Large-scale structure of the polar solar wind at solar
maximum: ULYSSES/URAP observations
Karine Issautier , Michel Moncuquet and Sang Hoang
Observatoire de Paris, LESIA, CNRS UMR 8109, 92195 Meudon, France
Abstract. We outline the recent in situ radio observations obtained by Ulysses during its second fast latitude scan near the
2001 solar maximum. From 72o N, Ulysses was embedded in a continuous fast wind associated with a northern polar
coronal hole. During that period, we enlight the variation of the electron density and thermal temperature with the heliocentric
distance and latitude, obtained with the quasi-thermal noise spectroscopy method. Since the scaled mass flux is observed
roughly constant, we derive the profile of the electron thermal temperature, assuming a simple power-law model. Indeed, we
find that the electron density varies as R 2 00 1 while the thermal temperature varies as R 0 70 1 , in good agreement with
the results obtained in polar coronal holes in 1995 near solar minimum.
INTRODUCTION
fast wind flows from small coronal holes. The unique
long interval of fast solar wind is observed at high northern latitudes above 72 o N nearly at the end of the polar
pass.
Ulysses is the unique out-of-ecliptic mission that gives
us the opportunity since its launch in 1990 to continuously study the 3-D structure of the heliosphere during
a complete solar cycle and over a wide range of latitude. During its first pole-to-pole latitude scan in 19941995, Ulysses confirmed the rather simple structure of
the corona near the solar activity minimum, and showed
that two types of solar wind dominate the heliosphere
during that period. Indeed, a steady-state fast solar wind
is continuously observed at high latitudes as coming
from large polar coronal holes, whereas within 20 o
a more complicated mixture of winds, corresponding to
slow, intermediate speed flows, interaction regions and
transient events predominates in the ecliptic plane. At
high latitude poleward 40 o S, the inverse-square-drop-off
of the density suggests that the large-scale latitudinal or
temporal variations of the solar wind were very small.
Thus the observed electron thermal temperature profile
of R 0 64 is considered to be a genuine radial profile [1].
Ulysses explores its second polar passage during the
rising solar cycle to solar maximum. The state of the
corona appears to be dramatically different and much
more complex than at minimum, as one can see from
the SOHO/LASCO coronograph images. In addition, the
pole-to-pole radio spectrogram acquired from November
2000 to mid-October 2001 [3] exhibits large-scale variations, and numerous solar radio emissions at high frequency are observed in consistency with the increasing
solar activity. During all its journey from pole-to-pole,
Ulysses encounters different regimes of wind, slow and
intermediate wind from streamers, in addition to sporadic
SOLAR WIND ELECTRON
PROPERTIES
In this paper, we focus on the large-scale electron properties of the steady-state fast solar wind associated with
this northern polar coronal hole observed by Ulysses for
a few weeks near the 2001 solar maximum. The data
were obtained from 4 September 2001 (when the radial
distance R was 1.76 AU and the heliolatitude was 72 o ) to
14 November 2001 (when R was 2.25 AU and the heliolatitude was 76o ), beyond the north pole (for which the
latitude 80 2o was reached on October 13 rd 2001), using
the quasi-thermal noise (QTN) method from the Unified
Radio and Plasma wave (URAP) experiment [11] as explained below. Indeed, the restricted period mentioned
above is based on solar wind speed observations [4] from
which we found the largest roughly constant period of
high-speed wind, around 750 km/s 50 km/s.
Thermal Noise Spectroscopy Analysis
The so-called "quasi-thermal noise" is due to the random motion of the ambient particles which excite plasma
waves near the plasma frequency f p . The voltage induced
on the wire electric antenna is measured by a sensitive
radio receiver. The theoretical interpretation of the QTN
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
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FIGURE 1. (Top) Radio spectrogram from URAP experiment obtained in the northern polar coronal hole near solar maximum.
(Middle) From the thermal noise analysis, we deduce the electron density ( 37 000 black dots, given by the L-M fit and 3000
blue dashes, deduced from the plasma frequency cut-off) and thermal temperature ( 27 000 red dashes, given by the L-M fit)
versus time, together with their corresponding typical uncertainties (near day # 56). (Bottom) Histograms of the electron density
and core temperature, normalized to 1 AU using radial variations obtained in the present study. The distributions roughly reveal a
single wind population, with a tail of outliers which may correspond to the slow, hot and dense wind coming from the edge of the
coronal hole.
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spectrum, assuming a sum of maxwellian velocity distribution functions for the core and halo electron populations, yields in situ plasma parameters [5]. In particular, it gives an accurate determination of the electron
density (within a few percent) since it is based on the
plasma frequency location, therefore nearly independent
of gain calibration and photoelectron perturbations, contrary to particle analysers. The overall shape and level
of the spectrum also give the thermal temperature T c ,
suprathermal parameters and solar wind speed [2]. In
practice, we compute a model of quasi-thermal noise
spectral, depending on all above-mentioned parameters
(but mainly on f p and Tc ), and we fit the model to each
measured spectrum by using the Levenberg-Marquardt
(L-M) least-squares method [8, p678], which also provides the standard errors on the fitted parameters. This
original and simple technique is a powerfull tool to obtain an accurate in situ solar wind plasma diagnostics and
can be used to cross-check other plasma sensors.
In the following section, we select the core temperature for which the fitting of the voltage power spectrum to
the observations is the best, corresponding indeed to the
sigma of the fit better than 2.5%, as we did for the data
set obtained near solar minimum. Moreover, to get the
more accurate temperature measurements, it is important
to take this constraint on the fit into account during solar
maximum, since many solar radio emissions often pollute the high-frequency part of the spectrum, where the
core temperature is partially sensitive.
vertical bar is the uncertainty on such estimated density, and corresponds to twice the difference between two
equally spaced frequency channels (0.75 kHz), whereas
the black bold vertical bar is the typical uncertainty (
5%) on the density as obtained from the L-M fit.
Statistical features of this polar wind can be enlighted
in the bottom panel of Figure 1 from the histograms of
the electron density and temperature normalized to 1 AU
using radial variations obtained in the present study in the
steady-state solar wind. The mean of the electron distribution is around 2.8 whereas the fitted Gaussian distribution to the data is centered at 2.6 (solid line), which
is exactly the same value as obtained at solar minimum.
On another hand, the histogram of temperature peaks at
8 5 104 K , computed from the fit of a Gaussian distribution to the data, and its mean value is around 9 3 10 4
K. Both distributions roughly reveal a single type of flow.
However, the departure from a Gaussian distribution of
the two histograms, which both present a “tail”, shows
that the fast wind is somehow "polluted" by other kind
of winds, probably coming from the edge of the coronal
hole. Even if the solar wind speed reaches the maximum
of 800 km/s for this period, the fast solar wind appears to
be less fast and much variable than during the solar minimum [4], as also observed in magnetic field data [10].
Radial Profiles
To analyse the basic trend of the electron density variation with the heliocentric distance, we fit a power law
to the data set of about 40,000 data points obtained for
that period. We get the radial profile for the density, represented in logarithmic scales in Figure 2, processing a
“robust” linear regression by minimizing absolute deviation [8, p694]. The reason we cannot perform a leastsquares linear regression, as we did in fast high-latitude
wind during solar minimum[1], lies in the presence of
numerous “outliers”, clearly visible in these data. These
outlying points, which form the tail of normalized histograms (bottom of Figure 1) are real (not artefact) but,
as explained before, out from the fast stationary solar
wind we want to focus on. In this case, the classical leastsquares method must be disqualified because it is too
much sensitive to these outliers, and a so-called robust
method has been used instead; however it provides larger
errors on the fitted line than least-squares technique used
in [1]. The lower solid line on Figure 2 thus shows the
robust linear regression result on density data; the power
law index, deduced from the slope of the straight line, is
2 0 0 1. The density extrapolated to 1 AU, given by
the intercept, is found to be 2.75 cm 3 , which is in very
good agreement with observations of the fast solar wind
from the southern coronal hole around solar minimum.
Electron Density and Core Temperature
Figure 1 shows the radio spectrogram, displayed as
frequency versus time, with intensity coded by a color
scale, obtained from 4 september 2001 to 14 November
2001, when Ulysses explored the polar coronal hole of
the Sun, from 72 o N to 76o N beyond the north pole. One
can see the plasma line, revealed by the intense noise
in red, which fluctuates between 6 and 14 kHz. Using
the thermal noise technique on 128-second radio spectra
on Ulysses, we obtain the scatter plot of the corresponding electron density (black and blue), deduced from the
plasma frequency (n e ∝ f p2 ), and the core electron temperature (red), shown in the middle panel. The red bold
vertical bar is the averaged standard error ( 20%) on
Tc provided by the L-M fit. For very low densities, it
is sometimes impossible to accuratly fit to the observed
power spectrum: we get indeed too few measurements
below f p , since that frequency is too close to the lowest frequency of the URAP low-frequency receiver (1.25
kHz). In this case, we may use instead the empiric cut-off
of f p and so deduce only the plasma density, shown as
blue vertical dashes in the middle panel. The blue bold
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This suggests that the density profile is independent of
latitude or time variations, and corresponds to a spherical expansion, since the corresponding bulk velocity is
roughly constant up to 76 o N beyond the passage of the
north pole. Moreover, the scaled mass flux is also observed [3] to be constant.
From the above finding, we consider this density data
set as a rather good sample of stationary high-speed
wind in spherical expansion and thus we may describe
the thermal temperature with a power law depending
on the radial distance only. In the same way as for the
density, we find that the electron thermal temperature
profile in such a flow varies as R 0 70 1 between 1.76
and 2.25 AU, which is midway between adiabatic and
isothermal behavior. The result of the fit is the upper solid
line shown in Figure 2. The index of the power law is
compatible with that found near solar minimum in 1995
in the southern polar coronal hole (Tc ∝ R 0 64 ), whereas
the intercept of the temperature at 1 AU is 910 4 K,
larger to the last solar minimum value of 7.510 4 K. The
value of the power index is also in good agreement with
the results of Scime et al. [1994], where the radial profile
was deduced from 1 to 5 AU at solar maximum in the
ecliptic plane.
features as the single and well-defined flow measured
poleward of 40 o , near solar minimum during the first
Ulysses fast latitude scan. However, slight discrepancies
are probably due to the fact that Ulysses was not completely immersed in the polar coronal hole, because of
its limited size, and might have measured the edge of the
hole, which gives an average of density and temperature
(see histograms) 5% and 20% larger respectively than at
solar minimum.
It is important to note that either fluid or kinetic models are tempting to try to explain the electron temperature
profile [7]. Thus, to correlate observations to any theory,
one should accuratly measure the total electron temperature. An improved plasma diagnostics using the thermal
noise spectroscopy with kappa velocity distribution function for the electrons is in progress, and would give in situ
this fundamental parameter, which could then be directly
compared with models and constraint them.
ACKNOWLEDGMENTS
The Ulysses URAP investigation is a collaboration of
NASA/GSFC, Observatoire de Paris-Meudon, University of Minnesota, and CETP, Velizy, France. The French
contribution is supported by CNES and CNRS.
REFERENCES
1. Issautier K. et al., J. Geophys. Res. 103, 1969-1979 (1998a)
2. Issautier K., Meyer-Vernet N., Moncuquet M., Hoang S.,
McComas D.J., J. Geophys. Res., 104, 6691 (1998b)
3. Issautier K., Moncuquet M., Hoang S., Geophys. Res. Lett.,
submitted (2003)
4. McComas et al., Geophys. Res. Lett. 29(9), doi
10.1029/2001GL014164 (2002)
5. Meyer-Vernet N. and Perche C., J. Geophys. Res. 94,
2405-2415 (1989)
6. Meyer-Vernet N. and Issautier K., J. Geophys. Res. 103,
29,705-29,717 (1998)
7. Meyer-Vernet N. et al., Solar Wind 10, AIP Proceedings
(2002)
8. Press, W.H., et al., Numerical Recipes, 2nd edition,
Cambridge Univ. Press, New-York (1992)
9. Scime et al., J. Geophys. Res. 99, 23,401-23,410 (1994)
10. Smith et al., Solar Wind 10, AIP Proceedings (2002)
11. Stone R.G. et al., Astron. Astrophys. Suppl. 92, 291 (1992)
FIGURE 2. For the northern polar coronal hole near solar
maximum, radial variations of the electron density (light grey
dots) and core temperature (dark grey dots) are obtained by a
robust linear fit. The solid black lines are the best fit power laws
to the data with the index values shown.
SUMMARY & FINAL REMARKS
The second polar pass of Ulysses at solar maximum also
provides an opportunity to measure the radial gradients
of solar wind parameters in the fast wind, poleward of
72o N. From plasma thermal noise spectroscopy, we find
a core electron temperature profile varying roughly between isothermal and adiabatic up to 2.25 AU. Likewise,
the corresponding high-speed wind observed near solar
maximum in a polar coronal hole has rather the same
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