and its orientation are well determined.
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The location of the scattered source was registered
on the LASCO C3 images. A cut through the C3
image is taken for comparison with the axial ratio and
turbulent intensity. Since we are searching for
correlation in the small-scale structure we used the
standard C3 daily average from which a long-term
lower-bound had been subtracted. This procedure
emphasizes deviations from spherical symmetry which
is what we are searching for.
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FIGURE 4. Observations over the north solar pole on Aug.
20, 21, and 22 of 2001 at a distance of 10 Rs.
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FIGURE 5. Observations under the south solar pole on
Sept. 1 and 2 of 2001 at a distance of 10 Rs. The tics on the
time axis mark intervals of 2 hrs.
FIGURE 3. Observations over the north solar pole on Aug.
2, 3, and 4 of 2001 at a distance of 10 Rs. The top panel is
the white light brightness, the middle panel is the axial ratio,
and the lower panel is the level of turbulence in the parallel
and perpendicular directions (parameterized by the phase
structure function at 10 km).
CONCLUSIONS
We undertook these observations with the
assumption that anisotropic scattering is caused by
obliquely propagating MHD waves. We searched for
variations in the behavior of these MHD waves in
different coronal structures using the white-light
brightness observed by the LASCO C3 instrument as a
In the first three observations the orientation of the
microstructure was radial within the statistical errors.
In the fourth case the orientation was significantly
non-radial. In all cases significant variations were seen
in the radio scattering and also in the C3 brightness.
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measure of the large scale coronal structure. During
the observations the scattering region passed through
different coronal structures and there were significant
variations in the axial ratio and in the level of the
scattering. However these variations were not
correlated in an obvious way with the coronal
structure. This was a surprise to us and we do not have
an explanation.
although both observations are line-of-sight integrals,
the weighting factors are quite different. The radio
scattering is weighted by the square of the electron
density, whereas the white-light brightness is weighted
linearly by the electron density. Thus the radio
scattering is particularly sensitive to thin dense
filaments whereas the white-light image is sensitive to
smaller variations in large-scale structures.
The observations should be repeated closer to the
Sun where the contrast, both in large-scale structures
and in radio scattering, is known to be larger.
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ACKNOWLEDGMENTS
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We are indebted to the GMRT telescope operators
who were very helpful in completing the observations.
One of us (WAC) was partially supported by a Sarojini
Damodaran International Fellowship during this work.
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REFERENCES
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(1995).
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FIGURE 6. Observations off the west limb on Sept. 23,
2001 at a distance of 10 Rs. The third panel is the orientation
of the structure in degrees. The tics mark 2 hr, or 2 105 km,
intervals.
4. Paetzold, M., Karl, J., and Bird, M. K., A s t r o n .
Astrophys. 316, 449-456, (1996).
5
It is clear that anisotropic scattering is observed in
all phases of the quasi-static solar wind: the fast polar
holes; the quiet slow wind; and in the coronal
streamers. We did not observe any transient events,
but other observations10 suggest that anisotropic
scattering is observed in CME’s aligned with the local
magnetic field. The angular scattering can vary
significantly in regions which appear to be
homogeneous in white-light. We also observed a case
where the orientation of the scattering (which we
assume is the direction of the magnetic field) remained
significantly non-radial over an extended region as
shown in Figure 6.
Coles, W. A., Liu, W., Harmon, J. K., and Martin, C. L.,
J. Geophys. Res. 96, 1745-1755, (1991).
6. Armstrong, J. W., Coles, W. A., Kojima, M., and
Rickett, B. J. , Astrophys. J., 358, 685, (1990).
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J. K. Harmon, J. Geophys. Res. 102, 263-273, (1997).
8. Massey, W., Measuring intensity scintillations at the
very long baseline array (VLBA) to probe the solar wind
near the Sun, M.S. Thesis, University of California, San
Diego, (1998).
9. Klinglesmith, M., The polar wind from 2.5 to 40 solar
radii: results of intensity scintillation measurements,
Ph.D. Thesis, University of California, San Diego,
(1997).
We have to conclude: (1) MHD waves are present
in all phases of the solar wind and (2) the waves can
vary significantly within large scale structures. It is
possible to have large variations in scattering with no
obvious change in white-light brightness because,
10. Lynch. B. J., Coles, W. A., and Sheeley, N.R., GRL, in
press, October (2002).
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