Simulations of the gross solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have simulated the evolution of the radial component of the solar photospheric magnetic field during 1976–1984 with a spatial resolution of about 34 000 km, and have derived the corresponding evolution of its absolute value averaged over the visible disk. For nominal values of the transport parameters, this simulated gross field is in close, though imperfect, agreement with the observed gross field and its associated indices of solar activity. By analyzing the response of the simulated gross field to variations in the transport parameters and the source properties, we find that the simulated field originates in newly erupted bipolar regions. The lifetimes of these regions are almost always less than 3 mo. Consequently, the strength of the simulated gross field is a measure of the current level of solar activity, and any recurrent patterns with lifetimes in excess of 6 mo must reflect the continuing eruption of new flux at active longitudes rather than the persistence of old flux in long-lived magnetic structures.E. O. Hulburt Center for Space Research.Laboratory for Computational Physics.Berkeley Research Associates, Springfield, VA.     

Simulations of the sun's polar magnetic fields during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have simulated the evolution of the radial component of the solar photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the line-of-sight polar fields as seen from Earth. The observed timing and strength of the polar-field reversal during cycle 21 can be accounted for by supergranular diffusion alone, for a diffusion coefficient of 800 km² s^-1. For an assumed 300 km² s^-1 rate of diffusion, on the other hand, a poleward meridional flow with a moderately broad profile and a peak speed of 10 m s^-1 reached at about 5° latitude is required to obtain agreement between the simulated and observed fields. Such a flow accelerates the transport of following-polarity flux to the polar caps, but also inhibits the diffusion of leading-polarity flux across the equator. For flows faster than about 10 m s^-1 the latter effect dominates, and the simulated polar fields reverse increasingly later and more weakly than the observed fields.Laboratory for Computational Physics and Fluid Dynamics.E. O. Hulburt Center for Space Research.     

Average properties of bipolar magnetic regions during sunspot cycle 21

We examine the statistical properties of some 2700 bipolar magnetic regions (BMRs) with magnetic fluxes 3 × 10²⁰ Mx which erupted during 1976–1986. Empirical rules were used to estimate the fluxes visually from daily magnetograms obtained at the National Solar Observatory/Kitt Peak. Our analysis shows the following: (i) the average flux per BMR declined between 1977 and 1985; (ii) the average tilts of BMRs relative to the east-west line increase toward higher latitudes; (iii) weaker BMRs had larger root-mean-square tilt angles than stronger BMRs at all latitudes; (iv) over the interval 1976–1986, BMRs with their leading poles equatorward of their trailing poles contributed a total of 4 times as much flux as BMRs with inverted tilts, but the relative amount of flux contributed by BMRs with inverted or zero tilts increased as the sunspot cycle progressed; (v) only 4% of BMRs had reversed east-west polarity orientations; (vi) although the northern hemisphere produced far more flux during the rising phase of the sunspot cycle, the southern hemisphere largely compensated for this imbalance during the declining phase; (vii) southern-hemisphere BMRs erupted at systematically higher latitudes than northern-hemisphere ones through most of sunspot cycle 21.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

The decay of the mean solar magnetic field

We have analyzed the effects that differential rotation and a hypothetical meridional flow would have on the evolution of the Sun's mean line-of-sight magnetic field as seen from Earth. By winding the large-scale field into strips of alternating positive and negative polarity, differential rotation causes the mean-field amplitude to decay and the mean-field rotation period to acquire the value corresponding to the latitude of the surviving unwound magnetic flux. For a latitudinally broad two-sector initial field such as a horizontal dipole, the decay is rapid for about 5 rotations and slow with a t ^–1/2 dependence thereafter. If a poleward meridional flow is present, it will accelerate the decay by carrying the residual flux to high latitudes where the line-of-sight components are small. The resulting decay is exponential with an e-folding time of 0.75 yr (10 rotations) for an assumed 15 m s^–1 peak meridional flow speed.E.O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

A pictorial comparison of interplanetary magnetic field polarity,solar wind speed,and geomagnetic disturbance index during the sunspot cycle

Observations of interplanetary magnetic field polarity, solar wind speed, and geomagnetic disturbance index (C9) during the years 1962–1975 are compared in a 27-day pictorial format that emphasizes their associated variations during the sunspot cycle. This display accentuates graphically several recently reported features of solar wind streams including the fact that the streams were faster, wider, and longer-lived during 1962–1964 and 1973–1975 in the declining phase of the sunspot cycle than during intervening years (Bame et al., 1976; Gosling et al., 1976). The display reveals strikingly that these high-speed streams were associated with the major, recurrent patterns of geomagnetic activity that are characteristic of the declining phase of the sunspot cycle. Finally, the display shows that during 1962–1975 the association between long-lived solar wind streams and recurrent geomagnetic disturbances was modulated by the annual variation (Burch, 1973) of the response of the geomagnetic field to solar wind conditions. The phase of this annual variation depends on the polarity of the interplanetary magnetic field in the sense that negative sectors of the interplanetary field have their greatest geomagnetic effect in northern hemisphere spring, and positive sectors have their greatest effect in the fall. During 1965–1972 when the solar wind streams were relatively slow (500 km s^-1), the annual variation strongly influenced the visibility of the corresponding geomagnetic disturbance patterns.Visiting Scientist, Kitt Peak National Observatory, Tucson, Arizona.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Short-term periodicities in sunspot areas during solar cycle 22

We have analyzed the daily record of sunspot areas during the current cycle 22 looking for the short-term periodicity of around 155 days which was present during some previous solar cycles. Two different methods have been used to compute the power spectra and the results indicate that such periodicity has been absent during the current solar cycle, which confirms the results obtained by other authors who used flares or flare-related data.However, we have found that, during some intervals of time, a periodicity close to 86 days is statistically significant. A similar periodicity was found by Landscheit (1986) in energetic X-ray flares, between 1970 and 1982 (second and first half of solar cycles 20 and 21, respectively), and by Bai (1992b) for important solar flares during solar cycle 20.     

The north-south asymmetry of sunspot areas during solar cycle 22

We have analyzed the asymmetry of sunspot areas during the current solar cycle 22, finding that it has been statistically significant and that the shape of the underlying trend within the full asymmetry time series (1874–1993) indicates that the dominance of solar activity has started to shift, during the current cycle, from the northern hemisphere to the southern one.     

Three-dimensional model for generation of the mean solar magnetic field

A three-dimensional (non-axisymmetric) model for the solar mean magnetic field generation is studied. The sources of generation are the differential rotation and mean helicity in the convective shell. The system is described by two equations of the first order in time and the fourth order in space coordinates. The solution is sought for in the form of expansion over the spherical function Y_n^m. The modes of different m are separated. A finite-difference scheme similar to the Peaceman-Rachford scheme is constructed so to find coefficients of the expansion depending on the time and radial coordinates. It is shown that a mode with a smaller azimuthal number m is primarily excited. The axisymmetric mode m = o describes the 22 year solar cycle oscillations. The modes of m o have no such periodicity, the oscillate with a period of rotation of the low boundary of the solar convective shell, The solutions which are symmetric relative to the equator plane are excited more easily compared with the antisymmetrical ones. The results obtained are confronted to the observational picture of the non-axisymmetric large-scale solar magnetic fields.     

Solar cycle according to mean magnetic field data

To investigate the shape of the solar cycle, we have performed a wavelet analysis of the large–scale magnetic field data for 1960–2000 for several latitudinal belts and have isolated the following quasi-periodic components: ∼22, 7 and 2 yr. The main 22-yr oscillation dominates all latitudinal belts except the latitudes of ±30° from the equator. The butterfly diagram for the nominal 22-yr oscillation shows a standing dipole wave in the low-latitude domain  (∣θ∣≤ 30°)  and another wave in the sub-polar domain  (∣θ∣≥ 35°)  , which migrates slowly polewards. The phase shift between these waves is about π. The nominal 7-yr oscillation yields a butterfly diagram with two domains. In the low-latitude domain  (∣θ∣≤ 35°)  , the dipole wave propagates equatorwards and in the sub-polar region, polewards. The nominal 2-yr oscillation is much more chaotic than the other two modes; however the waves propagate polewards whenever they can be isolated.
We conclude that the shape of the solar cycle inferred from the large-scale magnetic field data differs significantly from that inferred from sunspot data. Obviously, the dynamo models for a solar cycle must be generalized to include large-scale magnetic field data. We believe that sunspot data give adequate information concerning the magnetic field configuration deep inside the convection zone (say, in overshoot later), while the large-scale magnetic field is strongly affected by meridional circulation in its upper layer. This interpretation suggests that the poloidal magnetic field is affected by the polewards meridional circulation, whose velocity is comparable with that of the dynamo wave in the overshoot layer. The 7- and 2-yr oscillations could be explained as a contribution of two sub-critical dynamo modes with the corresponding frequencies.     

The dipole-quadrupole cycle of the background solar magnetic field

The evolution of the background magnetic field with the solar cycle has been studied using the dipole-quadrupole magnetic energy behaviour in a cycle. The combined energy of the axisymmetric dipole, non-axisymmetric quadrupole, and equatorial dipole is relatively lowly variable over the solar cycle. The dipole field changed sign when the quadrupole field was near a maximum, andvice versa. A conceptual picture involving four meridional magnetic polarity sectors proposed to explain these features may be in agreement with equatorial coronal hole observations. The rate of sector rotation is estimated to be 8 heliographic degrees per year faster than the Carrington rotation (P = 27.23^d synodic). Polarity boundaries of sectors located 180° apart show meridional migrations in one direction, while the boundaries of the other two sectors move in the opposite direction. A simple model of how the magnetic field energy varies, subject to specifying reasonable initial photospheric magnetic and velocity field patterns, follows the observed evolution of the dipole and quadrupole field energies quite nicely.     

A 14-day periodicity in the mean solar magnetic field

In the present paper we look for periodicities in the mean solar magnetic field observed at Stanford Observatory, using Fourier transform and autocorrelation techniques. Apart from the periodicity equal to that of the synodic rotational modulation of the Sun, other periods were also found by examining the time series formed at different epochs of the solar cycle. From the aforesaid analyses a 14-day periodicity has been confirmed, which is found to occur in all the cases taken under consideration.     

A solar cycle variation of the interplanetary magnetic field

Measurements of the north-south (B _z component of the interplanetary field as compiled by King (1975) when organized into yearly histograms of the values of ¦B _z ¦ reveal the following. (1) The histograms decrease exponentially from a maximum occurrence frequency at the value ¦B _z ¦ = 0. (2) The slope of the exponential on a semi-log plot varies systematically roughly in phase with the sunspot number in such a way that the probability of large values of ¦B _z ¦ is much greater in the years near sunspot maximum than in the years near sunspot minimum. (3) There is a sparsely populated high-value tail, for which the data are too meager to discern any solar cycle variation. The high-value tail is perhaps associated with travelling interplanetary disturbances. (4) The solar cycle variations of B _z and the ordinary indicators of solar activity are roughly correlated. (5) The solar cycle variation of B _z is distinctly different than that of the solar wind speed and that of the geomagnetic Ap disturbance index.Now at the Aerospace Corporation, El Segundo, Calif. 90245, U.S.A.     

Surface magnetic fields during the solar activity cycle

We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s^-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Variations of the radiation signatures of noise storm-emitting sunspot groups during a solar cycle

The flux density of a noise storm continuum is known to depend on importance parameters of the associated sunspot group, e.g., its total area A. A study of the continua at 287, 234, 113, and 64 MHz, however, reveals in case of the two cycles Nos. 20 and 21 that the radiation signatures of sunspot groups, with a value of A kept fixed, vary systematically with time indicating regular changes of relevant parameters of the overlying loop systems with the phase of the solar cycle. A trend of intense continua at high frequencies (for definition, cf. Figures 1, 2(b)) to occur preferably during the first activity maximum of a solar cycle has been obtained in either case suggesting a decrease of the emissivity of sunspot groups with time. Vice versa, intense continua at lower frequencies (for definition, cf. Figures 1, 2(b)) were mainly observed during the later phase of both cycles. The latter effect is shown to be attributed rather to a long-term variation of the spectral characteristics of the type-I continua than to an enhanced number of intense type-III continua. From the result obtained it follows that non-potential loops extending to great heights into the corona or developing at least conditions favourable for the generation of an intense type-I continuum even at the frequencies < 100 MHz tend to occur more frequently above sunspot groups during the later phase of a solar cycle than above the comparable groups of its first activity maximum.Furthermore, characteristic periods have been found for both cycles during which the emissivity, especially of the very large sunspot groups, was significantly diminished with reference to the comparable groups of the adjacent time intervals.     

A solar cycle variation of the interplanetary magnetic field configuration

The representation of the sector boundaries, published by Svalgaard (1974, 1975) in a superposed 27-days Bartels format showed that they have a significant preference to occur in certain days of the solar rotation. Further study of these data, as well as of the polarized days in the vicinity of them, pointed out that during the epoch of extrema of the 11-year cycle there is a well-established 2-sector structure, on the average. On the contrary, a mean 4-sector structure is more prominent during the intermediate years.     

On the short term variations of solar activity during solar cycle 21

Short-term variations of the last solar activity cycle were studied by the flare and coronal indices using Gleissberg method. Systematic short-term variations are found from their course during the 21st solar activity cycle. Comparison of their autocorrelograms constructed by the new set of data obtained from the magnitude of the fluctuations showed us the existence of the phase shift between the temporal variations of the two indices.     

Limb-darkening and solar cycle variation of sunspot intensities

New observations of the umbral limb-darkening are presented. We find a real and significant decrease in the umbra/photosphere intensity ratio towards the limb. This result contrasts the findings of previous authors and we believe this to be the first time such a decrease is reported. Our conclusion is based on broad band pinhole photometer intensity observations of 22 large sunspots covering the spectral region 0.387–2.35 m. The data are selected from measurements on approximately 600 days during the last 15.5 yr. The application of the limb-darkening data to the study of the temperature stratification in the umbra is briefly discussed. The observations confirm the suggestion that the umbra/photosphere intensity ratio seems to be a linear function of the phase in the solar cycle.