ELEVEN-YEAR CYCLES OF THE LOW-LATITUDE LARGE-SCALE SOLAR MAGNETIC FIELD, ITS ORIGIN AND SOURCES IN THE CONVECTION ZONE YU. R. RIVIN IZMIRAN, Moscow region 142092, Russia

(Received 28 April 1998; accepted 22 March 1999)

Abstract. The description of two components of the 11-year cycle of the large-scale solar magnetic field at the equator and at mid latitudes has been expanded. A conclusion is made that one of them is the result of detection of a dipole field, changing with a period of ∼22 years, and another is mainly the equatorial quadrupole field, whose diurnal values are modulated by oscillation with a period of ∼11 years. The second component is greater in amplitude than the first one, is similar in shape, and lags behind by ∼1 year over two solar cycles. It is suggested that generation sources of both fields are spaced in height inside the convection zone, the quadrupole field being generated at the bottom of the convection zone, and the dipole field – at the top of its middle layers. The probable mechanism of cyclic variations of the two components and the solar activity has been discussed.

1. Introduction Systematic measurements of the large-scale solar magnetic field, B (sometimes called background field) began in early 1970s. Therefore, the study of its 11year cyclic variation became possible not long ago. Obridko and Rivin (1996a) determined three spatial components of B at the equator, using the assumption of a potential character of slow magnetic field changes in the photosphere and above it, up to the source surface (R ≈ 2.5 R , where R is the radius of the Sun), as well as the method of spherical harmonic analysis and synthesis. The analysis of the annual mean B and |B| components showed that the B cycle at heliolatitudes ϕ ≤ 8◦ has one component, whereas the |B| cycle comprises two components of different origin. Analytic models of cyclic variations of B and |B| were suggested. When analyzing the value and the modulus of the magnetic field of the Sun as a star (Bs ), the boundaries of the region where the two components were manifested, were extended up to 40–50◦ . In this paper, we have refined the analytical model of time variations of the second component, have supplemented the description of time variations of two |B| components with their spatial variations, and have represented the mechanism of generation of 11-year variations of the solar background magnetic fields and solar activity in the form of two dynamo mechanisms, spaced in height (at the middle and bottom of the convection zone) and related by nonlinear turbulent pumping of the poloidal field of the upper dynamo to the bottom Solar Physics 187: 207–222, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.

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Figure 1. Annual mean values of three components of the original B at ϕ ≤ 8◦ (a), and of moduls curves (Bt r )1 − 1, (Bt r )2 − 2, B − 3, described in the text (b).

of the convection zone and the Parker mechanism of emergence of magnetic tubes from the bottom to the surface.

2. Model of Cyclic Variations of Large-Scale Magnetic Fields Variations of the annual mean values of three field components (radial, BR ; azimuthal, Bϕ ; and meridional, Bθ ) in the equatorial zone for 1970–1994 are given in Figure 1(a). According to Obridko and Rivin (1996a), these variations can be represented in a first approximation as a sum of two components (without taking into account the amplitude modulation of the first component and the phase shift in the amplitude modulation of the second component): B = B0 sin t + A[(1 + m| sin t|) sin ωt] ,

(1)

where B0 ≈ 0.5 G is the field amplitude of a quasi-axial dipole, changing with  = 2π/T , T ≈ 22 years, ω is the frequency of a higher frequency source (T  Tω ), whose amplitude, A, is modulated by the dipole field absolute value, and m is the modulation depth.

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The conclusion that the first component can be represented as field variation of the quasi-axial dipole with T , is based on the analysis of the amplitude ratio of the 22-year cycle of B components: BR ≈ Bϕ ≈ 0 (short-period variations of BR with T  11 years are neglected), and Bθ ≈ 0.5 G (Figure 1(a)). The second term in (1), relevant to the annual mean B values, is suppressed, since Tω  1 year, but it plays an important role when passing from the original field values to its absolute values. In Figure 1(b), one sees absolute values of B = |(BR2 + Bϕ2 + Bθ2 )0.5 | and the modulus of the transverse field component, Bt r = |(Bθ2 + Bϕ2 )0.5 |, plotted from the original, (Bt r )1 , and absolute, (Bt r )2 , values of the components. (Bt r )1 component characterizes mainly the variation of |Bθ |, where Bθ is calculated from the diurnal values, taking into account their sign. (Bt r )2 is calculated from the moduli of the diurnal values. Its amplitude is many times that of (Bt r )1 , and its maximum displays a delay of ∼1 year in solar cycle 21. Such transformation of (Bt r ) to (Bt r )2 is possibly due to linear detection of the original curve, B. As a result of detection, the annual mean variations of (Bt r )2 display an ∼11-year cycle, that modulates variations with Tω and has properties differing from those of the first component in (1). In fact, limiting our consideration to the first terms of the expansion and taking into account the restrictions, described above, we can write expression (1) after linear detection without regard for phase in the form |B| ≈ [k1 B0 sin 2t + k2 Am sin 2t] ≥ 0 ,

(2)

where k1 , k2 are constant coefficients, depending on the detector, and Amk2 > k1 B0 . Cyclic variation of the second oscillation is very similar (though not at all identical) in shape to |Bθ |, i.e., to periodic variation of the dipole field amplitude. Amplitude variations of |B| are even more significant if the phase remains the same as for (Bt r )2 (Figure 1(b)). The conclusion, that 11-year variation of the primary field B enhances (in all components) as a result of detection of B, is corroborated by Figure 2. Here, all three components vary in concord and have the amplitude of ∼1–1.5 G at the maximum of cycle 21, i.e., a factor of 2–3 larger than the initial field amplitude. In the same work (Obridko and Rivin, 1996a), the authors used the monthly mean values to analyze the phase shifts between |BR |, |Bϕ |, and |Bθ |, as well as with the Wolf numbers, (Rz ). Variations of |BR |, and |Bϕ |, displayed a lag of ∼7–8 months with respect to the corresponding |Bθ | values, and of ∼12 months relative to the Wolf numbers (Figure 3). Assuming that the phase shift, λ, takes place between two fields, represented by different terms in models (1–2), we can take it into account by introducing it into the second term, i.e., by correcting the model of Obridko and Rivin (1996a) and writing (1–2) in the form B = B0 sin t + A[1 + m| sin (t − λ/2)| sin ωt] = Bd + Bq ,

(3)

|B| ≈ [k1 B0 sin 2t + k2 Am sin (2t − λ)] ≈ |Bd | + |Bq | ,

(4)

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Figure 2. Annual means of the absolute values of B at ϕ ≤ 8◦ , magnetic field Sun as star and Wolf numbers. Solid line: original data, circles: smoothed values. Numerals under the Wolf number curve denote the Zürich number of the cycles. The curve for |Bs | before the vertical bar is plotted, using the data from the Crimean Astrophysical Observatory, normalized to the Stanford data; the curve beyond the vertical bar (from 1976) is based on the Stanford data.

d, dipole; q, quadrupole. However in doing that, one must remember that |Bθ | has a complex structure, that involves the 11-year cycles of both fields from (3)–(4). Therefore the actual phase shift between the fields from different sources can be somewhat more than 8 months – the lower shift boundary. The work by Obridko and Rivin (1996a) showed a complex character of time variations of |B| with T ≈ 11 years and allowed us to adopt their analytical model. However, some questions still remain unsolved. The main ones are as follows: (1) what value has the carrier frequency, ω, in the second term in (3)–(4); (2) what spatial features on the solar surface correspond to the two time components of the 11-year cycle; (3) whether the model can be used to specify the generation mechanism of cyclic variations, etc.

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Figure 3. Phase shift between the absolute values of different components of the large-scale magnetic field of the Sun, as well as between these and Rz . R(X, Y ) is the mutual correlation function.

Figure 4. Daily mean Bs values for ∼24 years.

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Figure 5. Amplitude spectrum of Bsi and |Bsi | over the interval of June 1975–December 1990, obtained by expansion in Fourier series (Rivin and Obridko, 1992). Numerals at the peaks are T . The data on Bs since 1991 suggests to us that the structure of the spectra will remain the same for a longer data series, too. In the spectrum of |Bsi |, the maximum at T ≈ 11 years occurs at the ordinate axis, the spectral amplitude is ∼0.2 G, k is the number of the harmonic, and SY is the variation with T equal to several years.

To determine Tω , let us consider diurnal variations of magnetic field as star Bs in Figure 4, the original data for which have been borrowed from the respective Solar-Geophysics Data (1994–1996). The high-frequency part (dashed) of the plot involves the diurnal variations of Bsi and their packets. The amplitude of the curve is modulated by the 11-year cycle. The spectral composition of Bsi was analyzed by Rivin and Obridko (1992) and was shown to be mainly determined by the harmonic with T ≈ 27 days and its two sub-harmonics (Figure 5). Hence, it seems reasonable to assume T ≈ 27 days in (3)–(4). The next question, important for refining models (1)–(4), is the field distribution for two components of the 11-year cycle in B on the photosphere. Ivanov (1995) describes two system of cells in the equatorial and mid-latitude photosphere regions (giant and supergiant cells), that correspond, respectively, to the dipole and quadrupole background magnetic fields in the Sun. Though the author deals with cells, the description can, obviously, be referred to the respective structures of the large-scale magnetic field. Thus, we may conclude that, both in space and time, there are only two field components in the Sun. One of them is a dipole and corresponds to the first term in (3)–(4) (see the analysis of Figure 1 above). The other is a quadrupole and corresponds to the second term in (3)–(4) (Figure 4). This interpretation of the spatial modes of the background solar magnetic field agrees with the one suggested by Saito and Akasofu (1989) for the fields of celestial bodies. A similar interpretation, based on the analysis of Hα maps and the shape of the corona, was given by Mikhailutsa and Gnerysher (1988), Mikhailutsa (1995) and

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Figure 6. Detailed amplitude spectrum of Bsi in the main maximum region, obtained by decreasing interpolation interval.

Fatyanov (1993). Moreover, they suggested that the quadrupole was an equatorial feature. Thus, we were able to describe the discounted and the unknown parameters of the model and to provide its spatial characteristics. Such a model of background fields (more complete than (1)–(2)) allows us to proceed to establish the nature of the two components and their sources.

3. The Origin of Two Components of Cyclic Variations of the Large-Scale Solar Magnetic Field at ϕ ≤ 50◦ and Their Relevance to Sunspots It is useful to begin the analysis of the origin of two components by considering the Bsi spectrum, represented in Figure 6. It is the same spectrum as in Figure 5, but with higher resolution in harmonics (the step dk = 0.2) and a frequency band, confined to the main maximum region. The predominant harmonic in the spectrum corresponds to T ≈ 27 days, but two other groups of harmonics are also present: with T ≈ 28–29 days and T ≈ 30 days. The existence of three independent sources of the background field was reliably established by other methods (Bumba, 1976; Grigoryev and Yermakova, 1986; Ivanov, 1995). Various authors give different interpretation of these sources, but all of them connect the ∼27-day variation with the solid-body rotation of the background field in the photosphere, and the ∼28–29-day component with differential rotation. The variation with T ≈ 30 days is usually disregarded. Let us interpret these variations by taking into account models (3)–(4). The variation of rigid rotation with T ≈ 27 days is predominant in the spectra in Figures 5 and 6. As shown below, it implies that diurnal variations of the background field at mid-latitudes and at the equator are mainly due to the quadrupole

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component. An additional, smaller contribution is made by the dipole field (the first component), rotating with a period of about 28–29 days, and the high-latitude field, rotating with a period of about 30 days. The latter is also a dipole field, but probably of some other origin than mid-latitudes. This relationship between the maximum amplitudes of the three sources in the spectrum (Figure 6) must change with latitude from the equator to the poles. Hence, the presence of two different mid-latitude components in (3)–(4) is indicative of two different systems of solar magnetic fields, which manifest themselves in the rotation periods of the background fields. This suggests that the quadrupole field, which rigidly rotates with T ≈ 27 days, lies at the bottom of the convection zone, and the dipole field, rotating with T ≈ 28–29 days, is situated above it, in the middle of the convection zone. In order to understand the origin of the second field component in (3)–(4), it is important to know where and how the amplitude of diurnal variations of the quadrupole field is modulated by the 11-year cycle. The solution of this problem is likely to depend on the choice of generation mechanism of cyclic variations of the solar magnetic fields. The first component of the large-scale magnetic field changes in the field of quasi-axial dipole with T ≈ 22 years and is obviously due to the quasi-axial dynamo (as follows from the morphologic properties of the latter). The high-latitude field has its own characteristic features, of which the main are as follows: (1) the sign reversal shifts by a quarter of the phase over a magnetic cycle; (2) the equatorial and mid-latitude fields are practically absent; (3) it is a dipole field that completes one rotation about its axis in ∼30 days. The observed properties of this field are still poorly understood. Thus, the recording of background solar magnetic fields gives us an opportunity to analyze the dynamics of the field, rigidly rotating with T ≈ 27 days, and therefore generated at the bottom of the convection zone, and to describe some of its properties, not detectable from sunspot observations. However, a model of cyclic variations, taking into account the background and local fields on the Sun, must consider some particular variations of sunspots and active longitudes. As shown in several studies, more than 99% of the sunspots that comprise the Wolf number index are characterized by lifetimes less than 10 days, small sizes, and differential rotation. However, sunspots with different characteristics (≤ 1%) are sometimes recorded on the active longitudes. Magnetic fields of active longitudes are complex features. As shown by Vitinsky, Kopecký, and Kuklin (1986), long-lived active regions include sunspots with the following properties: (1) sunspots rotate quasi-rigidly with the photosphere, (2) the active latitudes are most pronounced for major sunspots (with an average area >500 m.v.h.), (3) the number of major sunspot groups doubles and the total number of sunspot groups (independent of their area) has the lowest concentration, (4) the sunspots have on an average a more intensive magnetic field and longer lifetimes (∼4–10 rotations), (5) the active longitudes with these characteristics

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tend to cover both solar hemispheres, (6) generation mechanisms for these sunspots lie deeper than for others (probably at the very bottom of the convection zone), and (7) the maximum occurrence rate of such sunspots is recorded 1–2 years after the Wolf number maximum. The characteristics of these active longitudes and their sunspot population are described in more detail in the book mentioned above. In the present context it is sufficient to know that active longitudes contain very rare sunspots with special properties that characterize the deep-layer magnetic field, whose intensity changes over an 11-year cycle somewhat different from ordinary sunspots, also showing a phase delay relative to the Rz maximum. Specific sunspots, as described above (solar activity events, absent at high latitudes), display the same two systems of magnetic fields as observed in the background fields in various frequency bands. The properties of the specific sunspots, compared to the background field characteristics in models (3)–(4), suggest that these sunspots (active regions) are due to a deep-layer quadrupole field. Thus, the cyclic variation of the background fields and solar activity provides a self-consistent picture of variations of two magnetic field systems in the Sun with basically different properties, which implies a different origin of their generation mechanisms.

4. Phenomenological Generation Model of the 11-Year Cycle of the Large-Scale Magnetic Field and Solar Activity Comparing the principal characteristics of B and |B|, we arrive at the conclusion that there is a mechanism in the solar interior that generates two interconnected systems of magnetic fields with essentially different properties. Current theoretical models for the cyclic variation of solar activity with periods T ≈ 11 years or T ≈ 22 years admit the existence of such a mechanism provided the two dynamo regions, spaced in the convection zone along the radius, are supplemented, first, with an anisotropic turbulent pumping of the dipole magnetic from its generation region field towards the base of the convection zone, where the quadrupole magnetic field is generated, and second, with the subsequent emergence of magnetic tube clouds, where this field is enhanced several times and has somewhat altered characteristics (amplitude, phase, period), up to the photosphere in about a year after the dipole field undergoes the corresponding changes. In the past 10 years, significant progress was made in the study of anisotropic turbulent pumping of the large-scale magnetic field (Kichatinov, 1995) that is not directly connected with the dynamo mechanism. The pumping is realized as a transport of the large-scale magnetic field to the base of the convection zone by small-scale fluctuations of magnetic induction due to a strong vertical gradient of plasma density in the convection zone. Krivodubsky (1987) calculated the transport velocity of the horizontal magnetic field due to radial irregularity of the mat-

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ter density for three models of the convection zone. He shows that fields up to ∼104 –105 G (depending on the particular model and the emergence mechanism) are retained at the bottom of the zone, after which a large number of magnetic tubes emerges to the photosphere. However, Krivodubsky does not explain the origin of the initial magnetic field, nor the mechanism of its enhancement at the base of the convection zone. Krivodubsky and Kichatinov (1991) and Krivodubsky (1992) analyzed the effect of solar rotation on the pumping mechanism. They revealed the effect of anisotropic turbulent pumping and different transport directions of the large-scale poloidal and toroidal magnetic fields, the former being transported inside the convection zone and to its poles, and the latter having the meridional component of the transport velocity directed to the equator. Kichatinov and Rudiger (1996) studied the transition region between the convection and the radiative zones, where the solar rotation changes from differential to rigid. This region has a size of ∼0.1Rθ . An important role in creating this region and confining it in the radial direction belongs to a weak relic magnetic field (∼10−3 –10−5 G), that does not penetrate the convective shell. A curious morphologic feature of the theoretical model under consideration is a thickening of the transition layer at the poles. Taking into account the theoretical results, mentioned above, the generation model of the 11-year solar cycle of sunspots and |B| can be described to a first approximation as follows (Figure 7). The 11-year cycle of the large-scale field, |B|, is generated in two stages. This field is resulting from the dynamo action at the top of the middle layers of the convection zone. This location is determined by the following considerations: (1) The pumping rate, vρ , given by Krivodubsky (1987), and the phase shift between cyclic variations of the two components. The pumping rate varies from vρ ≈ 104 cm s−1 at the top of the convection zone to vρ ≈ 102 cm s−1 at its bottom. In our estimates we use vρ ≈ 103 cm s−1 . Let us assume, according to Krivodubsky, that the approximate pumping and emergence times are close, i.e., the transport of the large-scale magnetic field downwards takes ∼0.5 year. Then, the field is transported by ∼150 000 km, i.e., passes the most part of the convection zone (∼200 000 km) on its way to the transition region. The distance remains quite significant even if we assume a shorter transport time. This means that the dynamo region of the quasi-axial field must be located at the top, or at least at the center of the convection zone. (2) The dynamo must be located at a depth that allows it to be observed as poloidal field (∼1 G) at the source surface. (3) This region is where 99% of short-lived differentially rotating sunspots originate. (4) Recent helioseismological data (Kosovichev et al., 1997) do not exclude such possibility.

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Figure 7. A scheme of generation mechanism of the ∼11-year cycle of large-scale solar magnetic fields at ϕ ≤ 50◦ : D1 is the upper dynamo region (quasi-axial dipole), T ≈ 22 years; D2 is the lower dynamo region (quadrupole), Tω ≈ 27 days, T2 ≈ 11 years. D2 in the figure occupies the entire transition layer, whereas in the model it lies lower, occupying only the rigid rotation zone. vρ is the average rate of the anisotropic turbulent pumping (atp). The hatched tubes rise from the D1 region, blank tubes from the D2 region. The roman numerals on the right denote: I – the photosphere surface, II – III the middle and the bottom of the convection zone, respectively, and IV – the tachocline bottom (the rigid rotation zone). Sunspots and poloidal fields of various origin are shown on the photosphere surface. Brl is the relic magnetic field.

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The dynamo generates poloidal and toroidal modes of the quasi-axial field, that changes with a period T ≈ 22 years. The poloidal mode is observed as a large-scale photospheric field at mid and equatorial latitudes, and the toroidal field as shortlived differentially rotating sunspots, that make 99% of the total sunspot number. These sunspots occur during the solar cycle in the latitude zone of ∼8–400 in both hemispheres and are evenly distributed in longitude. On the other hand, this region can hardly be very close to the photosphere, because cyclic variations in granulation and supergranulation are not observed. In spite of the fact that quasi-dipole dynamo exists at the top of the convection zone, it is obviously connected with the transition region between the convection and the radiative zones. This relationship can be inferred from earlier works that involve the relic magnetic field to explain some characteristics of solar periodicity (Piddington, 1976; Rivin, 1993, 1995; Pudovkin and Benevolenskaya, 1984, etc.). The Wolf numbers are likely to describe the effect of this continuously working dynamo. The second generation region of the large-scale magnetic field is located at the base of the convection zone. According to (3)–(4), that is where the quadrupole field with T ≈ 27 days is generated and modulated by the quasi-dipole field. The up-to-date experimental data do not provide evidence for generation mechanisms of the lower and the upper dynamo in each region depend on one another. They only reveal a link between the regions with different carrier frequencies. This link is twofold and suggests that the generation mechanism of the main cycles of the solar magnetic fields is a complex unified closed system. The first link is the mechanism of anisotropic turbulent pumping. It drains part of the quasi-dipole field to the lower dynamo. On its way down or in the lower region, the magnetic cycle of the upper dynamo is detected, its second harmonic is significantly enhanced, and subsequently modulates the amplitude of the quadrupole, whose proper frequency corresponds to T ≈ 27 days. The flux of solar neutrinos, whose cycles are well correlated with the cycles of the quadrupole magnetic field (Obridko and Rivin, 1996b; Rivin and Obridko, 1997), is likely to be simultaneously modulated in the same region. The second link consists of the magnetic tube clouds, due to asymmetry of the quadrupole field (Parker, 1976). They move continuously upwards, piercing the upper dynamo zone. One of their manifestations in the photosphere are the active longitudes with specific active regions and sunspots in them. It is possible that the two fields interact. The processes of downward transport and emergence take ∼1–2 years, leading to a phase shift of the quadrupole with respect to the dipole field. The beginning of this process for every cycle of the upper dynamo seems to coincide with the beginning of the solar magnetic cycle (Rivin, 1993, 1995): the minimum before the even 11-year cycle, according to the Zürich classification. To some extent, this approach corresponds to the Waldmeier’s concept of the eruptive solar cycle, however on a new basis: if applied to the ∼22-year cycle. However,

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the possibility of such interpretation of the 22-year cycle is not proved: only some indirect evidence is available. So, for the upper dynamo, the generation of the main cycle can be considered a stationary quasi-harmonic process. Like any other solution of the inverse problem, the suggested model is one possible version of the mechanism, taking into account the background field and the solar activity characteristics. It only provides a general generation scheme and rises a lot of questions concerning its mechanism. Until now, we have considered the background field at ϕ = 50◦ . In the context of all said above, and taking into account the described theoretical results, the magnetic field at ϕ = 60◦ has a somewhat different, more complicated nature, than at the equator or at mid latitudes, where it is manifested, in particular, in a 5-year shift of the 11-year cycle (λ ≈ π ) relative to the B cycle (for the Wolf numbers and Bs ). The polar field may be assumed to be a product of the dynamo, the same as the dipole field at lower latitudes, its characteristics being determined by propagation from the source in the convection zone to the surface and by the field formation conditions at the pole. In terms of the suggested interpretation of the large-scale magnetic field components, the characteristics of this zone may be partly associated with the turbulent pumping to the pole in the solar convection zone (Krivodubsky, 1992).

5. Conclusion The recent observational data show that there are two components of the 11-year cycle of the large-scale solar magnetic field, differing in their origin. The properties of these components and their manifestation in solar activity imply that the existing dynamo models need a correction. The idea of two magnetic field components in the 11-year cycle is not new in heliophysics. It arose from the particular features of cyclic variation of large, long-lived, rigidly rotating sunspots and from the Gnevyshev’s second maximum of activity in the corona (Vitinsky, Kopecký, and Kuklin, 1986). However, it is only the analyses of space-time characteristics of three components of the background magnetic field that allow us to isolate the second component, to study its properties, to create an analytical model, and to show that this component (rather than the total magnetic field of the Sun) is generated in the tachocline region. It is of primary importance to the new dynamo models that its carrier frequency corresponds to Tω ≈ 27 days, rather than to the magnetic cycle or its second harmonic. The quadrupole magnetic field plays a decisive role in amplitude modulation of any corpuscular emission both from the core (neutrino), and from outside the Sun (galactic cosmic rays, solar wind). However, its contribution is different in different regions. This contribution is very important for solar and solar-terrestrial studies.

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6. Results (1) The 11-year cycles of the large-scale solar magnetic field near the equator and at mid-latitudes are due to two components in the temporal and spatial regions with essentially different properties. (2) The smaller component of the 11-year cycle is the result of detection of the original quasi-axial field, that changes with T ≈ 22 years and is, obviously, generated by the dynamo mechanism at the top or middle of the convection zone. The Wolf numbers contain very likely information on the cycles of the toroidal field of this particular quasi-dipole. (3) The greater quadrupole component of the cycle is generated at the bottom of the convection zone. It is due to modulation of the quadrupole magnetic field by the field modulus of the distorted quasi-dipole with T ≈ 22 years. Its minima coincide with the minima of the Wolf number cycle, however, the behaviour at the maximum epoch may be quite different. This component lags behind the quasi-dipole field by about a year. (4) The dipole and quadrupole background magnetic fields of the Sun originate at spaced sources and they have different T values (22 years and 27 days, respectively). They are accompanied by generation of sunspots (toroidal fields) with different characteristics. These properties of the background fields and sunspots have not been taken into account in the available models of generation of the main cycles of solar activity. (5) A similar form of both components in |B| at a phase shift of about a year between them suggests that the solar magnetic cycle and its second harmonic are generated by a closed complex of mechanisms. The complex comprises: (a) two independent dynamo regions in the convection zone at different radial distances from the center of the Sun; (b) anisotropic turbulent pumping of the upper dynamo field (quasi-dipole) to the region of the second one with simultaneous detection of the magnetic cycle and enhancement of its second harmonic; and (c) formation of magnetic tubes at the bottom of the convection zone and their emergence to the photosphere piercing the upper dynamo field. (6) The quadrupole magnetic field, generated at the base of the convection zone or in the transition region (tachocline), has its own rotation rate, corresponding to ∼27 days. This changing quadrupole field is modulated by the second harmonic of the magnetic cycle. No observational data are so far available to suggest generation of the solar magnetic cycle and its harmonics in this zone.

Acknowledgements The author is grateful to E. I. Mogilevsky and V. N. Obridko for valuable discussions and to E. I. Prutenskaya and I. V. Dmitrieva for assistance in preparation

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of the manuscript. The work was sponsored by the Russian Foundation for Basic Research (grant No. 96-02-17054) and Astronomy Program (grant No. 4-264).

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