Temperature Anisotropies of Heavy Solar Wind Ions from
Ulysses-SWICS
R. von Steiger and T. H. Zurbuchen†
International Space Science Institute, Hallerstrasse 6, CH-3012 Bern, Switzerland
†
Dept. of AOSS, Univ. of Michigan, Ann Arbor, MI 48109, USA
Abstract. We report the first in-situ measurements of temperature anisotropies of heavy ions in the solar wind, obtained
with the Solar Wind Ion Composition Spectrometer (SWICS) on the Ulysses spacecraft. Since SWICS measures only 1dimensional cuts through the full, 3-d velocity distribution functions we resort to a statistical approach, separating the particle
data according to the instantaneous magnetic field angle. We apply this analysis to the ions of He and O6 during extended
time periods in the fast streams from both the south and the north polar coronal holes that Ulysses traversed in 1993–96.
In both cases we find anisotropies of the order of T T 08. The results of this study are discussed in relation to the
observations made on Helios for He in the 1970s, and to recent observations made on SOHO-UVCS, which show extreme
temperature anisotropies of O VI, or O5 , at a few solar radii.
MOTIVATION
suprathermal tails and anisotropies. The principal question is whether or not we can find any residual signature
in interplanetary space of the anisotropy in heavy ions
found with SOHO-UVCS in the corona.
The kinetic properties of heavy ions in the solar wind are
indicative of processes affecting their distribution functions in the solar corona and in interplanetary space.
Earlier observations at 1 AU have established that all
heavy ion species flow approximately at the same bulk
speed and have approximately equal thermal speeds
(i.e., mass-proportional temperatures), with exceptions at
times when the solar wind density was unusually high. At
5 AU such exceptions no longer occur and the basic picture applies with very high accuracy [1, 2, 3]. This was
interpreted as evidence for the growing dominance of
wave-particle interactions over Coulomb collisions with
increasing heliocentric distance.
Even though the solar wind is often modelled by fluid
or MHD equations, it is important to understand the underlying physics and processes that determine its expansion and acceleration. These processes seem to occur
on a kinetic scale, leading to deviations from a thermal
Maxwell distribution.
Recent results from SOHO-UVCS [4, 5] suggest that
kinetic processes may even dominate very close to the
Sun. Of particular interest is the temperature anisotropy
in O VI, or O5 , which is observed to be very large,
T T 1. All these UVCS remote solar wind measurements of the outer corona are done using emissions from
heavy ions, such as from O and Fe.
In this paper we address these topics by investigating the distribution functions of heavy ions observed
on SWICS/Ulysses at several AU, with emphasis on
PREVIOUS RESULTS
Anisotropies were found both in the H and He distribution functions with the Helios plasma experiment in
the 1970s [cf. 6, and references therein]. The core of the
distribution functions often showed an anisotropy perpendicular to the field direction, i.e., in the same sense
as now seen with SOHO-UVCS. At the distances closest to the Sun, 0.5 AU, it sometimes was as strong as
T T 2, but decayed with increasing distance out to
1 AU. The decay was more pronounced in the slow solar
wind, most likely owing to the longer expansion time [6,
Fig. 8.1]. On the other hand, the full distribution functions were often associated with a component drifting
outwards along the magnetic field direction, i.e., with an
opposite anisotropy of T T 05.
A similar, yet weaker, anisotropy was found with
Ulysses-SWOOPS in the distribution functions of He at larger heliospheric distances of 1.5–4.2 AU: Reisenfeld et al. [7] report T T 087, which was essentially
constant with distance.
Observations of heavy ions with Ulysses-SWICS
[8] at
5 AU show no differential streaming between species, nor any significant deviation from
mass-proportional temperatures. This demonstrates the
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
526
Eq.
N.Pole
10
400
2.0
1.0
1.0
rvst, ISSI, vatofa.grf, 11-Jul-02
cos(Field Angle)
TO [MK]
3.0
0.5
0.0
-0.5
-1.0
1993
1994
1995
1996
South PCH
Parallel Field
Perpendicular Field
5
Ulysses-SWICS
800
He2+ Phase Space Density [s3/km6]
vα [km/s]
S.Pole
4
10
103
102
101
600
1997
700
800
900
Speed [km/s]
Year
1000
1100
FIGURE 2. Sample distribution functions of He obtained
in the southern fast stream. Red: magnetic field parallel to the
radial direction; blue: perpendicular field. Note the presence of
suprathermal tails except in the Sunward direction.
FIGURE 1. Overview of the time periods selected for this
analysis. Red shade: He at full, 13-minute time resolution;
blue shade: O6 at 3-hour time resolution.
increasing importance of wave-particle interactions,
which are heating and accelerating the heavy species,
with heliocentric distance [3]. Extending these observations we now search for possible anisotropies in these
heavy ion distribution functions.
resolution of 1 minute, which is then averaged over the
accumulation period. A plot of the thermal speed as a
function of the field angle finally reveals the average
anisotropy.
Two sample distribution functions of He are shown
in Fig. 2, one for parallel field (red) and another, taken
at a different time, for perpendicular field (blue). The
cores of both samples are very closely approximated by
Maxwellian fits. However, at 1 % below the maximum
significant suprathermal tails can be seen except on the
low-speed side of the parallel spectrum, i.e., in the direction back towards the Sun.
The thermal speed is obtained as the second moment
of the full distribution functions observed by SWICS
including the tails. The thermal speed determined from
a 1-d cut at a field angle φ through the 3-d velocity
distribution function is related to its field-parallel and
field-perpendicular components by
OBSERVATIONS
We analyse distribution functions of He and O6
obtained in polar high-speed streams at
2 AU with
Ulysses-SWICS, with particular aim at the kinetic temperatures and their anisotropies. We picked two time periods each in the high-speed streams from the south and
the north polar coronal holes during solar minimum (see
Fig. 1). In the case of He the flux was sufficient so
spectra could be taken every 13 minutes, which is the the
full time resolution of SWICS. We therefore only analysed two short time periods at high latitudes for this ion,
shaded in red in Fig. 1. Since the flux of O 6 ions is
much lower, we had to accumulate the distribution functions over 3 hours (corresponding to about 14 spectra) in
order to obtain sufficient statistics. Consequently, a much
longer time period was analysed for this ion, shaded in
blue in Fig. 1.
Strictly speaking, it is not possible with SWICS to
observe a temperature anisotropy, as the sensor measures only 1-d cuts along the radial direction through the
full, 3-d distribution functions. We therefore have to rely
on a statistical approach in order to determine thermal
anisotropies (a similar approach was used for alpha particles from Ulysses-SWOOPS by Reisenfeld et al. [7]).
The spectra are sorted according to the average magnetic field angle during their accumulation. This angle
between the radial direction and the magnetic field, φ ,
is measured on Ulysses with the VHM/FGM experiment
[9] and obtained from the Ulysses Data System at a time
1
2
vth φ φ sin
cos
v2
2
v
φ
2
2
th
th
(1)
In the limit of small anisotropy, i. e. v th vth , this can
be shown to yield a linear relation in cos 2 φ ,
vth φ v
th
vth vth cos2 φ (2)
Plotting vth from a large number of spectra obtained at
all field angles versus cos2 φ thus may reveal an average
anisotropy if it shows a systematic trend. This is done
in Fig. 3 for He and in Fig. 4 for O 6 . The data
from the southern stream (left panels) are plotted versus
cos2 φ simply to illustrate that the field was pointing
inward there. Thick green data points indicate periods
when the average magnetic field direction was welldefined over the accumulation time of the spectrum, i.e.
the variability of φ remained below a certain threshold,
527
80
80
Helium, South Coronal Hole, Tperp / Tpar = 0.79
60
He2+ Thermal Speed [km/s]
He2+ Thermal Speed [km/s]
60
40
40
20
20
Helium, North Coronal Hole, Tperp / Tpar = 0.79
Ulysses-SWICS, Days 100-109, 1995, 13-Min Data
Ulysses-SWICS, Days 340-349, 1994, 13-Min Data
0
0
-1
-0.8
-0.6
-0.4
-cos2(Field Angle)
-0.2
0
0
0.2
0.4
0.6
cos2(Field Angle)
0.8
1
FIGURE 3. He thermal speed from 1000 13-minute spectra each in the southern (left) and northern (right) fast stream,
plotted vs. cos2 of the field angle. The thick, green data points indicate spectra taken when the magnetic field variability was small,
while the others are marked with thin blue symbols. The anisotropy is found from the parameters of the fit, which is marked as a
thick red line for the green data points only and a thin orange line for all data points. Both plots show a consistent trend, which is
interpreted as an average anisotropy of T T He 079.
80
80
Oxygen, North Coronal Hole, Tperp / Tpar = 0.83
Oxygen, South Coronal Hole, Tperp / Tpar = 0.81
60
O6+ Thermal Speed [km/s]
O6+ Thermal Speed [km/s]
60
40
20
40
20
Ulysses-SWICS, Days 182-273, 1994, 3-Hr Data
Ulysses-SWICS, Days 182-273, 1995, 3-Hr Data
0
0
-1
FIGURE 4.
-0.8
-0.6
-0.4
-cos2(Field Angle)
-0.2
0
0
0.2
0.4
0.6
cos2(Field Angle)
0.8
1
Same as Fig. 3, but for 750 3-hour spectra of O6 . Again, an average anisotropy of T T O6 082 is found.
whereas the thin blue data points refer to periods with
more variability. A fit is calculated according to Eq. 2 to
all data points, indicated as a thin orange line, and to the
subset of the green points, indicated as a thick red line.
From the fit parameters we finally obtain the anisotropy,
T T v2th π 2v2th0.
It is evident from these figures that an anisotropy exists
in all cases. For helium (Fig. 3) we find T T He 079 both in the southern and the northern polar stream,
although with larger scatter there. This is smaller (i.e.,
the anisotropy is larger) than the result from SWOOPS
[7], but considering the 10 % accuracy of both results
they are consistent. In both panels of Fig. 3 it is irrelevant
whether all data points are included in the fit or only
those with small field variability, i.e. on the time scale
of 13 minutes the variability has no effect on the result.
For oxygen (Fig. 4) we first note that there are significantly fewer data points near cos φ 1. This was to
be expected since these spectra were accumulated over
3 hours, and it is less likely for the field to remain parallel on this longer time scale. When we restrict ourselves to the spectra with little field variability we obtain an anisotropy of similar magnitude as for He both in the southern and the northern polar stream. If
we had taken all data points we would still have found
an anisotropy, albeit a weaker one. Disregarding the
points with large field variability we obtain an average
anisotropy of T T O6 082. Once again, we stress
that this is not the anisotropy of individual spectra, but a
gross average over the two three-month periods indicated
in Fig. 1.
528
anisotropies 1, slow energy diffusion (and therefore
very weak tails), and mass-per-charge dependencies between different heavy ion species, neither of which is observed in the outer heliosphere.
A statistical model has qualitative advantages because
it implies a temperature anisotropy 1, the development
of tails that are broadly directed away from the Sun
(since most waves propagate outwards in coronal holeassociated wind [14]), and the similarities of He and O
(and other heavy ions). However, no quantitative theory
is currently available that can be used to compare with
our data.
DISCUSSION
Many theories in the corona and heliosphere predict or
assume T T 1 [10, 11, 12]. The interaction of particles with the ambient turbulence occurs through cyclotron interactions, and the energy is dissipated from
resonant waves through cyclotron resonance, i.e., ω k
k v Ωmq. These theories therefore dissipate only
high-frequency waves, whereas most of the energy generally resides in low frequency waves. Also, there should
thus be a mass-per-charge dependency in the interaction
term that should be observable.
On the other hand, T T 1 is predicted for a statistical acceleration process [13] that assumes the energy
being dissipated by Landau resonance, i.e., ω k k
v 0. The energy is directly dissipated from magnetic
field compressions. This heating can happen at all wavelengths as outwards-propagating waves interacting with
outwards-propagating particles (relative to the plasma
frame). Statistical theories also predict that there should
be tails on the distribution functions, as is observed.
While the first, cyclotron resonant picture probably applies in the corona and innermost heliosphere our results,
taken at 2–3 AU, appear to favour the second, statistical
picture: We observe T T 1 in both species investigated, equal to within a few percent although their massper-charge differs by 30 %, and we find outward-directed
suprathermal tails. This is consistent with the Helios results mentioned above that saw the opposite anisotropy
decay with increasing distance, while suprathermal tails
were building up.
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1.
2.
3.
4.
5.
6.
7.
CONCLUSIONS
8.
We have reported the first in-situ measurements of a
temperature anisotropy of oxygen ions at a heliocentric
distance of 2–3 AU:
9.
T T O6 082
These are the first measurements of the full dynamic properties of O, particularly of its temperature
anisotropy. The velocity distribution functions of He and O6 are found to be very similar, and both show
a very similar anisotropy. The distribution functions of
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non-Gaussian, with extended suprathermal tails, except
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These observations rise questions about the approximation of bi-Maxwellians commonly used in coronal
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They show that there are significant deviations in both
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10.
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