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Russian Academy of Sciences
Central Astronomical Observatory at Pulkovo

SIXTH US/RUSSIAN
SPACE SURVEILLANCE WORKSHOP

August 22-26, 2005

Proceedings
Edited by P. Kenneth Seidelmann and Victor K. Abalakin

St. Petersburg, 2005


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

V. I. Makarov

Pulkovo Astronomical Observatory, 196140, Saint-Petersburg, Russia

Abstract. New indices of the global solar activity have been obtained based on the H? synoptic charts during 18872004 and the observations of the polar activity at the Kislovodsk Solar Station in 19602004. The index A(t) is a sum of the dipole and oktopole moments of the background magnetic field, and the index Apz(t) is the area of high - latitude unipolar regions. Strong fluctuations in the polar activity expressed by the polar faculae cycle, NPF(t), modulate the sunspot areas of the next cycle, SSP(t), in 56 years. It was shown that the global solar cycle rises at the high latitudes and the sunspot activity is a continuation of the polar activity. The 11-year cycles of the indices A(t) and Apz(t) have the maximum at the minimum of sunspot activity, and they precede the Wolf number cycles, W(t), during 5 - 6 years. These data can be used for the forecast of the sunspot activity at a different time - scale.
1. INTRODUCTION

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 Suns 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 crω < 0, from the equatorial zone, where crω > 0, and it almost coincides with the latitude ~ 37, where crω = 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 DATA

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).
3. INDICES OF BACKGROUND MAGNETIC FIELD OF THE SUN
3.1. 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 rest-latitudes, θ2m, and θ1m. The annual average of θ2m 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 (θ2m) and low rest latitude (θ1m) zonal boundaries of the background magnetic field during the minimum sunspot activity had a parallel trend: θ2m - θ1m = 23.1, Figure 1.

Fig. 1. The annual mean of the high-latitude (θ2m) (upper part) and low-latitude (θ1m) (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, APZ, 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, APZ(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 α 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, WLIM ≈ 40 (Makarov, Tlatov, and Sivaraman, 2003). The absence of a polar reversal means really weak sunspot activity. The WLIM ≈ 40 corresponds to φMAX ≈ 11, in accordance with the relationship of Waldmeier (1935), Ribes and Nesme-Ribes (1993).

φMAX ≈ 8.2 + 0.07 × WMAX.

We assume that φMAX ≈ 11 corresponds to the value θ1m. 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, θ1m ≈ 11. Then, using the average value θ2m,N - θ1m,N ≈ 23.1 for the northern and southern hemispheres, we obtain by adding 11, θ2m,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 θ1m it cuts the latitude θ = 11 just after cycle 26.

We have compared <APZ> 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, <APZ>11, in the minimum activity, it is possible to determine the latitude boundary of the high-altitude zone (θ2m) in the deep minimum of the activity. Using the "11-years" average of <aa>11 and <APZ>11, we obtained

<aa>11 = 1.2<APZ>11 3.0
sin θ2m = - 0.014<aa>11 + 0.96

One can show that <APZ>11 in the Maunder Minimum corresponds to latitude θ2m ~ 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) = 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).
3.3. The number of the polar faculae, NPF(t), and the sunspot area, SSP(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 low-latitude solar activity at the photospheric level for the four cycles during 1960 - 2004. Observational data of the polar faculae NPF(t)|OBS and the sunspot areas SSP(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 ΔNPF(t) = NPF(t)|OBS NPF,SM(t) and the monthly sunspot areas ΔSSP(t) = SSP(t)|OBS SSP, 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, ΔNPF(t), and the sunspot areas, ΔSSP(t), have been calculated. The maximum correlation between the polar faculae and the next sunspot area cycles corresponded to the time-shift, TPF,SP = 5.7 0.3 years for cycles 20, 21, 22. Figure 4 shows the residual data for the polar faculae ΔNPF(t) = NPF(t)|OBS NPF, SM(t) and the next sunspot areas ΔSSP(t) = SSP(t)|OBS SSP, SM(t) with the time-shift, TPF,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 ΔNPF(t) during 1990 1999 and the sunspot areas ΔSSP(t) during 1997.5 2005.2. Again the polar faculae cycle 23, ΔNPF(t), is developed prior to the sunspot cycle 23, ΔSSP(t). The maximum correlation between the polar faculae and next sunspot area cycle 23, however, had the time- shift, ΔTPF,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 ΔNPF(t) = NPF(t)|OBS NPF,SM(t), and the monthly excess sunspot areas ΔSSP(t) = SSP(t)|OBS SSP, 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 ΔNPF(t) = NPF(t)|OBS NPF,SM(t) and the monthly excess sunspot areas ΔSSP(t) = SSP(t)|OBS SSP, 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, ΔTPF,SP = 7.6 years in Figure 5. We call attention to the strong fluctuation of the polar faculae, ΔNPF(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 05-02-16299, and Program of the Russian Academy of Sciences.
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