Turbulence Regimes of the Solar Wind in the Region of its
Acceleration and Initial Stage of Supersonic Motion
L.N. Samoznaev, A.I. Efimov, V.E. Andreev, M.K. Bird† , I.V. Chashei and P.
Edenhofer, D. Plettemeier, R. Wohlmuth‡
Inst. for Radio Engineering & Electronics, Russian Academy of Science, Moscow, 101999, Russia
†
Radioastronomisches Institut, Universität Bonn, 53121 Bonn, Germany
Lebedev Physical Institute, Russian Academy of Science, Moscow, 117924, Russia
‡
Institut für HF-Technik, Universität Bochum, 44790 Bochum, Germany
Abstract.
Coronal radio sounding experiments were carried out during the solar conjunctions of the spacecraft Ulysses and Galileo,
providing information on the solar wind plasma over a wide range of heliocentric distances and heliolatitudes on both East and
West limbs of the Sun. An important component of these investigations is to identify the turbulence regimes of the solar wind
in its acceleration and initial supersonic regions. This work concentrates on the variation of the spectral index of the temporal
frequency fluctuation spectrum α f . The analysis leads to the following preliminary conclusions: (1) At low heliolatitudes the
turbulence becomes ‘developed’, with α f reaching the Kolmogorov value of 2/3, at distances beyond 20 R ; (2) At high
heliolatitudes (poleward of 65Æ ) the solar wind turbulence remains undeveloped out to distances of at least 30 R ; (3) At
distances close to the Sun (less than 7 R ) the spectrum sometimes becomes a double power-law with small spectral index
α f ' 0.03-0.11 at low fluctuation frequencies (ν < 0.02 Hz), but a sharp decrease (α f > 1.2) in the fluctuation regime beyond
the break frequency.
INTRODUCTION
Many years of solar wind plasma investigations by radio occultation (Yakovlev et al., 1980; Bird, 1982; Bird
and Edenhofer, 1990; Wohlmuth et al., 2001) and in situ
methods have shown that turbulence is a permanent property of the interplanetary plasma at all heliocentric distances and heliolatitudes. Fluctuations of the electron
density, magnetic field, velocity, etc. are characterized by
spatial and temporal spectra covering many decades in
the wavenumber or temporal frequency domains, respectively. Turbulence evolution and its interaction with the
background plasma is of great importance for solar wind
physics, especially near the Sun where the plasma flow
accelerates to supersonic and superalfvenic velocities.
This paper presents some results of coronal sounding experiments carried out during four extended intervals with the spacecraft Ulysses (1991 DOY 218-248;
1995 DOY 053-073) and Galileo (1995/96 DOY 336014; 1996/97 DOY 360-045). Temporal frequency fluctuations of the spacecraft’s downlink signals at the carrier
frequency 2295 MHz were measured over a wide range
of heliocentric distances, between 4.3 and 79.8 R , heliolatitudes up to 89 Æ , and solar activity levels with sunspot
numbers from 0 to 300. Analysis of the frequency fluctu-
ation spectra shows that the shape of the electron density
spatial spectrum is strongly dependent on heliocentric
distance, heliolatitude and solar activity. Double powerlaw spectra with sharp breaks in spectral density at temporal frequencies near 0.01–0.03 Hz were detected for
the first time.
OBSERVATIONS
Coronal sounding experiments were conducted using radio signals of the spacecraft Galileo and Ulysses during
their active missions in the years 1991-1997. The signal
frequencies were recorded at a 1 s 1 sampling rate during the spacecraft solar conjunctions at the large ground
stations of the NASA Deep Space Network (DSN). The
radio subsystem configuration on the Ulysses spacecraft
for radio science investigations consists of an S-band
uplink and dual-frequency S/X-band downlinks, both
downlink frequencies being phase coherent with the uplink. The plasma-induced frequency variations (differential Doppler residuals) were calculated by subtracting
out the nondispersive effects imposed onto the two coherent downlinks. In the case of Galileo, the single Sband downlink was generated by an ultrastable oscilla-
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
473
FIGURE 1. Differential Doppler residuals ∆ f of the Ulysses
signals during simultaneous observations at the DSN ground
stations Goldstone (DSS 14) and Canberra (DSS 43); time
interval: 21:10:54 to 23:27:26 UT on 27 Aug 1991 (occultation
egress phase). The heliodistance of the ray path proximate point
was R = 18:9 R , the heliolatitude was ϕ 19Æ .
tor (USO) and the Doppler residuals were determined as
a difference between the measured frequencies and the
predicted nondispersive values calculated from navigational data.
Descriptive information about the four coronal sounding experiments discussed in this work is presented in
Table 1. The heliolatitude of the ray path proximate point
is ϕ and the mean sunspot number for the interval is W .
As seen in Table 1, the solar activity levels differed
strongly between the 1991 and the 1996/1997 observation sessions. Whereas the solar activity was high with
W reaching 290-300 on some days of 1991, W was essentially zero during 25 days of the 1996/97 Galileo occultation.
An example of Ulysses differential Doppler residuals
measured simultaneously at two DSN ground stations is
presented in Fig. 1.
Temporal power spectra of the frequency fluctuations
were calculated using an FFT algorithm for all observational intervals with a duration of more than 44096
samples within the periods shown in Table 1. Spectral indices α f were determined for the spectral ranges where
the power density can be represented as a power law.
The spectral index α f is related to the power exponent
of the spatial 3D density turbulence power spectrum α d
by αd = α f + 3. We also investigated the possibility of
a break in an individual temporal power spectrum that
could be described by a distinct change in α f . The frequency fluctuations are better for detecting such breaks
because the power spectra are flatter than the temporal
spectra of phase (index p) or amplitude (index a) fluctuations, α p = αa = α f + 2 (Yakovlev et al., 1980).
474
FIGURE 2. Average FFT spectra (2 4096 data points)
of Ulysses frequency fluctuations shown in Fig. 1. For comparison, the dashed lines are theoretical Kolmogorov spectra
(α f = 2/3) for ν > 1 mHz.
THE POWER EXPONENT OF
FREQUENCY FLUCTUATION SPECTRA
Frequency fluctuation spectra for the data of Fig. 1,
which are typical for a comparatively large heliocentric
distance, are illustrated in Fig. 2.
The two spectra of Fig. 2 are similar and have a power
law shape in the frequency range 10 3 Hz < ν < 10 1
Hz. The spectral index is found to be very close to the
Kolmogorov value α f 2=3 (see dashed lines).
The dependence of the frequency fluctuation spectral
indices on heliodistance is summarized in Fig. 3 for all
Galileo and Ulysses observations at low heliolatitudes
(ϕ < 10Æ ). The measurements indicate that the spectral
index is roughly constant for R > 20 R and corresponds
to developed turbulence with α f 2/3. The value of α f
increases with R from about 1/3 to about 2/3 over the
range 5 R < R < 20 R , in agreement with the phase
scintillation analysis of Woo and Armstrong (1979).
The Ulysses 1995 data are well suited for investigating
the heliolatitude dependence of the spectral index α f . As
shown in Fig. 4, α f 2=3 in the range of heliolatitude
-50Æ < ϕ < 0Æ , but has a tendency to decrease when the
line of sight approaches the south polar region. These
results agree with the spectral changes found in phase
fluctuation spectra by Pätzold et al. (1996).
The data of Fig. 4 most likely reflect a real heliolatitude dependence, because the variations in solar offset
were rather small (22 R < R < 32 R ) during this measurement interval. Furthermore, no changes in α f were
detected within this distance range at low latitudes (see
Fig. 3). It may thus be concluded that the solar wind
turbulence remains undeveloped in the high latitude regions, at least for heliocentric distances out to 30 R .
TABLE 1.
Coronal sounding experiments 1991-1997
Observation period
1991 Aug 06 – 1991 Sep 06
1995 Feb 22 – 1995 Mar 14
1996 Dec 02 – 1996 Jan 14
1996 Dec 25 – 1997 Feb 14
Spacecraft
Solar offset [R ]
ϕ [Æ ]
W
Ulysses
Ulysses
Galileo
Galileo
4.3 – 40.8
21.5 – 32.2
4.3 – 79.8
6.9 – 73.9
1.4 – 89
–89 – +1
1 – 14
2 – 20
183
34
12
6
FIGURE 3. Dependence of spectral index α f on heliocentric
distance. Average values of α f are presented for 10 R bins in
the range 30–80 R , 5 R bins in the range 10–30 R , and
2.5 R bins in the range 5–10 R . The solid circles (squares)
denote measurements on the West (East) solar limb. Triangles
represent data averages from both solar limbs.
FIGURE 4. Dependence of α f on heliolatitude ϕ (Ulysses
1995).
SPECTRAL FEATURES OBSERVED AT
SMALL HELIOCENTRIC DISTANCES
Many Galileo frequency fluctuation spectra recorded at
small heliocentric distances were found to have a sharp
spectral break. As a rule, the spectral breaks are observed
inside 10 R at relatively low levels of RMS frequency
fluctuations. Contrasting examples of single power law
475
FIGURE 5. Average FFT power spectra (3 4096 points):
(a) single power law, high solar activity; (b) double power law
with break frequency, low solar activity.
and double power-law (broken) spectra are presented in
Fig. 5.
Descriptive data for the spectra in Fig. 5 are as follows:
(a) Ulysses, very high solar activity level W = 212 (22/23
Aug 1991), heliolatitude ' 40 Æ , and (b) Galileo, extremely low solar activity W < 9 (16/17 Jan 1997), heliolatitude ' 20Æ . Whereas the heliocentric distances were
nearly identical (R ' 7.0 R ), the levels of the RMS frequency fluctuations were very different: (a) σ f = 2:552
Hz; (b) σ f = 0:662 Hz. The power exponents for spectrum (a) and for the low-frequency part of spectrum (b)
are approximately equal, and are close to the values presented in Fig. 3 for the corresponding heliocentric distance.
The break in spectrum (b) of Fig. 5 takes place at the
frequency ν b 0:024 Hz. Spectra with obvious break
frequencies are not observed at high fluctuation levels or
in regions outside 10 R . More data would be required
to determine just what environmental conditions (heliolatitude, solar activity level, others?) are necessary for
producing the unusual spectra with the break frequency.
Fig. 6 presents all observed values of the spectral
break frequency ν b measured at different heliocentric
distances. One can see from Fig. 6 that the measured values of νb range between the limits 0.01 Hz and 0.03 Hz.
There appears to be a slight tendency for an increase
of νb with increasing solar offset distance R, but the
ACKNOWLEDGMENTS
This work presents results of a bi-national research
project partially funded by the Deutsche Forschungsgemeinschaft (DFG) and by the Russian Foundation for
Basic Research (RFBR), Grant 00-02-04022. Additional
support from the RFBR, Grant 00-02-17845, and from
the Russian Ministry of Industry, Technology and Science, is acknowledged.
REFERENCES
FIGURE 6. Dependence of the break frequency on solar
offset distance R (Galileo 1997).
data statistics are insufficient for drawing a more definite
conclusion about this dependence.
CONCLUSIONS
The power exponent of the 3D density turbulence spectrum in the low-latitude solar wind increases with increasing heliocentric distance for R < 20 R , reaching
a roughly constant value α d 3.6–3.7 for R > 20 R , in
agreement with the previous findings of Woo and Armstrong (1979). The high-latitude solar wind turbulence
near solar activity minimum, on the other hand, definitely
remains undeveloped out to 30 R .
The turbulence spectra are sometimes found to display
a spectral break at frequencies 0.01–0.03 Hz in the range
R < 10 R for low solar activity levels. Breaks were
not observed for R > 20 R , or for R < 10 R under
high solar activity conditions. The origin and properties
of these spectral breaks are a topic for future theoretical
and experimental investigations.
The turbulence regimes may well be closely connected
to the regimes of solar wind flow. While the flat 3D turbulence spectra with α d ' 3 are typical for the region
of plasma acceleration and transition to supersonic and
superalfvenic flow, the steep spectra with α d ' 3:6 3:7
occur in the developed flow with constant speed. The
rearrangement of turbulence spectra is apparently yet
another manifestation of the mechanism that supplies
the energy needed for the additional acceleration of the
solar wind.
476
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