Astronomy Reports, Vol. 44, No. 2, 2000, pp. 103–111. Translated from Astronomicheskiœ Zhurnal, Vol. 77, No. 2, 2000, pp. 124–133. Original Russian Text Copyright © 2000 by Obridko, Shel’ting. The Large-Scale Magnetic Field on the Sun: The Equatorial Region V. N. Obridko and B. D. Shel’ting Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation, Russian Academy of Sciences, Troitsk, Moscow oblast, 142092 Russia Received February 24, 1999 Abstract—The sector structure and variations in the large-scale magnetic field of the Sun are studied in detail using solar magnetic-field data taken over a long time interval (1915–1990). The two-sector and four-sector structures are independent entities (i.e., their cross correlation is very small), and they are manifest in different ways during the main phases of the 11-year cycle. The contribution of the two-sector structure increases toward the cycle minimum, whereas that of the four-sector structure is larger near the maximum. The magnetic-field sources determining the two-sector structure are localized near the bottom of the convection zone. The well- known 2–3-year quasi-periodic oscillations are primarily associated with the four-sector structure. The varia- tions in the rotational characteristics of these structures have a period of 55–60 years. The results obtained are compared with the latest helioseismology data. © 2000 MAIK “Nauka/Interperiodica”. 1. INTRODUCTION all data was one day. In general, the structure recon- structed from the Hα data is in satisfactory agreement The present work continues a series of papers [1–3] with that derived from geomagnetic data, especially, devoted to studies of cyclic variations in the structure of after 1958, when both data series coincide in detail. For the large-scale magnetic field on the Sun over a long earlier periods, our data seem to be more reliable. time interval (1915–1996) using both direct measure- ments of the magnetic fields [4–7] and computations of To obtain more accurate comparisons between the the fields derived from Hα spectroheliograms. The GMF and IMF data, we calculated mean annual spectra main problem here was the development of a method for the entire data set and constructed the patterns of for polar correction, enabling us to calculate the field these spectra (Fig. 1). Both spectra show two- and four- structure on the source surface and, therefore, to reveal sector structures (27 and 13 days) and demonstrate sim- the main harmonics of the global field. We describe this ilarity in the time variations of their amplitudes. method in [1–2], together with a comparison between In the present paper, we study the cyclic variation the computed polar field and the number of polar facu- and rotation of the two- and four-sector structures of the lae. These two quantities have almost the same time large-scale magnetic field. We emphasize that, every- behavior. where, we refer to synodic rotational periods. Our computation of the field at the source surface, in A detailed comparison between the structure of the fact, corresponds to a spatial filtration and automati- reconstructed global magnetic field (GMF) at the cally separates the field harmonics that vary most source surface and the sector structure of the interplan- slowly with height. Consequently, all subsequent con- etary magnetic field (IMF) was presented in [3]. We used clusions about the structural characteristics refer to the most complete series of IMF data (1926–1990), some unknown depth under the photosphere, which we obtained by Svalgaard and coworkers (see [8–11]) and will call the generation region of the corresponding Mansurov et al. [12] from geomagnetic measurements. structure of the global magnetic field. The method developed by Mansurov and Svalgaard enables reconstruction of the sign of Bx component of the interplanetary magnetic field using ground-based 2. PREVIOUS STUDIES geomagnetic data. In the optimal case, this procedure OF THE SECTOR STRUCTURE requires data from several geomagnetic observatories The concept of the sector structure of the interplan- in the Arctic and Antarctic. Unfortunately, this condi- etary magnetic field appeared in 1965, when Wilcox tion was fully satisfied only after 1958. Restoration and Ness, via direct observations using the IMP 1 satel- results for earlier times are considerably less reliable, lite, discovered that the interplanetary magnetic field is and IMF data are completely absent before 1926. usually directed toward or away from the Sun over quite We used computed values of the magnetic field long time periods, of the order of several days [13, 14]. amplitude on the source surface at the helioprojection This structure exists for several years and rotates with a point of the Earth as GMR data. The time resolution of period close to 27 days. It was believed for a long time 1063-7729/00/4402-0103 $20.00 © 2000 MAIK “Nauka/Interperiodica” 104 OBRIDKO, SHEL’TING 40 20 40 20 Period, days 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 0.05 0.10 0.15 0.05 0.10 0.15 Frequency, days–1 GMF IMF Fig. 1. Spectra of the GMF (left panel) and IMF (right panel). that this structure is primarily composed of four sec- recurrent period. At the cycle minimum, the structure of tors, as at the time of its discovery. However, this was the IMF either disappears as a result of the Rosenberg– later subject to question [15–19]. Unfortunately, the Coleman effect or acquires the form of a two-sector relation between these two modes has not yet been fully structure with a recurrent period of about 27 days. Of studied. It is not clear how often the four-sector struc- course, the Rosenberg–Coleman effect is absent when ture occurs, how well it is correlated with the main analyzing the solar magnetic field; nevertheless, we mode, and how these structures rotate when they are expect that the sector structure will disappear due to a studied separately. weakening of the zonal coefficients. The two-sector It is now quite clear that the sector structure (at least, structure that is finally formed plays the leading role up from the point of view of its basic characteristics) is a to the next cycle maximum, with the rotational period continuation of the global magnetic field into interplan- increasing to 27.5–28.5 days. It is interesting that the etary space. Therefore, subsequent analysis of the sec- secondary solar-activity maximum in 1972 led to a dis- tor structure reduces, in effect, to analysis of the struc- ruption of the already-formed four-sector structure with ture and cyclic variations of the global magnetic field of a period of about 27 days, typical for the decline phase, the Sun. and a short-time re-establishment of a two-sector struc- As shown previously in [15, 18], there are clearly- ture with a rotational period 28.0–28.5 days, character- detected cyclic variations in the sector structure of the istic of the cycle maximum. IMF. A two-sector structure with a rotational period of Thus, a higher level of solar activity corresponds to over 27 days (27.5–28.5 days) is always observed at the lower rotational velocity and (somewhat unexpectedly) cycle maximum. Next, in the decline phase, the struc- to better-defined two-sector structure. In general, four- ture acquires a four-sector character with a clear 27-day sector structure is a quite rare phenomenon: It does not ASTRONOMY REPORTS Vol. 44 No. 2 2000 THE LARGE-SCALE MAGNETIC FIELD ON THE SUN 105 exist in a pure state at all and appears as a substantial ( 2 2) ( 2 3) addition to the two-sector structure in the decline A12 = A1 + A2 , A34 = A3 + A4 , phase, just after the field reversal. tanϕ = A /A , tanϕ = A /A , T = 27.275 days. In general, these results of our analysis of the struc- 1 1 2 2 3 4 ture and rotation of the IMF are in agreement with the It is obvious that the period T = 27.275 days, equal results of other studies. For example, Svalgaard [20] to the Carrington rotation period, was taken only as a obtained the following periods for various phases of the ϕ ϕ test period. The phases 1 and 2 specify the positions cycle: 27.1 days at the minimum, up to 28.3 days at the of the maxima for the two- and four-sector structures in phase of increasing activity, and a nearly constant value of a heliographical longitude system, and the phase varia- 27.2 days in the second part of the cycle. Wilcox and Col- tions can easily be recalculated to determine the real burn [21, 22] obtained rotational periods of 27.5 days for rotational periods T2 and T4, respectively. All ampli- the period of increasing activity and ~27.0 days for the tudes are expressed in units of the mean-square approx- second part of the cycle. We emphasize that no differ- imation errors. Next, we smoothed the data using a ence between the two sector-structure modes was taken standard moving interval composed of 13 points, where into account in [20–22], and their results essentially we took the window boundary points into consideration correspond to the entire IMF. Since, as noted above and with half the statistical weight, and the smoothed value shown below, the two-sector mode is the most signifi- corresponds to the middle point of the window. In this cant, the results of [20–22] should correspond prima- way, we obtain four characteristics of the structure: The rily to this mode. relative significance of the two-sector structure A , the An attempt to analyze only the four-sector structure 12 relative significance of the four-sector structure A34 in [10, 11, 23] was not entirely successful in our opin- (in our subsequent discussion, these two quantities will ion.