Alfvénic turbulence in high-latitude solar wind:
Is latitude a relevant parameter?
Bruno Bavassano1 , Ermanno Pietropaolo2 , and Roberto Bruno1
1
Istituto di Fisica dello Spazio Interplanetario (CNR), Roma, Italy
2
Dipartimento di Fisica, Università dell’Aquila, L’Aquila, Italy
Abstract. Plasma and magnetic field measurements by Ulysses during its first out-of-ecliptic orbit have
allowed extensive investigations on the behavior of Alfvénic turbulence in high-latitude solar wind. Most
analyses have shown that the turbulence evolution in high-latitude wind is radial, rather than latitudinal,
in nature. However, a recent study based on magnetic field fluctuations has suggested that latitude
might play a non negligible role. Here we further examine this possibility by using Elsässer’s variables,
that directly are related to the Alfvénic content of solar wind fluctuations. Our conclusion, supported by a
comparison between polar and ecliptic observations, is that latitude does not appear to have an appreciable
influence on the turbulence evolution in high-latitude solar wind.
INTRODUCTION
Observations by Ulysses during its first out-ofecliptic orbit have shown that, at low solar activity,
the high-latitude (or polar) solar wind is a fast and
relatively steady flow. A relevant feature of the polar wind is the ubiquitous presence of an intense flow
of Alfvénic fluctuations (e.g., Goldstein et al. [1995];
Horbury et al. [1995]; Smith et al. [1995]). Similarly
to previous ecliptic observations in fast streams (e.g.,
Tu and Marsch [1995]), a largely dominant fraction
of these fluctuations is outward propagating, with
respect to the Sun, in the solar wind frame. These
outward fluctuations mainly have a solar origin (or,
more precisely, inside the Alfvén critical point). Conversely, inward propagating fluctuations observed in
the interplanetary space can only be generated outside such critical distance.
A relevant point to be discussed is the nature of
the Alfvénic turbulence variations observed in highlatitude solar wind (i.e., radial, or latitudinal, or
both), given that both distance and latitude change
along the Ulysses trajectory. Several analyses of
Ulysses data have indicated that the variation of turbulence properties in high-latitude wind is essentially
radial, rather than latitudinal, in nature (e.g., Goldstein et al. [1995]; Horbury et al. [1995]; Forsyth et
al. [1996]). A further robust argument in favor of the
radial character of the turbulence variation comes
from the agreement between gradients observed in
high-latitude wind and in fast streams on the ecliptic.
This has been seen to hold both for magnetic field
fluctuations (as observed by Forsyth et al. [1996]
in high-latitude wind and by Bavassano and Smith
[1986] in ecliptic wind) and for outward and inward
Alfvénic fluctuations (as shown by Bavassano et al.
[2000] and [2001]).
In spite of all these pieces of evidence, we have decided of re-examining the role of latitude on Alfvénic
turbulence variations in high-latitude solar wind. We
have been motivated to this by the recent results
of Horbury and Balogh [2001], showing that fluctuations in magnetic field components at time scales
shorter than about 1 day (in the spacecraft frame)
exhibit a non negligible dependence on latitude. In
present analysis the same method of Horbury and
Balogh [2001], based on a multiple regression, will be
used, but we will directly look at the Alfvénic component of solar wind fluctuations, rather than at the
magnetic fluctuations. This is a remarkable difference. In fact, magnetic fluctuations, though obviously related to the Alfvénic turbulence, also include
non negligible contributions from other disturbances
and structures convected past the spacecraft by the
plasma flow. A problem with the regression analysis
is that it is based on variables (distance and latitude
of Ulysses) that are not mutually independent. For
this reason, when discussing the regression results,
we will take advantage of comparisons between polar and ecliptic observations.
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
449
DATA ANALYSIS
The analyzed intervals are highlighted in Figure 1,
where the solar wind velocity V , the proton number
density N normalized to 1 AU (assuming an inverse
square scaling with distance), the spacecraft heliocentric distance r, and the spacecraft heliographic
latitude λ are shown for years 1993 to 1996. The two
thick lines at the top, labeled s and n, indicate the
two intervals (southern and northern, respectively)
of full immersion of Ulysses in polar wind. The two
thin horizontal lines with label f highlight two polar
wind intervals selected in the phase of ‘fast latitudinal scan’ around the perihelion. The first interval is
from the maximum southern latitude (dashed vertical line on the left) to the exit from southern polar
wind, the second one from the entry into the northern polar wind to the maximum northern latitude
(dashed vertical line on the right). These two intervals allow to get a quick, but complete, latitudinal
survey of the polar wind for a reduced range of distances (see the r and λ variations in the two lower
plots). Finally, the horizontal line (of intermediate
thickness) labeled nHB indicates the period investigated by Horbury and Balogh [2001].
900
V
s
f
f
n
700
nHB
500
300
10
N
6
2
5
r
3
1
60
0
-60
93
94
95
96
97
year
FIGURE 1. Solar wind data and spacecraft coordinates
for years 1993 to 1996. Ulysses data have been made
available, through NASA/GSFC World Data Center, by
D. J. McComas and A. Balogh.
A point to be stressed in Figure 1 is the presence of spike-like variations of the normalized density N also during polar wind phases. These spikes
are weaker than those observed at lower latitudes,
nevertheless they indicate that also in polar wind
non negligible compressive effects are developed by
interacting flows (see also the velocity profile in the
top plot). They mainly affect polar wind observations towards the aphelion phase, when the spacecraft moves slowly in latitude and spends a lot of
time close to the low-latitude boundary of the polar wind region. Here stream interactions, typical of
the ecliptic wind, still persist, though with weaker
effects. All this indicates that in order to get a clean
evaluation of the polar turbulence variation a data
selection is needed, especially when observations at
large distance are involved. This point has already
been stressed by Bavassano et al. [2000] (hereafter
BPB), who derived, starting from the s and n polar
phases, a ‘selected’ data sample where all intervals
with large changes in plasma velocity, and/or plasma
density, and/or magnetic field magnitude were rejected. In the present study we will use this ‘selected’
sample, exceptions will be explicitly indicated.
Our analysis is based on the use of the Elsässer’s
variables (z± ), a well known tool to identify Alfvénic
fluctuations. They are defined as z± =v±b, where
v and b are the velocity and magnetic field vectors,
respectively,√ and b is scaled to Alfvén units (i.e.,
divided by 4πρ, with ρ the mass density). Taking
into account how the sign of the Alfvénic correlation
depends on the propagation direction with respect to
the background magnetic field, we will use the above
definition for the case of a background magnetic field
pointing to the Sun, while the equation z± =v∓b will
hold for the opposite polarity. In this way z+ (z− )
fluctuations will always correspond to modes with an
outward (inward) propagation, with respect to Sun,
in the plasma frame.
Analogously to the analysis of Bavassano et al.
[2000] (hereafter BPB), the results discussed here refer to hourly variances of z+ and z− . These variances
have been radially averaged on bins of 0.05 AU and
the resulting values (in the following e+ and e− ) have
been used, similarly to Horbury and Balogh [2001],
for a multiple regression study based on the equation
log(e± ) = A± + B± log(r) + C± sin(θ), where θ is
the absolute value of λ.
A relevant point to be stressed is that r and θ, being coupled each other by the equation of the Ulysses
orbit in a very specific manner, do not represent a set
of independent variables. Violating the assumption
that the variables in the regression are independent
is risky and renders the results of doubtful validity,
so that they can hardly be trusted. Though obvious,
this caveat has to be kept well in mind in the following. Our approach is that of performing the multiple
450
regression analysis mainly to highlight, with respect
to that of Horbury and Balogh [2001], the effect of using clean data samples and of looking at the behavior of z+ and z− , instead of the magnetic field. Our
conclusions about the role of latitude on the polar
Alfvénic turbulence evolution will mosty come from
comparisons with other observations on the ecliptic,
where latitudinal effects are absent.
Helios
104
Ulysses
e+
e+, e- e
2 2
-
_1.39
r
(km /s )
103
_0.42
r
_1.46
r
102
0.3
0.5
1
r
3
5
(AU)
FIGURE 2. This plot combines Ulysses observations in
polar wind with those by Helios inside 1 AU on the ecliptic plane. The values of e+ (e− ) are shown as squares
(diamonds), small for Ulysses and large for Helios. Best
fit lines and radial power laws for Ulysses data are given.
The figure is adapted from Bavassano et al. [2000] (copyright 2000 American Geophysical Union, modified by permission of American Geophysical Union).
Since our analysis is based on the same data set of
Bavassano et al. [2000], with the only difference that
they used radial bins of 0.1 AU (instead of 0.05 AU),
it is useful to briefly recall their results. To this end
we show in Figure 2 a slightly modified version of one
of their figures. This is a composite plot combining
Ulysses observations in polar wind with those by Helios 1 and 2 in the trailing edge of fast streams on the
ecliptic (as obtained from average spectra around 0.4
and 0.8 AU, see Tu and Marsch [1990]). It easily seen
that the e+ values observed by Ulysses exhibit the
same radial gradient over all the investigated range
of distances. In contrast, for e− a change of slope
around 2.5 AU is clearly apparent. Another remarkable feature is the good agreement of the Ulysses
gradients with Helios data.
OUTWARD FLUCTUATIONS
The values of the B+ and C+ coefficients for the
investigated samples are shown in Table 1. The first
row is for the Horbury and Balogh [2001] interval
(nHB ). Then, in the other rows, we give the results
for the northern hemisphere (n), the southern hemisphere (s), the northern and southern hemispheres
altogether (n+s), and finally the fast latitudinal scan
f (with and without data selection).
A first comment is about the nHB interval, the
same used by Horbury and Balogh [2001]. Here we
find, without any data selection, a value of C+ of
−0.11 ± 0.04, while at the same scale they observed
a value around −0.3. Thus, just by using z+ instead
of magnetic field, we are led to a remarkable reduction of the latitudinal effect. When selected data
are used, C+ becomes even smaller. For instance,
for both northern and southern polar phases (n+s
sample) we obtain a C+ value of −0.03 ± 0.03. A latitudinal effect, if any, surely is far to be significant.
We would like to stress the results obtained for
the sample f . In this case, with a latitudinally fast
moving spacecraft, the effect of disturbances close to
the low-latitude boundary of polar wind is greatly
reduced and data selection becomes less important.
As a matter of fact, using all available data in the
sample a value for C+ of −0.02 ± 0.07 is obtained.
This does not leave doubts about the absence of a
significant role of latitude in the e+ variation.
The above conclusion is definitely confirmed by the
good agreement (see Figure 2) between the e+ radial
gradient observed by Ulysses in polar wind and the
Helios observations on the ecliptic (i.e., done in the
absence of any significant change of latitude).
Table 1. Outward fluctuations regression: Radial
(B+ ) and latitudinal (C+ ) coefficients
sample
nHB ∗
n
s
n+s
f
f ∗
∗
451
B+
−1.44 ± 0.05
−1.44 ± 0.04
−1.41 ± 0.04
−1.42 ± 0.03
−1.50 ± 0.17
−1.48 ± 0.17
without data selection
C+
−0.11 ± 0.04
−0.06 ± 0.04
−0.01 ± 0.04
−0.03 ± 0.03
−0.01 ± 0.07
−0.02 ± 0.07
INWARD FLUCTUATIONS
Table 2. Inward fluctuations regression: Radial
(B− ) and latitudinal (C− ) coefficients
r (AU )
1.4 - 2.6
2.6 - 4.3
B−
−0.54 ± 0.16
−1.01 ± 0.23
C−
0.07 ± 0.10
0.28 ± 0.12
EQ
EQ
EQ
POL POL
TBN=0.3 TBN=0.5 TBN=1.0
-0.5
radial slope
As seen in Figure 2, the variation of e− cannot
be explained by a simple radial power law as for e+ .
Rather, two different radial regimes seem to characterize its behavior, with a break at a distance of
∼ 2.5 AU. The dual regime is probably related to
local generation effects that, important in the inner
region, become negligible at larger distance (e.g., see
Malara et al. [2001] and Del Zanna [2001]).
Applying the multiple regression separately to distances below and above 2.6 AU (see BPB), it has
been found (Table 2) that C− , negligible in the inner
region, becomes significantly different from zero in
the outer region. This inconsistency (why should latitude be important at large distance only?) confirms
that it is hard to trust on a multiple regression analysis based on variables that are not independent. This
is especially true in the region outside 2.6 AU, where
the e− signal has become quite noisy, due to both
ambient (i.e., related to local plasma structures) and
instrumental disturbances. Thus, to get a reliable
view about the role of latitude on the e− variation
we have to look for other arguments, in particular we
have to compare the polar trends with observations
done on the ecliptic plane.
Under this approach, the lack of a latitudinal effect for e− in polar wind inside 2.6 AU comes from
the agreement of the Ulysses gradient in this region
with Helios observations on the ecliptic (Figure 2).
As regards the region outside 2.6 AU, Figures 2 and
3 show that there e− declines at approximately the
same rate as e+ . Having established that e+ is not appreciably affected by latitude, we may infer that this
holds for e− too. A second, unequivocal, argument
in favor of this conclusion comes from the agreement,
within errors, with the e− gradient observed at these
distances in the ecliptic leg of the Ulysses trajectory
(Figure 3 and Bavassano et al. [2001]).
All these pieces of evidence offer a robust conclusion in favor of a radial nature for the inward Alfvénic
turbulence evolution in polar wind.
0.0
r>2.6
r<2.6
e+
e-
-1.0
-1.5
-2.0
FIGURE 3. Radial slopes of e+ (squares) and e− (diamonds) observed by Ulysses in ecliptic and polar winds.
The first three columns (label EQ) indicate ecliptic results obtained with different upper limits TBN for density
and magnetic intensity fluctuations. Last two columns
(label POL) refer to polar wind results outside and inside 2.6 AU, respectively. This figure is from Bavassano et
al. [2001] (copyright 2001 American Geophysical Union,
modified by permission of American Geophysical Union).
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