Sunspot nests as traced by a cluster analysis

The appearance of sunspot groups between August 1959 and December 1964 is investigated in search of sunspot nests. A sunspot nest is a relatively small space on the surface within which a succession of spot groups appears. A single-linkage clustering technique is used to trace clusters in the three dimensions longitude, latitude and time. The number of genuine sunspot nests is estimated and their properties are determined.At least one third of the sunspot appearances belong to intrinsically physical clusters. Even a substantial fraction of the clusters of two-member groups is genuine.The clustering criteria are set such that the smallest scales in the clustering are brought out. The sizes of the nests turn out very small: the typical (1-) spread about the longitude-time regression line is about 2°, and the spread about the mean latitude is about 1°. The lifetimes range from one to seven months. The nests follow the rotation rate-latitude relation of recurrent sunspots within a small but intrinsic spread of about 15 m s^–1. In the present sample the displacements in latitude are extremely small: the amplitude of any large-scale flow pattern must be less than 3 m s^–1, whereas the intrinsic proper motions in latitude are less than 5 m s^–1.The appearance of spot groups in a nest is intermittent. On one hand, in an active nest spots may be absent for nearly two complete rotations. On the other hand, in many nests more than one spot group has been recorded during one disk crossing.There is a strong tendency for the nests to cluster once again in larger nests: more than 1/3 of the compact nests are components in larger nests. Within such a large nest the components overlap in time, their mean latitudes differ by less than 2°.5, but the difference in longitude may extend up to 55°.The present and earlier results are either in harmony, or seemingly discordant results are readily explained by properties of the nests and differences in the search criteria.     

Cluster analysis of the space-time distribution of sunspot groups during solar cycle no. 20

Cluster analysis (a Bayesian iteration procedure) was used to study the space-time distribution of sunspot groups in the time interval from 1965 to 1977. (Data were taken from the Greenwich and Debrecen Heliographic Results.) The distribution proved to be significantly non-random for the 8–10 groups cluster^–1 (gr cl^–1) level of clustering. Convincing evidence also favours non-random behaviour for other levels of clustering from the lowest (3–4 gr cl^–1) up to the highest ( 150 gr cl^–1) level. The rotation rate of the non-random pattern is generally slightly lower than the Carrington rate.The 8–10 gr cl^–1 level, crudely corresponding to the sunspot nests investigated earlier, was studied in more detail. The cycle- and latitude-averaged rotational rate of the nests is slightly ( 1%) but significantly lower than the Carrington rate. Their differential rotation is strongly reduced: the cycle-averaged rotational rate varies only by 2–3% within the sunspot belt. A slight but significant bimodality is seen in the differential rotation curve: the intermediate latitudes ( 10°–20°) show a somewhat slower rotation than both the equatorial and the higher latitude regions. This might be explained by a time-dependence of the rotation rate coupled with the butterfly diagram.     

The Clustering Properties of Active Regions During the First Part of Solar Cycle 23

In this paper we study the longitudinal distribution of solar magnetic regions, using the synoptic magnetic maps from Kitt Peak National Observatory, the active region data from Solar Geophysical Data and the Hobservations from Prairie View Solar Observatory. The clusters of activity were identified by comparing the positions of sunspot groups between successive Carrington rotations. We have found that a large percentage of active regions was involved in the clustering process (40–50%, if we only take into account clusters with a minimum lifetime of 4 rotations). The nests followed the differential rotation of the solar surface, within an intrinsic spread. A remarkable feature of sunspot nests detected in our study is their high degree of complexity, with a large number of nests being organized in diverging, converging, or parallel structures. Of the flares which occurred during the time interval of interest, the great majority originated from the sunspot nests; the distribution of the flares between these nests was not uniform, revealing active and quiet nests. A high flaring rate was recorded at the intersection points of diverging or converging nests, suggesting that these points represent violent interactions of magnetic fluxes. The complexes were in continuous interaction, which impacts their properties and future evolution. The behavior of the nests indicate that they are maintained by repeated injection of magnetic flux rather than by the evolution of the surface magnetic fields.     

Detailed comparison between sunspot activity in ‘hot spots’ and galactic cosmic-ray intensity

The influence of sunspot activity on the condition of the solar-terrestrial environment during cycle 21 was examined using the data of sunspots and the modulation of the galactic cosmic-ray intensity. The hot spots discussed by Ichimoto et al. (1985) and Bai (1987a, 1988) were also found by analyzing the longitudinal distribution of sunspot groups.A detailed comparison between the time change of the sunspot activity in hot spots and that of the galactic cosmic rays observed by the neutron monitor reveals that several transient diminutions of the GCR intensity (with much longer duration than a Forbush decrease) occur at nearly the same time as the sporadic enhancement of sunspot area in the hot spots.Contributions from Kwasan and Hida Observatories, Kyoto University No. 303.     

STATISTICAL PROPERTIES OF THE PULSES IN THE SOLAR p-MODE POWER

We have revealed the periods of good visibility for each individual mode of low spherical degree using irradiance data from the IPHIR experiment. Their statistical properties and the influence on the resulting line shapes are discussed. The analysis of the temporal change of each mode power by Fourier transform with a running temporal window was performed. The running mean power of p-modes (=0, n=17–24 and =1, n=16–23) apparently changes with the rotation of the Sun. There is well visible an anticorrelation of the p-mode power with the mean solar magnetic field and less significant correlation with daily sunspot number.     

Duration of Polar Activity Cycles and Their Relation to Sunspot Activity

We have defined the duration of polar magnetic activity as the time interval between two successive polar reversals. The epochs of the polarity reversals of the magnetic field at the poles of the Sun have been determined (1) by the time of the final disappearance of the polar crown filaments and (2) by the time between the two neighbouring reversals of the magnetic dipole configuration (l=1) from the H synoptic charts covering the period 1870–2001. It is shown that the reversals for the magnetic dipole configuration (l=1) occur on an average 3.3±0.5 years after the sunspot minimum according to the H synoptic charts (Table I) and the Stanford magnetograms (Table III). If we set the time of the final disappearance of the polar crown filaments (determined from the latitude migration of filaments) as the criterion for deciding the epoch of the polarity reversal of the polar fields, then the reversal occurs on an average 5.8±0.6 years from sunspot minimum (last column of Table I). We consider this as the most reliable diagnostic for fixing the epoch of reversals, as the final disappearance of the polar crown filaments can be observed without ambiguity. We show that shorter the duration of the polar activity cycle (i.e., the shorter the duration between two neighbouring reversals), the more intense is the next sunspot cycle. We also notice that the duration of polar activity is always more in even solar cycles than in odd cycles whereas the maximum Wolf numbers W _\max is always higher for odd solar cycles than for even cycles. Furthermore, we assume there is a secular change in the duration of the polar cycle. It has decreased by 1.2 times during the last 120 years.     

A new method for the analysis of equivalent widths and its application to solar photospheric oxygen

Six neutral atomic oxygen Fraunhofer multiplets were observed at nine disk positions at Sacramento Peak Observatory. I filtered the data, corrected them for the instrumental profile and obtained equivalent widths.The equation of transfer for a plane-parallel atmosphere is solved to yield an expression for the equivalent width of a line or multiplet as a function of disk position; line source function, S _L, and relative population of the lower energy level of the transition. Comparison with the observations gives the abundance, average levels of formation of the lines and S _L.The numerical results show that the weak lines are formed either in L.T.E. or pure scattering (i.e., S _L B _v (T _e) J _c), but for 7770 Å S _L/B (T _e) 0.6 ± 0.1 at _c = 0.1. An analysis of the central intensities of 7770 Å yields essentially the same results. The results for 8446 Å are not reliable due to a possible blend with an iron line. The abundance of oxygen in the photosphere may be slightly less than that found by previous investigators.The results are consistent with the assumption that all levels of photospheric oxygen are populated as in L.T.E. with the exception of 3⁵S, which is overpopulated by approximately 50% at _c = 0.1. The overpopulation may be due to the metastability of this level.Based on National Center for Atmospheric Research Cooperative Thesis No. 9.     

Preferred longitudes of sunspot groups and high-speed solar wind streams: Evidence for a ‘solar memory’

Correlation analysis of the mean longitude distribution of sunspot groups (taken from the Greenwich Photoheliographic Results) and high-speed solar wind streams (inferred from the C9 index for geomagnetic disturbances) with the Bartels rotation period P = 27.0 days shows anti-correlation for individual cycles.In particular, the longitudes of post-maximum stable streams of cycle 18 and 19 are well anticorrelated with the preferred longitudes of sunspot groups during the maximum activity periods of these cycles. This is further analyzed using the daily Zürich sunspot number, R, between 1932 and 1980, which reveals a conspicuous similarity of cycle 18 and 19 as well as cycle 20 and 21.We conclude that there is a solar memory for preferred longitudes of activity extending at least over one, probably two cycles (i.e. one magnetic cycle of 22 years). We conjecture that this memory extends over longer intervals of time as a long-term feature of solar activity.     

The abelian higgs sunspot endowed with a local conformal symmetry

We show that the requirement of alocal conformal symmetry of the Abelian Higgs sunspot leads, at least formally, to a complex-valued electromagnetic potential, whose imaginary part is a conformal compensating potential. It is shown that there exists a fundamental difference between conformal and ordinary electromagnetic fields; whereas the ordinary total magnetic flux of a spot is quantized its conformal analogue has to vanish if the Higgs field is to be single-valued. We further stress that such a complex-valued Abelian Higgs field configuration mimics quite well, under certain conditions (all the salient features of) the classical Abelian Higgs sunspot.     

Regularities of variation of the heliospheric current sheet orientation during the solar activity cycle

Evolution of spatial orientation of the heliospheric current sheet (HCS) has been studied in detail using synoptic maps of the HCS configuration over the period 1971–1989. Analysis involves all phases of the sunspot cycle except for two years of maximum solar activity. The helmet-like coronal streamers are confirmed to be structural elements of the HCS. The r.m.s. deviation of a real HCS configuration from a plane does not exceed about 10° during most of the sunspot cycle length. Hence, minimum-type corona should be observed every time the HCS is oriented parallel to the line-of-sight, independent of the cycle phase. Such occasions have been observed apart from the sunspot minimum epochs at the solar eclipses of 31 August, 1932 and 11 July, 1991.Regularities of variation of the two following parameters of the HCS orientation have been revealed: obliquity to the solar equator plane (heel or tilt) and longitudinal orientation (yawing). Behaviour of the above parameters is repeated in different cycles. However, heeling and yawing occur probably not synchronous but rather independent of one another.     

Cycle latitude effects for sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine meridional motion and rotation properties as a function of latitude and distance () from the average latitude of activity (₀) in each hemisphere. Latitude dependence similar to previous results is found, but only for spot groups whose areas are decreasing from one day to the next. A previous study of active region magnetic fields, using this technique of motions as a function of the average latitude of activity, had shown meridional motions on average toward ₀. In this analysis of spot data some evidence is seen for motion away from ₀, with some slight evidence for faster rotation equatorward of ₀ and slower motion poleward of ₀, similar to the torsional oscillation phenomenon. For reasons that are not clear, both of these effects are significantly more pronounced for sunspot groups whose areas are decreasing.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

An apparent ‘even-odd’ cycle distribution in Mt. Wilson ‘numbers of spots’ data

Mt. Wilson numbers of spots data (as defined in Howard et al., 1984) appear to be distributed according to even-odd cycle numbering. Linear fits of annual numbers of spots versus annual sunspot number for even- and odd-numbered cycles have slopes which are statistically different at the 5% level of significance. The existence of an even-odd split in Mt. Wilson numbers of spots data may be due either to a real difference in even- and odd-numbered cycles on the Sun or to a difference in weather at Mt. Wilson (perhaps, related to the 22-yr rhythm of drought in the western United States) during even- and odd-numbered cycles, or both. For cycle 22, an even-numbered cycle, the peak numbers of spots is estimated to be near 2600.     

Sunspots Observed to Physically Weaken in 2000–2001

The strength of a sunspot depends on its magnetic field and umbral darkness, factors which go together. The strongest field in an umbra is always found at the darkest position. We use this relationship, B=f(1/T), to demonstrate that at the maximum of cycle 22 (1990–1991) sunspots were statistically stronger than at the same phase of cycle 23 (2000–2001). Within our sample of 195 spots, cycle 23 exhibits an excess of small bright spots, and possibly, a dearth of large dark spots. This could alter the total solar irradiance (TSI)–sunspot number relationship.     

Longitudinal and temporal variations of sunspot regions and coronal holes during Cycle 21

The relationship between sunspot activity in heliographic longitude and coronal holes is investigated for the period corresponding to Cycle 21 (Carrington rotations 1623–1779). The major result is that, based on He i 10830 Å data, a strong inverse association is found between the longitudinal positions of sunspot groups and the size and number of coronal holes (especially, the equatorial extensions of polar holes). Frequencies of coincidences in longitude were determined for both types of activity and the evolution of coronal holes over Cycle 21 is depicted in the form of a butterfly diagram displaying their latitudinal and longitudinal extents. A tabular listing identifies average longitude and persistence of sunspot active longitudes.     

The solar minimum temperature determined by the CO (A 1Π-X 1Σ)

The synthetic Voigt profile of the following transitions (v=0,v=0), (v=0,v=1), (v=1,v=1), (v=1,v=0) have been computed for different concentrations and temperatures of CO and compaed to the measured intensities of the UV sunspot spectrum by a high resolution spectrograph. From this comparison the solar minimum temperature has been determined.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

Robustness of truncated α Ω dynamos with a dynamic α

In a recent work (Covas et al., 1996), the behaviour and the robustness of truncated dynamos with a dynamic were studied with respect to a number of changes in the driving term of the dynamic equation, which was considered previously by Schmalz and Stix (1991) to be of the form AB. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form |B|². We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the Sun.     

Periodicities in the solar differential rotation,surface magnetic field and planetary configurations

Using Greenwich data on sunspot groups during 1874–1976, we have studied the temporal variations in the differential rotation parametersA andB by determining their values during moving time intervals of lengths 1–5 yr successively displaced by 1 yr. FFT analysis of the temporal variations ofB (orB/A) shows periodicities 18.3 ± 3 yr, 8.5 ± 1 yr, 3.9 ± 0.5 yr, 3.1 ± 0.2 yr, and 2.6 ± 0.2 yr at levels 2. This analysis also shows five more periodicities at levels 1–2. The maximum entropy method is used to set narrower limits on the values of these periods. The reality of the existence of all these periodicities ofB (orB/A ) except the one at 2.8 yr is confirmed by analyzing the simulated time series ofB andB/A with values ofA andB randomly distributed within the limits of their respective uncertainties. Four of the prominent periods ofB agree, within their uncertainties, with the known periods in the the large-scale photospheric magnetic field. The deviations from the average differential rotation are larger near the sunspot minima. On longer time scales, the variations in the amount of sunspot activity per unit time are well correlated to the variations in the amplitudes of the torsional oscillation represented by the 22-yr periodicity inB. All the periods inB found here are in good agreement with the synodic periods of two or more consecutive planets. The possibility of planetary configurations providing perturbations needed for the Sun's MHD torsional oscillations is speculated upon and briefly discussed.     

Periodicities of solar irradiance and solar activity indices,I

Using a standard FFT time series analysis, our results show an 8–11 months periodicity in the solar total and UV irradiances, 10.7 cm radio flux, Ca-K plage index, and sunspot blocking function. The physical origin of this period is not known, but the evidence in the results exclude the possibility that the observed period is a harmonic due to the FFT transform or detrending. Periods at 150–157 and 51 days are found in those solar data which are related to strong magnetic fields. The 51-day period is the dominant period in the projected areas of developing complex sunspot groups, but it is missing from the old decaying sunspot areas. This evidence suggests that the 51-day period is related to the emergence of new magnetic fields. A strong 13.5-day period is found in the total irradiance and projected areas of developing complex groups. This confirms those results (e.g., Donnelly et al., 1983, 1984; Bai, 1987, 1989) which show that active centers are located 180 deg apart from each other.Our study also shows that the modulation of various solar data due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion. This arises from that the active regions and their magnetic fields are better organized and more long-lived during the maximum and declining portion of solar cycle than during its rising portion.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.