1993; Habbal et al. 1995),
in part because
it is difficult to detect plume structure in the extremely faint
corona at the high solar altitudes, where the plumes are thought either
to fade or to merge with the solar wind.
The Ulysses spacecraft has observed density structures by
sampling directly the high speed solar wind about 1 A.U. over the
solar poles; however, these structures do not appear to vary with
latitude as would be expected for rigid plume-like structures rotating
past the spacecraft (Poletto et al. 1996; Reisenfeld, McComas,
& Steinberg 1999; McComas et al. 1995), and they appear to
be much more homogeneous than the density structure of polar plumes at
2 R
(Feldman et al. 1996). The outflow
rate in plumes has been measured through Doppler dimming
(Cranmer et al. 1999) to be at least sonic at 2 R; thus, it seems likely that the plumes do not
fade out through lack of flow, but rather that they contribute somehow
to the solar wind. The question remains: if the plumes contain high
speed wind streams and hence impose structure on the high speed solar
wind, why is that structure not seen by Ulysses?
Possible explanations for the plumes' disappearance at high altitude include the
Kelvin-Helmholtz two-stream instability (Parhi, Suess, & Sulkanen 1999) and
cross-mode wave scattering near the Alfvénic point in the wind's
acceleration (Kagashvili 1999). These mechanisms allow the
plumes to contribute to the solar wind, but cause their contribution
to be distributed across radial lines by fluid-dynamic instabilities,
spoiling their azimuthal structure above a critical altitude that is
an adjustable parameter of each model. It has also been shown
(DeForest 1998) that time variability in the plumes themselves
may be sufficient to spoil the expected frequency signature of plumes
in the Ulysses observations, even should their azimuthal structure
persist to Ulysses' altitude of approximately 1 AU; but time
variability alone cannot account for the comparative homogeneity of
the Ulysses observations. If turbulent mixing by
instabilities is in fact the mechanism at play, then the plumes should
appear to fade above a critical altitude somewhere above 10 R.
There is currently some uncertainty (Woo 1996; Pätzold &
Bird 1998; Del Zanna, von Steiger, & Velli 1998) over how far the
plumes actually extend into the interplanetary medium. Plumes have
been observed in Thomson scattered visible light to extend from the
solar surface up to image-plane altitudes of 10-15 R (DeForest et al. 1997), using the Large
Angle Spectrometric Coronagraph's C-3 camera. Woo (1996) reports
observing plumes at solar altitudes as high as 40 R in the image plane using radio sounding of the
corona with the Ulysses transponder beam, but several factors
require clarification of this result. In particular, the time scale
of the plumes' passage in the Woo result (1.0 day) is suspiciously
similar to the diurnal rhythm of the Deep Space Network coverage that
was used to make the measurement (Pätzold & Bird 1998); and without
a full two-dimensional image of the structures being studied, it is
difficult to draw inferences about geometry and structure.
We sought to address the issue of whether
plumes actually extend to very high heliocentric altitudes by
improving the signal-to-noise ratio in LASCO wide-field observations
of the coronal hole, and imaging the plumes in visible light
as with previous, lower coronal observations.
Using a high cadence observing sequence, we have generated LASCO C-3
images with effective exposure times of thousands of seconds
and actual durations of less than four hours. These images, which are
accumulated over a short enough time that polar plumes are not smeared
by more than about 1/4 of their width, show that the brightest plumes
extend to the outer edge of the LASCO C-3 field of view at 30 R (in
the image plane). We are able to estimate the excess electron density
in the plumes and hence, using the global polar magnetic field, the
parameter within the plumes. (, the dimensionless ratio
of the gas dynamic pressure over the magnetic pressure, determines the
degree of control which the magnetic field exerts over the plasma.)
OBSERVATION AND DATA REDUCTION
Because the LASCO C-3 field of view spans great variation in
brightness, single images saturate the detector near the occulting
disk after only 30 seconds of exposure, while there is still little or
no signal from the outer portions of the coronal hole. Indeed, during
the first few months of the SOHO mission, the LASCO synoptic
images excluded the top and bottom parts of the image plane, because
individual images do not contain significant coronal signal. However,
multiple exposures may be averaged together on the ground, where
available dynamic range is virtually infinite, in order to increase the
effective exposure time and bring extremely weak signals above the
photon shot-noise floor.
The practical limit to effective exposure time when viewing static
structures is the longest acceptable time before solar rotation blurs
the coronal image, reduced by the maximum duty cycle of the C-3
shutter. In 6 hours, the Sun rotates approximately 3O, which is
sufficient to blur plumes tilted 45O out of the image plane by
1/3 of their apparent width; this may be regarded as a practical limit
to acceptable exposure duration. The shutter duty cycle is determined
by the ratio of the longest feasible exposure time to the fastest
possible observing cadence. The cadence is limited by the telemetry
resources available to LASCO. By reading out only half of the CCD and
binning the C-3 images 2x2 to produce a 512x256 pixel image of the
northern half of the corona, we were able to generate and downlink one
30-second losslessly-compressed C-3 exposure approximately every
90-100 seconds, for a 30% duty cycle. Frame selection on the ground
to avoid frames with missing data blocks and/or large cosmic ray hits
further reduced the effective duty cycle to just over 20%. Lossy
compression would have reduced the number of telemetered bits per
frame, increasing the overall duty cycle of the exposure; but it would
have discarded valuable information about the very structures we
sought to identify.
On 24 March 1999, we ran a special observing sequence on LASCO for
several hours using the program described above, yielding 3,120
seconds of handpicked exposures during a single four hour period. The
data were normalized for actual exposure time, despiked to remove
stars as well as cosmic rays, and background-subtracted with a
smoothed monthly F-corona estimate generated from minimum image values
in the surrounding four weeks, following the technique of
Wu (1997). For further enhancement, we transformed the data into
the conformal azimuthal coordinates used by DeForest et al. (1997), and
applied several spatial filters to the data to reduce the radial
intensity gradient and enhance contrast for plume-like features.
The first filtering step on the transformed image was smoothing
with a 4O (in azimuth) full-width half-maximum, circularly
symmetric two-dimensional Gaussian kernel. This operation works well
in the chosen conformal azimuthal coordinates, because the scale factor
between physical CCD pixels and transformed pixels changes with altitude,
so that the outermost, faintest parts of the image are smoothed over
more CCD pixels than are the innermost, brighter parts of the image.
To maintain uniform feature contrast and eliminate the residual radial
background gradient, we equalized the first and second moments of the
brightness distribution across all horizontal rows in the
transformed image. First we subtracted the average brightness value
of each row from all the pixels in that row; then we divided the
resulting brightness values by the standard deviation across the
row. Finally, we subtracted out low spatial frequencies by
one-dimensional unsharp masking: we subtracted a smoothed version of
each row from the original data. The unsharp masking kernel was a
1-D Gaussian with a full width at half-maximum of 30O (in
azimuth). The total effect of the processing was to limit resolved
spatial structures to the 4O-30O range in azimuthal sizes,
and to over 10% in radius: only azimuthal structures that subtend more
than 4O and less than 30O are seen, and radial
resolution is limited to structures whose radial extent is more than
1/10 of the structure's distance from disk center.
FIGURE 1
|
Figure 1 shows the fully processed image in azimuthal space, complete
with data from the LASCO C-2, HAO Mk 3 K-Coronameter, and
SOHO/EIT instruments for context. The masked-out region near
+30O azimuth is a foreground streamer that was removed from the
final image. Several plumes are clearly visible, extending through
the C-2 field of view and out to the edge of the C-3 field of view at 30
R from disk center. Stars are not visible in Figure 1, as they are
in other published C-3 images, because they were filtered out in the
despiking step. The HAO and EIT images are filtered by the same
technique as the C-3 data (with a smaller smoothing kernel); but the C-2
data are only radial-filtered and not unsharp-masked. Figure 2 shows
the C-3 data re-transformed back to the original image plane, for
context.
|
FIGURE 2
|
The use of unsharp masking, particularly in the presence of the
foreground streamer, gave rise to the concern that the ``plumes'' in
Figure 1 might in fact be artifacts of the filtering process. To
address such concerns, we used smoothing and unsharp masking with
Gaussian convolution kernels to prevent ringing of high spatial
frequency components in the images, as can occur with boxcar or ``top hat''
kernels. As an additional check, the bases of the structures seen in
the C-3 field correspond well with the bright structures at the top of
the C-2 field of view, even though the C-3 images are unsharp masked and
the C-2 images are not. This indicates that the C-3 structures are
solar and not artificial in origin.
|
RESULTS
FIGURE 3
|
Figure 3 is a plot of the observed intensity in the plumes, in C-3
digitizer count pixel-1sec-1,
versus azimuth for several
altitudes in Figure 1. The plots show intensity that is
zero-subtracted and unsharp masked, but not radially filtered by
standard deviation division as in Figures 1 and 2. The plumes visible
in Figure 1 are also visible in the plot, with reduced contrast (as
expected) at the higher altitudes. The lowest intensity plot, at
25 R in the image plane, shows an intensity contrast of
0.2 count pixel-1sec-1
peak-to-peak (under
0.1 count pixel-1sec-1
RMS). Because of the unsharp-masking and zero-subtraction steps that
we used, no absolute contrast (plume brightness versus background K-corona
brightness) measurement is possible.
|
FIGURE 4
|
Figure 4(a) is a plot of measured
brightness along each of
three plumes (perpendicular to the plot in Figure 3), showing the
excess brightness of these plumes compared to their adjacent
interplume regions. Because mass is conserved in the solar wind,
radial structures such as we observe at high altitude should fall off
in density as R-2 if they support a
constant-speed flow, or as
R-2/V(R) if they support variable flow.
Because LASCO C-3
sees primarily scattered light from the photosphere, with illumination
decreasing as R-2 at high solar altitudes,
the observed plume
brightness falls more rapidly than the density falloff with altitude.
Because the plasma is optically thin and the LASCO intensity signal is
linear in the electron column density (modified by local
illumination), the observed excess intensity of the scattered light in
an imaged plume is proportional to the total excess column density in
the plume. Neglecting brightness variations within
the plume and using the radial geometry found in the outer corona (shown
in Figure 5),
|
where Iplume is the plume's excess brightness above background,
D is the plume's diameter,
is the plume's
projection angle out of the plane of the sky,
n'e is the plume's
excess electron density over background,
t is the differential Thomson scattering cross section
('t
=
t (1+ sin2)(8 
/ 3)),
B is the local illumination brightness,
R is the actual radius along the plume from the Sun's center,
is the plume's subtended angle relative to the Sun's center,
v(R) is the outflow rate,
n'e0 and v0 are extrapolated values at 1 R,
and I is the Sun's surface brightness.
Collecting terms and converting to image plane coordinates,
where b is the impact parameter of the line of sight (in other
words, radius from disk center in the image plane), and the quantity
in square brackets is constant along each plume.
The quantity b3 Iplume, plotted in
Figure 4(b), varies inversely as radial outflow speed. Figure 4(b) is
consistent with either a rising or a decreasing trend with altitude,
so this measurement does not indicate whether the wind in plumes is
still undergoing acceleration at these altitudes.
FIGURE 5
|
Assuming that the plumes are visible only in Thomson scattered
photospheric light, and that they are circular in cross section (so
that D, and hence , may be measured by the apparent width
of each plume), it
is possible to invert (1) from the data, and derive the excess density
within the plumes using the LASCO photometric calibration. With a
uniformly dense plume of thickness D, and far enough from the
Sun that 1/R ~ sin(1/R), the plume's excess electron
density at an observed point is:
|
where s is the line-of-sight depth of the plume.
With D=4R,
b=30R,
Iplume=0.2 count pixel -1 sec-1,
LASCO C-3 intensity calibration of
(5x10-13I
count-1 pixel sec), and
=0
(plume in the plane of the sky), we derive a ``minimum'' density excess of
2.6x103cm-3 at
30R.
Using =45O, we derive a similar excess of
2.0x103 cm-3
at R=42R, or (assuming constant radial outflow)
3.9x103cm-3 at
R=30R. The a priori
uncertainty in the typical density of our observed plumes is a factor of
~2 around these figures.
It is useful to normalize the observed densities relative to a
constant-speed, radially expanding model wind. Conservation of
mass requires that such wind decrease its density with altitude as R-2;
a factor of R2 is multiplied back into the normalized
``electron-flux density'', yielding a figure that is comparable between
measurements at different heliospheric distances
(Feldman}. Our estimated excess density values of
2.6 x 103 - 4 x 103 cm-3 at R=30R
are equivalent to excess electron-flux densities
of 51 - 77 cm-3 AU2; this
is 20-30 times more than the value of 2.5 cm-3 AU2
measured by Ulysses for the total proton flux in the fast solar wind
(Feldman et al. 1996), and a factor of 3-5 greater than the average
total density of 800 cm-3 at 30 R that was obtained by
Bird et al. (1994) by radio sounding of the solar minimum coronal hole.
The excess shows that plumes are significantly denser than the
surrounding media at these altitudes. The plumes with the greatest
observed azimuthal angle relative to the pole extend over 70O
away from the pole in the plane of the sky (Figure 1). If the plumes
near the center of Figure 1 are inclined at that angle to the line of
sight, then we are detecting them at actual altitudes as high as 80
R in three dimensional space.
We have calculated the plasma parameter based on an assumed
average value for the magnetic field in the coronal hole, an estimated
temperature for the plumes, and the measured density. Neglecting
differential-temperature effects between ions and electrons, the
plasma is:
with kB the Boltzmann constant,
T the plasma temperature, and B the
magnetic field strength. We approximate B by using the coronal hole
average radial field of 10 Gauss at the photosphere and applying
superradial expansion and flux conservation. DeForest et al. (1997)
observed plumes with a linear superradial expansion coefficient of 6
between the solar surface and 10 R, above which the plumes were
approximately radial. Using this superradial expansion factor yields
a total areal expansion of approximately 3x104 in the plumes'
cross-section between the surface and 30 R, for an estimated field
strength of 3x10-4 Gauss inside the plumes. Using
T=106 K for the plume temperature yields a of
200-300 at R = 30R.
This should be regarded as an order-of-magnitude estimate, because of
significant uncertainty in the magnetic field strength.
DISCUSSION
Our observation of plumes at three dimensional altitudes of
~30-45 R supports the conclusion by Woo and Habba (Woo 1996; Woo & Habbal 1997; Woo & Habbal 1998) that
plume structures
persist to at least 40 R, despite concerns
(Pätzold & Bird 1998)
about systematic errors in that radio sounding measurement. Our
structures subtend approximately 10O
relative to solar center, so
they would take about 2.5 days to pass through the Ulysses
beam at 4O /day (Pätzold & Bird 1998).
This is somewhat longer
than the 1-day period claimed by Woo & Habbal (1997); but the
smoothing steps in our image preparation could prevent us from seeing
a hypothetical signal at 4O azimuthal frequency, so our
observation does not contradict the radio sounding results.
Because we are able to trace individual high altitude plumes (even at
azimuths, and hence colatitudes, as high as 70O) to root
structures in the polar coronal holes within 20O of the pole, our
data suggest that the ``low latitude plumes'' detected by the
Woo & Habbal (1997) measurement may in fact be polar plumes that
expand superradially to low equivalent latitude at high altitudes. At
altitudes above 5 R, plumes are
approximately radial simply because
they trace lines that are essentially straight and that have solar
impact parameters of less than 1 R
(Fisher & Guhathakurta 1995):
any linear feature is approximately radial at distances that are large
compared to the feature's impact parameter with the origin.
Because of the faintness of the plume signal at high solar altitudes,
we are able to detect only a few of the brightest plumes that were
present on the day of our observation. The present result is that the
very brightest plumes have overall azimuthal structure that extends to
~45 R in three dimensions; but we can draw no conclusion about what
happens to the internal structure in the plumes. At 6 R in the
image plane (the top of the C-2 field of view), the brightest plumes
have obvious internal structure and fainter, smaller plumes are
visible in the interstices between the brightest structures; but we
have smoothed over such features in constructing the deep-field image
with C-3. Hence, we cannot eliminate models that predict turbulent
behavior or cross-field-line mixing of momentum or gas on spatial
scales smaller than the width of a plume. Our observations eliminate
only those that would cause the plumes themselves (on spatial scales
of order 10O azimuth) to dissociate at altitudes below 30-45 R.
There are 7 plumes visible at 20 R in the image plane in the left
half of Figure 2, each subtending approximately 5O-10O of
azimuth. If the plumes are approximately circular in cross section
(the assumption used for the density derivation above), then together
they subtend ~25 millisteradians, or approximately 1% of the 3
steradians subtended by the left half of the coronal hole. If their
density is 10 times that of the surrounding medium and they are
traveling at approximately the same speed as the overall wind, then
these few brightest plumes alone account for about 10% of the mass flux in
the fast solar wind emerging from their portion of the coronal hole,
with more numerous but fainter plume structures presumably contributing
3-5 times more.
The existence of high density streams 30-45 R above the surface of
the Sun does not negate instability models such as that of
Parhi, Suess, & Sulkanen (1999); rather,
it both restricts the altitude range in
which they can occur and lends strength to the argument that they do
occur. Density fluctuations of an order of magnitude are not observed
by Ulysses (Feldman et al. 1996), and fluid dynamic
instabilities remain the most credible model to explain the
disappearance of the observed density fluctuations between the top of
the observable corona and the solar wind at 1 AU.
The lack of order-of-magnitude density fluctuations in the Ulysses
measurements, coupled with the present observation, provide strong
evidence for plume dissociation by mixing: if the plumes are not
subject to mixing at high altitudes, then the disparity in density
between plume and interplume regions must either be resolved by
further superradial expansion of the plumes, or be matched by an
opposite disparity in outflow speed along the plumes to keep the
outward mass flux constant across field lines. However, there is a
known compositional mismatch between plumes, which have enhanced
abundances of elements with low first ionization potential, and the
bulk of the high speed solar wind, which does not
(Feldman et al. 1998; Reisenfeld, McComas, & Steinberg 1999).
Hence, the plumes cannot expand
to form the bulk of the wind via very high altitude
superradial expansion. Mixing or speed disparity must account for
their disappearance.
In the absence of mixing across field lines, the plumes would have to
move slowly at our observed altitudes and then be accelerated
somewhere above 45 R
to match the outward flow of the interplume
regions. If the interplume flow speed is 700 km sec-1 and the
interplume densities are to be consistent with Ulysses' mass
flux measurements, then in the absence of lateral mixing the flow
speed in the plumes would have to be only
~40 km sec-1
at 30-45 R
to match our observed excess densities. This speed is smaller
than the observed wind speeds measured by direct tracers
(Wood et al. 1999; Breen et al. 1999) and by Doppler
dimming (Cranmer et al. 1999),
implying that cross-field mixing, presumably due to turbulent
instabilities in the plumes, is the most likely cause of the plumes'
demise between 45 R and 1 AU.
Our figure for the plasma parameter within the plumes
represents a lower-bound estimate. We underestimated by
using only the excess
density within the plumes, rather than the total density, to calculate
the gas pressure. Due to the large amount of
both spatial and temporal averaging which we have used to bring out
the weak signal in the outer reaches of the C-3 field of view, the
present measurement is not sensitive to such substructure at higher
solar altitudes, but at the top of the LASCO C-2 field of view (6 R
in the image plane), the observed plumes have a considerable amount of
substructure (Fig. 1). If the plumes are in fact as inhomogeneous at
the top of the C-3 field of view as they are in the C-2 field, then
D would be significantly reduced in equation (2), raising
the peak density and parameter estimates by another factor of
perhaps 3-10, and reducing the filling factor estimates by a similar
amount. Finally, pressure balance effects are likely to reduce the
field strength in the plumes below the average for the coronal hole,
increasing further.
CONCLUSIONS & SUMMARY
We have identified several bright polar plumes extending out to
altitudes of 30 R in the image plane, or ~45 R in 3-space,
well above the conventional top of the solar corona at 10 R and
into the constant-velocity wind regime as determined by interplanetary
radio scintillation measurements (Breen et al. 1997;
Breen et al. 1999). The
plumes that we identify are imaged in white light, lending support to
previous reports of high altitude plume detection using radio sounding
(Woo 1996). We are able to estimate the typical density
enhancement in the plumes compared to the rest of the interplume
corona, and find values of a few x 103
cm-3, or R2-normalized density excess of 50-80
cm-3 AU2. Our values for plume density at
these altitudes are significantly larger than the in situ
R2-normalized density for the solar wind as measured by
Ulysses during its north polar pass. The discrepancy between
the high observed plume densities at 30-45 R and the uniformity of
the interplanetary high speed solar wind remains a puzzle. The
present observation may be used to constrain the physics of the
transition from inhomogeneous corona to homogeneous solar wind. We
have demonstrated that high altitude breakup of the plumes through
hydrodynamic instabilities, such as are proposed by Parhi, Suess, & Sulkanen
(1999),
is likely (in that >> 1), and that it is
currently the most plausible explanation for the discrepancy between
the coronal hole's inhomogeneity and the wind's uniformity.
ACKNOWLEDGEMENTS
We would like to thank the EIT Consortium for their willingness to
interrupt the ongoing SOHO/EIT Synoptic Program to make this
observation. We are also indebted to S. Suess of NASA/MSFC for
helpful discussion of the results we present here. Comments from the
referees and from A. Stern and W. Colwell at SWRI helped significantly
to improve the write-up. CED's work was supported through NASA Grant
NSG-5131. SPP was supported through NASA contract S-8670-E. MA is
supported through NASA grants and through
the Naval Research Laboratory. SOHO is a mission of
international collaboration between NASA and ESA.
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