International Journal of Geomagnetism and Aeronomy
Vol. 3, No. 3, February 2003
Relation of cyclic variations of the solar wind and
interplanetary magnetic field to the cycles of
solar magnetic fields
Yu. R. Rivin and L. I. Gromova
Institute of Terrestrial Magnetism, Ionosphere, and Radio
Wave Propagation, Troitsk,
Russia
Contents
Abstract
Annual mean values of dynamical parameters of the solar
wind and interplanetary magnetic field during 1964-1996 and the
errors of their determination were obtained from the data of the
King catalogue electron version presented on the Internet.
The 11-year
cycles of all characteristics of the interplanetary plasma and
their relation to cycles of various solar magnetic fields were
analyzed from them. Using this analysis, the difference in cycles
of various characteristics of the interplanetary medium is
demonstrated. Attention is paid to systematic
discrepancies in cycling variations
of the plasma density
before and after the beginning
of the 1970s and to nonadequacy of variations of the initial
interplanetary magnetic field vector to variations of its
components.
1. Introduction
The current knowledge on plasma flows from the Sun (these flows
will below be called solar wind, the definition being broader than
the
Parker [1976]
definition which referred to the plasma
flow related only to the corona hydrodynamical expansion into the
interplanetary space: quiet solar wind with a velocity of
300 km s
-1 ) shows that the flows are rather complicated formations which
are influenced by the variations of the large-scale solar magnetic
fields including the cyclic variation with
T 
11 years. The
variation of the annual dynamical parameters of the solar wind (SW)
and also "frozen" into it interplanetary magnetic field (IMF,
BI )
are below analyzed from these positions. The relation (different
for different parameters) between the cyclic variations of the
solar magnetic fields and interplanetary medium parameters is
demonstrated, and some features of the experimental data in the King
catalogue which
complicate
their analysis are indicated.
2. Dynamical Parameters of the Plasma
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Figure 1
|
The initial and smoothed annual values of three dynamical
parameters of solar wind (the velocity
V, density
n, and momentum
nV ) calculated for 1964-1996 from the data of the King catalogue
(http://nssdc.gsfc.nasa.gov/omniweb) and
Rivin [1989]
are shown in Figure 1a.
The annual parameters and their root mean square error ( s )
were determined in the calculation, the smoothing being performed
with a running interval ( L = 3 years). Figure 1a shows the errors
only for the initial curve of the solar wind velocity. Their
average value for the entire temporal interval is
s 
10 km s-1;
this value is almost by a factor of 1.5 higher in
1986-1996 than earlier during 1964-1985. The values of
s for
the plasma density has smaller representation scale
( s 0.5 cm
-3 and slightly changes in the entire temporal interval).
|
|
Figure 2
|
The comparison of the momentum variations with the velocity
and density variations shown in Figure 1a and also the analyzes of
the dependencies
nV(t) = f(V),
nV(t) = f(n) shown in Figure 2
make it possible to conclude that the cyclic variations of
nV are not an independent characteristic since they are determined
mainly by the cyclic variations of the plasma density:
 | (1) |
where
V const, and in the following consideration
the
main attention should be paid only to analyzes of
V and
n.
|
|
Figure 3
|
Figure 3 shows the spectra of three dynamical parameters of
the
plasma. They were obtained by an expansion of the curves in Figure 1a
into Fourier series with fractional harmonics. The harmonic with
T 10-11 years is quite visually (in
comparison with other
harmonics) seen in the spectrum of
V , the spectra of
n and
nV are
distorted by the lower-frequency (than the cycle) variation which
may be related to the variations of these two parameters before the
beginning of the 1970s (Figure 1a). Its exclusion (by shortening of
the series expanded into spectrum) shows presence of a harmonic
with
T 11 years (which is visually seen
in the initial data
(Figure 1a)) in the variations of these two parameters. The nature
of the trend in curve
n is not probably related to cyclisity, that
fact being discussed below.
Figure 1b shows (smoothed by the same
L ) curves of the annual
values of:
(1) the Wolf numbers ( W ) as the characteristic of the
cyclic variation of the toroidal component of the
solar
magnetic field
1B generated above the basic of the convective zone,
and (2) the magnitude of the radial component of the
large-scale magnetic field
BR,
2B generated within the basis of the convective zone, and the
field of the Sun as a star
|Bs| which plays a determining role in processes in
the interplanetary medium.
Obridko and Rivin [1996] and
Rivin [1998a, 1998b, 1999a,
1999b]
discussed these characteristics in detail
and called the former and latter fields dipole and quadrupole,
respectively.
A complete comparison of
the cycles of these magnetic fields with the interplanetary medium
parameters is difficult because of the short series of observations
(2-3 cycles). However to distinguish cycles of various fields, the
difference in their amplitude modulation was taken into account:
for
BR the amplitude of cycle 22 is several times
lower than the amplitude of cycle 21, for
W and
Bs the
amplitudes in both cycles are approximately equal, or the amplitude
of
Bs is even slightly higher in cycle 22. These
differences and also the phase variations are used in the
interpretation below.
|
|
Figure 4
|
|
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Figure 5
|
The comparison of cyclic variations of
V and
n with the cycles of
the large-scale solar magnetic fields was carried out on the
correlation plane (Figure 4) and by calculation of
inter-correlation function
r(t)
(Figure 5).
Taking into account the
spectra in Figure 3,
one can derive the following conclusions from
this comparison:
1. In the main dynamical parameters of SW there exists a
~11-year cycle which is mainly in antiphase to the cyclic variations
of
BR . Its amplitude decreases in
n and
V from cycle
20 to cycle 22 and the spectral amplitude exceeds by several times
the amplitudes of other harmonics including the harmonics with
T 22 years.
2. The cycle with
T 11 years in the data on
V is
additionally shifted in phase by 2-3 years (it lags) relative the
cycle of
BR , that is, by ~3-4 years relative to
the
W cycle. Its spectral amplitude for 3 cycles is ~20 km s-1
and that is only slightly higher than
s .
3. The properties of the ~11-year cycle in
n till the beginning
of the 1970s are considerably different from the properties of the
following two cycles (on the
n-W plane in Figure 3 the data for
the years before the beginning of the 1970s form such a point
distribution which is approximated by a straight line having
essentially different coefficients than those for the following
cycles). That requires individual consideration of this parameter
before and after the years indicated. It is possible that this
difference is the cause of the distortion of the
n and
nV spectra
in Figure 3.
The cycle of the plasma density according to the data
from 1971 (practically after the doubtful interval) occurs strictly
in antiphase to the
BR cycle without any delays. Its
approximate average amplitude is 0.5-1 cm
-3 that is close to
s as in case of the SW velocity.
Hence some properties of the
n and
V cycles (properties 1-3)
correspond to the properties of the cycles of the
2B magnetic field. However, it is possible that the correlation
is
still
more informative at the
n-W plane than at the
n- BR plane.
3. Interplanetary Magnetic Field
More than 30 years ago
Severnyy [1966]
suggested that the
interplanetary magnetic field is a continuation of the total
magnetic field of the Sun
Bs into the interplanetary
space and proposed observations of this solar field as a field of a
star for diagnostics of
IMF
variations. The modern experimental
data on
the
|Bz| and
Bs 11-year cycles support this suggestion.
|
|
Figure 6
|
|
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Figure 7
|
Figure 6 shows the initial and smoothed by the
L interval annual
values of the vector of the interplanetary magnetic field
BI and
its three orthogonal components
Bx,
By, and
Bz. Comparing
variations of the latter with the former makes it possible
to
conclude that there is no coordination in their occurrence: the
vector variations demonstrate the 11-year cyclisity, such cyclisity
being absent in the components. At the same time, the
BI variations
agree well with the modulus values of the vector and the component
module (Figure 7).
Also the variations of the
By and
Bx components (particularly the former which occur in phase
with the
IMF variations and so may be used as an analog of the initial IMF
variations near the Earth) are well correlated with the variation
of the total magnetic field of the Sun which is shown at the bottom
of Figure 6.
Figure 7
shows variations of the modules of the IMF vector and
components and also variations of the solar magnetic fields. Here
the identity of the variations of the vector and its components
with the variations of
Bs is already visually seen.
|
|
Figure 8
|
Figure 8 shows the results of consideration of the relation
between
BI and
Bs on the correlation plane
separately for each cycle. The adjacent points are connected by
line, and the arrows and dates show the motion direction in time.
The absence of phase shifts between two fields is seen even from
this figure. The linear approximation of this distribution results
in a high correlation coefficient ( r = 0.95 0.06 ) and a
regression equation
BI = (5.2 0.15) + (6.02
0.46) 
10-5
Bs ,
where
BI is in nT and
Bs is in Gs (1 Gs
= 105 nT). The following
conclusions were derived from the analysis performed:
1. The amplitude attenuation of the cyclic variation of the modulus
of the total magnetic field of the Sun near the Earth is a
factor of
2 104.
2. The amplitude of the ~11-year cycle of IMF increases from
cycle 20 to cycle 22 and is approximately equal in cycles 21 and 22
(even is slightly higher in the latter), this fact being
principally different from the amplitude modulation of the
V and
n cycles.
3. No phase shifts between the
BI and
Bs cycles were discovered.
4. The cyclic variation of the modulus of the total magnetic field
of the Sun ( Bs ) is the main source of the cyclic variation of
IMF.
5. The variations of the initial annual values of
BI and its
components do not contain explicitly expressed cyclisity with
T 11-22 years. The best correlation
is detected between the
phase of the total solar magnetic field variation with the
By component of the interplanetary magnetic field.
6. The scatter of points relative the approximating line
in Figure 8
has a tendency to be lower in the middle part of the cycle and to
increase in the epochs of its extremes.
4. Discussion
The cyclic variation of
Bs contains a superposition of
the
|1B| and
|2B| magnetic fields;
the
|1Bs| input
prevails in the amplitude variations and the
|2Bs| input is
manifested in the phase shift of the
Bs cycle relative
the
W cycle by 1-2 years
[Rivin, 1998b, 1999a,
1999b].
The
corresponding properties of the cyclisity of the solar magnetic
fields are "inherited" by the modulus of the interplanetary
magnetic field, that is, the variations of
BI with
T 11 years are on the whole identical
to similar variations
of
Bs . At the same time the variations of the
By and
Bx (the latter in antiphase) components of the initial
IMF
correspond to the variations of
Bs.
It is principally important and in some way unexpected that
the cyclic variations of the two main dynamic parameters
of SW,
probably
first, differ from the variations of
BI and,
second, have somewhat different properties: the phase of the
V cycle is shifted by ~3 year relative the phase of the
W cycle,
whereas the phase of the
n cycle coincides with the phase of the
|2Bs| magnetic field cycle. Probably, this difference
indicates
similar but slightly different formation sources of the cycles
of these two parameters. At the same time the amplitude attenuation
of the cycles of both parameters shows that probably the
field
|2Bs| influences each of them more than the
|1Bs| field, that
is, the plasma has a much deeper origin.
Annual mean values of
n before the early 1970s are systematically
underestimated by 3-4 cm
-3.
It follows from the "
n-W " plot (Figure 4) that this
underestimation is not caused by random errors.
It is not yet clear whether it manifests a systematic error
in the
n determination in
King catalogue
for the corresponding year or has some physical sense.
The results of this paper correct partially the assumptions (made
by
Rivin [1989]
earlier) on the cyclisity nature of the
interplanetary medium parameters varying with
T 11 years.
Acknowledgments
This work was performed under partial financing
by the Russian Foundation for Basic Research (projects 99-02-18346,
99-05-64296) and the Astronomy program (project 4-264). The authors
thank A. E. Levitin for his help.
References
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near-equatorial solar photosphere,
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and I. Klechek, D. Reidel,
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