Topology and dynamics of the Sun’s magnetic field
E. Gavryuseva † and N. Kroussanova †
Florence University, Largo E. Fermi 5, 50125 Florence, Italy
†
OAC, via Moiariello 19, Naples, Italy
Sternberg Astronomical Institute, Moscow, Russia
Abstract.
The distribution of the magnetic field on the solar surface from 1975 up to 2002 is analyzed using the observations taken
on the WSO observatory, revealing remarkable latitudinal zonal structure in both the northern and southern hemisphere.
A preliminary model combining the dipole, quadrupole, octupole and other components for the longitude distribution is
discussed. The active longitude problem has been investigated. The new active regions seem to appear with the sideral period
of about 25.0 .1 days, corresponding to the solar rotation rate at 10 degree latitude at the 0.85.03 solar radii.
1. DATA
2. LATITUDE DISTRIBUTION OF THE
MAGNETIC FIELD THROUGH SOLAR
CYCLES
We used the Wilcox Solar Observatory data about the
Sun’s magnetic field (MF) in the form of the Global
Magnetic Field (GMF) and Local Magnetic Field (LMF)
from the Synoptic Charts of the whole Sun [1, 2]. GMF
data confirm the results obtained from the LMF analysis.
WSO’s Babcock solar magnetograph measures the lineof-sight component of the photospheric magnetic field
using the Zeeman splitting of the 5250.2 A Fe I spectral
line since May 1976. The noise level of each measurement is less than 10 mcT l. The resolution of the LMF
in longitude is 5 degrees. In the latitude grid there are
30 data points of arcsine from +14.5/15 to -14.5/15. The
magnetic field for the Carrington Rotations since 1642
to 1984 have been used. Carrington Rotations (CR) are
a convenient coordinate system for locating positions on
the Sun, defined a fixed solar coordinate system that rotates in a sideral frame exactly once every 25.38 days.
This period was determined by watching low-latitude
sunspots. CR 1642 begins at 1976:05:27.
The synodic rotation rate varies a little during the year
because of the eccentricity of the Earth’s orbit and its
mean value is about 27.2753 days. The differential rotation of the Sun has to be taken into account in the further
analysis. The problem of the rotation rate of the coordinate system is very important for the study of the longitude MF distribution, and it is less relevant for the latitude structure investigation until the corotation between
the MF distribution and solar rotation is assumed.
There is a common view on the MF distribution on the
Sun. A global dipole field describes the North–South polarity which is flipping each solar activity (SA) maximum. The total period of the dipole field is about 22-year.
Additionally there are famous 11-years solar activity cycles known as an increase of the sunspots number on the
middle latitudes.
We revealed the magnetic field temporal change on
the latitudes from about + 75 degrees arcsin14 515 North to - 75 degrees South with 30 steps in between and
around the Sun with a 5 degree longitude step. Then we
studied how the MF which is averaged along the longitude and along the latitude behaves in time. In this section we discuss the properties of the latitude distribution
over the last three SA cycles.
A very well formed zonal structure in the MF latitude
distribution has been revealed, and its temporal evolution
was investigated. In the solar activity minimum the latitude distribution is almost linear, then as the activity increases three zones of alternative polarity appear in each
hemisphere. They are mirror-symmetric to the equatorial
plain. The polar and pre-equatorial zones have the polarity of the previous cycle with the corresponding mean
MF 120 and 50-70 McT l. The intermediate zones occupy
the latitudes from about 50 to 25 degrees in the North
and in the South hemispheres during the solar activity increase. During the SA maximum the middle zone boundaries are shifted very little from the 25 degrees, instead
the high latitude boundaries are moving to the poles, 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
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3. LONGITUDE DISTRIBUTION
polar field is changing the sign, and its values continue
to increase up to 120 mcT l while the activity is decreasing. At the same time the amplitude of the mean field in
the pre-equatorial zones increases during the maximum
of the activity up to 120 mcT l, and then decreases slowly
until it becomes almost zero inside the zone from 40 N
to 40 S degrees. The latitude distribution of the magnetic
field is turned to be of the opposite polarity in the SAC 22
minimum but with the same dependence on the latitude.
It turns back in the next cycle, so the cycle 23 is similar to
SAC 21. The most North latitude magnetic field changes
from the positive value of 100-150 mcT l (depends on
the longitude) at the beginning of the Carrington Rotation 1642, through zero fifty rotations later (about CR
1692, during the solar activity maximum) to the negative
value of -(100-200) mcT l at the end of 21 cycle in the
CR 1777. The high South latitude field is changing from
the -100 mcT l in CR 1642 through zero in CR 1696 to
150 mcT l in CR 1984. The mean MF on the - 75 S degree is equal to about + 30 mcT l, on the + 75 N is equal
to -(20-30) mcT l, and almost indifferent to the longitude.
The yearly MF variations due to the Earth orbital motion
take place on the high latitudes. Yearly MF variability
on the high South latitudes are less visible than on the
North.
In 22 solar activity cycle the situation is similar, while
some small differences take place. For example, the MF
yearly variation in the high latitude regions on the North
and on the South are smaller than in the SAC 21. The
23th solar activity cycle is not yet finished, it is decreasing now. The change of the polarity took place during
about CR 1966 about, 60 Carrington rotations since the
beginning of the SAC 23 in CR 1906.
The latitude MF distribution is almost symmetric
(with the polarity change) from the South to the North
and from the increase to the decrease of the activity. In
this sense we can talk about remarkable mirror-symmetry
of the latitude MF distribution relatively to the equatorial
plain.
Such a dynamic of the latitude distribution of the solar
magnetic field is described by the following model:
F=a1*(x-a5)*cos(a2*t)+a3*sin(a4*x)*sin(a2*t), where
a1 -8.2758 mcT l, a2 2π 270 0.02327, a3 120 mcT l, a4 2π 14 5 0.43332, a5 14.5, x is an
argument along the latitudes (the number of steps in the
arcsin 14 5 n15 , and t is the time expressed in the
CR rotation numbers.
The described properties of the latitude MF distribution are illustrated by the Fig. 1 with the LMF averaged
over the periods of minimum, increasing, maximum and
decreasing of SA in 21 and 22 cycles. The dotted lines
correspond to the model described above related to the
latitude distribution over the periods of SA maxima.
The longitude structures are mainly formed in zone below the latitude of 40 degrees. Magnetic field polarity
distribution along different mid-latitudes is reproduced
in each rotation as it is expected due to the long living active regions. But it is interesting to mention that there are
global large scale structure (dipole, quadruple) as well
as small scale structure (composed of the 5, 6, 7, 8-th
spherical harmonics) presented in the solar surface MF
distribution over the cycle, slowly changing the polarity
through the cycles. Large scale structures are better visible during the periods of low and high solar activity. An
addition of higher harmonics is more significant during
the intermediate periods of SA increasing and decreasing. The set of the main harmonics depends on the interval of a cycle.
The small scale longitude magnetic structures are well
formed at the mid latitudes with the maximal amplitude
deviations from the mean level at the latitude of 17.5 degrees about where they reach about 100mcTl. Latitude
zone boundaries stay about at the +25 N, 0 and -25 S
degree.
It is important to stress that the position of the longitude structures are relatively stable over the cycle. The
polarity in longitude cells is changing to the opposite one
from the minimum to the maximum of solar activity in
the SAC 21. There is a correlation between the longitude
deviations from the mean level from 35 to 0 degree in the
North and in the South hemispheres around the Sun. The
averaging over the total 21-th cycle composed of the 135
Carrington rotations shows well correlated polarity distribution along the longitudes on the different latitudes.
They are so stable that even the averaging over 11 years
doesn’t remove them.
There is an obvious relation between the behavior of
the MF in the North and in the South hemispheres during all periods of solar activity cycles. Fig. 2 illustrates 3
examples of such relation for different intervals SAC 21.
There is a significant correlation during the period of decreasing activity (Kcorr =0.8) and an anti-correlation during the maximum of activity (K corr =-0.8). The intermediate picture takes place during the period of increasing
activity, when for one half of the Sun there is a correlation between the North and the South hemispheres, while
there is an anti-correlation for other half of the Sun. For
different intervals of SAC 22 and SAC 23 the relationship
between the MF in the North and the South is similar but
not identical. It needs an additional investigation of the
physical origin of this difference and its dependence on
the rotation rate.
The models to describe the longitude and latitude distribution of the solar magnetic field and its variation in
time are in progress. The best results probably could be
achieved by fitting the longitude distribution to the sum
243
FIGURE 1. Latitude distribution of the solar magnetic field in the 21th (on the left) and in the 22th (on the right) solar cycles
over the intervals of low activity, increasing activity, maximum and decreasing activity.
244
than the CRR (the sideral period of about 25.0 .1 days).
This NewARs period corresponds to the solar rotation at
the 10 degree latitude at the 0.85.03 solar radii [3] and
very close to the main rotation rate shorter than the CRR
found by many authors [4] .
The position of the longitude variability maxima
doesn’t coincide with the latitude variability maxima at
the 10 degree latitude as it can be seen in Fig. 1. The appearance of sunspots at about 25 degrees coincides well
with the position of the boundary between the zones of
the opposite polarity in the latitude distribution of the MF
averaged around the Sun through all the longitudes.
There is some North-South asymmetry, better visible
during maxima of the solar activity in the cycles 21
and 22. This is probably attributed to the deviation of
the rotation axis from the axis of the magnetic field
distribution.
5. CONCLUSIONS
From our analysis of the MF distribution we can reach
an important conclusion.
1. The magnetic field distribution has a very clear
latitude zonal structure which is changing during the 22year period.
The next two statements have a preliminary character.
2. Large scale (dipole and quadruple) and small scale
(8,5,6,7th harmonics) structures have been revealed on
the Sun during 21, 22, 23 SAC. Quadruple, dipole and
octupole structures play an important role in the modulation and in the variation of the MF distribution during
solar activity cycles.
3. New active regions appear with the sidereal period
of about 25.0 .1 days. They are originated at the
internal layers rotating faster than the CRR, and they
have an "exit" from the solar interior on the boundary
between the latitude zones of the opposite polarity on the
20-25 degrees.
FIGURE 2. The correlations between the behavior of MF
in the North and in the South hemispheres for the periods of
intermediate and high activity of SAC 21.
of the three harmonics with the periods related to each
other as about 1:2:4.
4. DIFFERENTIAL ROTATION
.
For the first stage of our analysis we assumed a rigid
rotation for the MF data plotting on the solar surface
coordinate system. The longitude variability is strongest
over the SA cycle at the latitudes of 17-26 degrees. The
longitude variability maxima lays in the North and in the
South hemispheres at the 17.5 degree latitude. The MF
at this latitude rotates with the Carrington rotation rate
(CPR). The rotation of the MF at the higher latitudes is
slower (up to the 8.5-10% at the 56 degree), and 2-3%
faster at the 1.9 degree on the North and on the South.
There is the remarkable property of the appearance
of the new active regions (NewARs) or new sectors of
the activity. At the latitudes from 40 to 20 degrees the
NewARs appear with a rotational rate 1.4.1% faster
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