INDICES OF THE BACKGROUND MAGNETIC FIELD AND THE POLAR ACTIVITY OF THE SUNV. I. MakarovPulkovo Astronomical Observatory, 196140, SaintPetersburg, Russia
1. INTRODUCTIONAs early as 1959, scientists have noticed a connection between the intensified solar activity
and increases in the drag on artificial Earth satellites (AES). This increased drag was
attributed to an increase in atmospheric density at high altitudes (Jacchia, 1959, 1964). Since
that time, the work is done in an attempt to understand the real nature of these effects, e.g., at
the Laboratory for Atmospheric and Space Physics (LASP) where researchers are working on
methods of providing an estimate of the Ap index for an application to evolution of the AES
orbits after a single solar event like a solar flare occurs. Because the principal inaccuracies in
the determination of lowEarth orbits and in prediction of positions of objects are due to
errors in atmospheric density models the influence of solar activity has to be taken into
consideration as shown in the paper (Yurasov et al., 2003). Until the upper atmosphere
dynamics is fully understood, the atmosphere models should be updated and methods based
on them refined, so that analysis of the precision of the solar activity prediction will continue
to link usefully theory to reality, and the present paper is devoted to these topics.
The active regions of the sunspots situated in the latitude range of +40° and –40° are
usually considered to determine the solar activity. The Wolf numbers, the sunspot areas, the
faculae in CaIIK line, the flare index, the radio emission on the wave 10.7 cm and so on are
used. These indices are, however, connected with the sunspot active regions only, and they all
have practically the same 11year cycles. This activity is limited by the latitude zone between
+40° and –40°, and it does not take into account the activity at the Sun’s high latitudes. It has
been shown, however, that the solar activity should be considered from the pole to the pole as
a global process, (Makarov, Makarova and Koutchmy, 1985; Makarov, Ruzmaikin and
Starchenko, 1987). The first, second, and third components of the global cycle manifest
themselves as the butterfly diagrams of the polar faculae and sunspots. The components of the
global cycle are connected with the latitudetime distribution of unipolar regions of the
background magnetic field (Makarov and Sivaraman, 1989; Makarov and Sivaraman, 1990; Callebaut and Makarov, 1992). At present the "butterflies" of sunspots and polar faculae are separated by the 38° latitude, (Makarov and Makarova, 1999). This latitude separates the polar zones, where c_{r}ω < 0, from the equatorial zone, where c_{r}ω > 0, and it almost coincides with the latitude ~ 37°, where c_{r}ω = 0 and ω(r, θ) is the angular velocity of the solar rotation (Kosovichev at al., 1997). Clearly these zones differ in
the sign of their angular velocity and correspond to the polar faculae and sunspot activities, respectively.
In this paper we have considered new indices for the minimum of sunspot activity on a
basis of the H? synoptic charts and the polar activity.
2. OBSERVATIONAL DATAThe long series of observations in H? and in white light images of the Sun at all latitudes have been used. More detailed observational data were described in (Makarov et al., 2001;
Makarov et al., 2002; Makarov et al., 2004).
3. INDICES OF BACKGROUND MAGNETIC FIELD OF THE SUN3.1. The index of the area of high  latitude unipolar regions of the magnetic field, Apz(t)After the polar magnetic field reversal, the zone boundaries of the magnetic field stay at the
restlatitudes, θ_{2m}, and θ_{1m}. The annual average of θ_{2m} during the minimum sunspot
activity decreased from 53° in 1878 up to 37.5° in 1996, (Makarov et al., 2002). The annual
mean of the high rest latitude (θ_{2m}) and low rest latitude (θ_{1m}) zonal boundaries of the background magnetic field during the minimum sunspot activity had a parallel trend: θ_{2m} 
θ_{1m} = 23.1°, Figure 1.
Fig. 1. The annual mean of the highlatitude (θ_{2m}) (upper part) and lowlatitude (θ_{1m})
(lower part) zone boundaries of the background magnetic field during the
minimum sunspot activity in the solar cycles 12 – 23, (x – the northern and o –
the southern hemisphere).
The area of polar zones of the Sun, A_{PZ}, occupied by the magnetic field of one polarity
in the minimum activity, was calculated using the Hα synoptic charts for 1878 – 2001, Figure
2. The maximum of the index Apz(t) has been observed in the minimum activity, W(t). The
greatest area of the unipolar regions at the polar zones was observed in the minimum before
the greatest cycle 19. The smoothed annual index, A_{PZ}(t), precedes the average annual Wolf
numbers, W (t), by 5.5 years (Makarov et al.,2001). The correlation factor between Apz(t) and W(t) equals r ~ 0.78. This correlation may be exploited to predict the beginning of a new
cycle and a deep minimum of the sunspot activity.
Fig. 2. (Upper curve) The area of high  latitude unipolar regions, Apz (t), according to
Íα charts for 18872001. (Lower curve) The average annual Wolf numbers, W(t).
A polar magnetic field reversal requires at least the limiting annual mean of the Wolf
number, W_{LIM} ≈ 40 (Makarov, Tlatov, and Sivaraman, 2003). The absence of a polar reversal
means really weak sunspot activity. The W_{LIM} ≈ 40 corresponds to φ_{MAX} ≈ 11°, in accordance with the relationship of Waldmeier (1935), Ribes and NesmeRibes (1993).
φ_{MAX} ≈ 8.2° + 0.07° × W_{MAX}.
We assume that φ_{MAX} ≈ 11° corresponds to the value θ_{1m}. This value agrees with the
data during the Maunder Minimum; very few spots occurred in the northern hemisphere and
below 11°, Ribes and NesmeRibes (1993). Hence, no polar reversal occurred in the northern
hemisphere, while in the southern hemisphere some spots reached 15°, so that there the polar
reversal was maybe possible for some cycles. We suggest that the lowlatitude zonal
boundary, θ_{1m} ≈ 11°. Then, using the average value θ_{2m,N}  θ_{1m,N} ≈ 23.1° for the northern and southern hemispheres, we obtain by adding 11°, θ_{2m,N} ≈ 34.1° for the deep minimum. The restlatitude was 37.5° (average) in 1996. The average decrease is about 1.2° per cycle. It means that a deep minimum will perhaps start in three solar cycles, that is, say, in the solar
cycle 26 or about in 2030 (Callebaut, Makarov and Tlatov, 2002; Callebaut and Makarov,
2005). If we prolong the average line for θ_{1m} it cuts the latitude θ = 11° just after cycle 26.
We have compared <A_{PZ}> with the geomagnetic index <aa>, (Makarov et al., 2002).
Using the correlation factor between the geomagnetic index <aa>_{11} and the area of the polar
zone of the Sun occupied by the magnetic field of one polarity, <A_{PZ}>_{11}, in the minimum
activity, it is possible to determine the latitude boundary of the highaltitude zone (θ_{2m}) in the
deep minimum of the activity. Using the "11years" average of <aa>_{11} and <APZ>_{11}, we obtained
<aa>_{11} = 1.2<A_{PZ}>_{11} – 3.0
sin θ_{2m} =  0.014<aa>_{11} + 0.96 One can show that <A_{PZ}>_{11} in the Maunder Minimum corresponds to latitude θ_{2m} ~
60°. It enables one to estimate the temperature deficiency during the Maunder Minimum (1°)
with respect to the present (~ 0°), obtaining an increase of temperature of about + 1°.
3.2. The index of the dipole  octupole magnetic moments, A(t)The photosphere background magnetic field of the Sun can be represented as a function of
latitude θ and longitude φ using the decomposition on spherical harmonics. By use of the
dipole – octupole index
A(t) = μ_{1}^{2} + μ_{3}^{2}/3,
the well expressed 11year activity cycles were demonstrated (Makarov, Tlatov, 2000). Figure 3 shows that the index A(t) precedes the Wolf numbers, W (t). We used the dipole and
octupole components of the background magnetic field only, i.e. modes L = 1 and 3. The even
modes L = 2 and 4 have faint intensities.
The maximum of the index A(t) has been observed in the minimum activity, W(t). The
greatest value of A(t) was observed in the minimum before the longest cycle 19.
Fig. 3. (Upper curve) The cycles of the background magnetic field of the Sun, A(t),
during 1887 – 2001. (Lower curve) The average annual Wolf numbers, W (t).
The smoothed annual, A(t), precedes the average annual Wolf numbers, W (t), by 5.5
years. The correlation factor between Apz(t) and W(t) equals r ~ 0.78. This correlation may
be exploited to predict the beginning of a new cycle and a deep minimum of the sunspot
activity. Figure 3 shows that the index A(23) < A(22) and A(23) > A(24). It corresponds to
the Wolf number 75 ± 10 in the maximum activity, W(24).
3.3. The number of the polar faculae, N_{PF}(t), and the sunspot area, S_{SP}(t)A relationship between the polar magnetic field and the sunspot number in the next sunspot
cycle has been used for predictions of future sunspot numbers (Schatten et al., 1978; Schatten,
1986). Then, we have noticed that the monthly numbers of the polar faculae and the monthly
sunspot areas of the following solar cycle have strong correlation with each other in each
hemisphere (Makarov, Makarova and Sivaraman, 1989; Makarov and Makarova, 1996). Here
we analyze the Kislovodsk Solar Station observations of the high and lowlatitude solar
activity at the photospheric level for the four cycles during 1960  2004. Observational data of
the polar faculae N_{PF}(t)_{OBS} and the sunspot areas S_{SP}(t)_{OBS} have been smoothed by the twenty four point running mean (Waldmeier, 1955) to exclude the yearly fluctuations
The monthly excess numbers of the polar faculae ΔN_{PF}(t) = N_{PF}(t)_{OBS} – N_{PF,SM}(t) and
the monthly sunspot areas ΔS_{SP}(t) = S_{SP}(t)_{OBS} – S_{SP, SM}(t) (SM stands for smoothed) have
been calculated for the solar cycles 20, 21 and 22 in the northern, N , and southern, S,
hemispheres during 1960 – 1995. The correlation factors between the number of the polar
faculae, ΔN_{PF}(t), and the sunspot areas, ΔS_{SP}(t), have been calculated. The maximum correlation between the polar faculae and the next sunspot area cycles corresponded to the timeshift, T_{PF,SP} = 5.7 ± 0.3 years for cycles 20, 21, 22. Figure 4 shows the residual data for
the polar faculae ΔN_{PF}(t) = N_{PF}(t)_{OBS} – N_{PF, SM}(t) and the next sunspot areas ΔS_{SP}(t) = S_{SP}(t)_{OBS} – S_{SP, SM}(t) with the timeshift, T_{PF,SP} = 5.7 years for the solar cycles 20, 21 and 22
in the –northern,N, and –southern,S, hemispheres during 1960 – 1995. Hence, the structures
of the highlatitude and lowlatitude activities are connected. The basic features of the polar
activity are kept in the features of the sunspot activity.
Figure 5 shows the relationship between the number of the polar faculae ΔN_{PF}(t) during
1990 – 1999 and the sunspot areas ΔS_{SP}(t) during 1997.5 – 2005.2. Again the polar faculae
cycle 23, ΔN_{PF}(t), is developed prior to the sunspot cycle 23, ΔS_{SP}(t). The maximum
correlation between the polar faculae and next sunspot area cycle 23, however, had the time
shift, ΔT_{PF,SP} = 7.6 ± 0.3 years. This maximum correlation was equal to 0.78. Again one can
see that in most cases the peaks on the high – latitude activity curve coincide with the peaks
on the sunspot area curve.
Fig. 4. The curves are the plots of the monthly excess numbers of the polar faculae
ΔN_{PF}(t) = N_{PF}(t)_{OBS} – N_{PF,SM}(t), and the monthly excess sunspot areas ΔS_{SP}(t) = S_{SP}(t)_{OBS} – S_{SP, SM}(t) for the solar cycles 20, 21 and 22 (the northern,N, and southern,S, hemispheres) during 1960 – 1995. The polar faculae precede the
sunspot areas by the shift of 5.7 years.
Fig. 5. The curves are the plots of the monthly excess numbers of the polar faculae
ΔN_{PF}(t) = N_{PF}(t)_{OBS} – N_{PF,SM}(t) and the monthly excess sunspot areas ΔS_{SP}(t) = S_{SP}(t)_{OBS} – S_{SP, SM}(t) for the solar cycle 23 (N+S) at the –northern,N, and –southern,S, hemispheres (combined since they were very similar) during 1990 
2007.
We draw the attention to the strong fluctuation of the polar faculae in 1991.9, 1992.6,
1994.0, 1994.8, 1995.9, 1997.0, and the corresponding bursts of the sunspot activity in
1999.4, 2000.3, 2001.8, 2002.4, 2003.8, 2004.5. We used the average timeshift, ΔT_{PF,SP} = 7.6
years in Figure 5. We call attention to the strong fluctuation of the polar faculae, ΔN_{PF}(t),
during the year 1997.0 ± 0.5 that was accompanied by the powerful flares during 2004.0 ±
0.5. Thus, the observations of the polar activity offer the possibility to forecast strong
fluctuations of the sunspot and flare activity.
Acknowledgments. This paper was supported by the Russian Fund of Basic Researches, projects 050216299, and Program of the Russian Academy of Sciences.
REFERENCES
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