INDICES OF THE BACKGROUND MAGNETIC FIELD AND THE POLAR ACTIVITY OF THE SUN

V. I. Makarov

As 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 low-Earth 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 CaII-K 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 11-year 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 latitude-time 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_rω < 0, from the equatorial zone, where c_rω > 0, and it almost coincides with the latitude ~ 37°, where c_rω = 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.

The 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).

After the polar magnetic field reversal, the zone boundaries of the magnetic field stay at the rest-latitudes, 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 high-latitude (θ_2m) (upper part) and low-latitude (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 Нα charts for 1887-2001. (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 Nesme-Ribes (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 Nesme-Ribes (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 low-latitude 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 rest-latitude 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 high-altitude zone (θ_2m) in the deep minimum of the activity. Using the "11-years" 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°.

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) = μ₁² + μ₃²/3,

the well expressed 11-year 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).

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 low-latitude 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 time-shift, 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 time-shift, 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 high-latitude and low-latitude 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 time-shift, 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.

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Размещен 24 декабря 2006.