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.     

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.     

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 mean solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have computed the evolution of the photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the mean line-of-sight field as seen from Earth. We obtained a good, but imperfect, agreement between the observed mean field and the field computed for a nominal choice of flux transport parameters. Also, we determined the response of the computed mean field to variations in the transport parameters and the source properties. The results lead us to regard the mean-field evolution as a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow (if present), and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation (relative to the strength and orientation of the mean field) and on the time elapsed before the next eruption (relative to the decay time of the field). Thus the mean field evolves principally due to the contributions of the larger sources, which produce a strong, gradually evolving field near sunspot maximum but a weak, sporadically evolving field near sunspot minimum.E. O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

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.     

Positions of sunspot groups and solar rotation

The question is studied whether the one-year solar oscillation found by V. F. Chistyakov for the years 1965–1973 can be traced in the observations of sunspots of 1874–1971 published by Greenwich Observatory. The result is negative. But the study leads to the following two conclusions: (1) The average observable centres of gravity of spot groups are variably displaced towards the central meridian or towards the limb, the time scale of this variability being of the order of 70 years. Thus the angular velocity should be determined from recurrent groups in transit of the central meridian only. (2) The angular velocity will be smaller when determined from older spots.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Statistical behavior of sunspot groups on the solar disk

In the present study we have produced a diagram of the latitude distribution of sunspot groups from the year 1874 through 1999 and examined statistical characteristics of the mean latitude of sunspot groups. The reliability of the observed data set prior to solar cycle 19 is found quite low as compared with that of the data set observed after cycle 19. A correlation is found between maximum latitude at which first sunspot groups of a new cycle appear and the maximum solar activity of the cycle. It is inferred that solar magnetic activity during the early part of an extended solar cycle may contain some information about the strength of forthcoming solar cycle. A formula is given to describe latitude change of sunspot groups with time during an extended solar cycle. The latitude-migration velocity is found to be largest at the beginning of solar cycle and decreases with time as the cycle progresses with a mean migration velocity of about 1.61° per year.     

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.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

Rapid sunspot motion during a major solar flare

A major solar flare on 15 November, 1991 produced a striking perturbation in the position and shape of the sunspot related most closely to the flare. We have studied these perturbations by use of the aspect-sensor images from the Soft X-ray Telescope on board YOHKOH, and with ground-based data from the Mees Solar Observatory. The perturbation occurred during the impulsive phase of the flare, with a total displacement on the order of 1 arc sec. The apparent velocity of approximately 2 km s^–1 exceeds that typically reported for sunspot proper motions even in flare events. We estimate that the magnetic energy involved in displacing the sunspot amounted to less than 4 × 10³⁰ ergs, comparable to the radiant energy from the perturbed region. Examination of the Mees Observatory data shows that the spot continued moving at lower speed for a half-hour after the impulsive phase. The spot perturbation appears to have been a result of the coronal restructuring and flare energy release, rather than its cause.     

On the latitude drift of sunspot groups and solar rotation

The N-S drift of sunspot groups has been studied in a different way than previously, using positions of recurrent groups of the years 1874–1976. The existence of the meridional motions, the general shape of the drift curves, and the dissimilarity between these curves around sunspot maxima and minima, are all confirmed. In addition, also for the angular velocity of the Sun the same material gives differences around the times of sunspot maxima and minima.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

Prediction of maximum sunspot number in solar cycle 23

Instantaneous predictions of the maximum monthly smoothed sunspot number in solar cycle 23 have been made with a linear regressive model, which gives the predicted maximum value as a function of the smoothed sunspot numbers corresponding to a given month from the minimum in all preceding cycles. These predictions indicate that the intensity of solar activity in the current cycle will be at an average level.     

Statistics of the largest sunspot and facular areas per solar cycle

The statistics of extreme values is used to investigate the statistical properties of the largest areas of sunspots and photospheric faculae per solar cycle. The largest values of the synodic-solar-rotation mean areas of umbrae, whole spots and faculae, which have been recorded for nine solar cycles, are each shown to comply with the general form of the extreme value probability function. Empirical expressions are derived for the three extreme value populations from which the characteristic statistical parameters, namely the mode, median, mean and standard deviation, can be calculated for each population. These three extreme value populations are also used to find the expected ranges of the extreme areas in a group of solar cycles as a function of the number of cycles in the group. The extreme areas of umbrae and whole spots have a dispersion comparable to that found by Siscoe for the extreme values of sunspot number, whereas the extreme areas of faculae have a smaller dispersion which is comparable to that found by Siscoe for the largest geomagnetic storm per solar cycle. The expected range of the largest sunspot area per solar cycle for a group of one hundred cycles appears to be inconsistent with the existence of the prolonged periods of sunspot minima that have been inferred from the historical information on solar variability. This inconsistency supports the contention that there are temporal changes of solar-cycle statistics during protracted periods of sunspot minima (or maxima). Indeed, without such temporal changes, photospheric faculae should have been continually observable throughout the lifetime of the Sun.     

Coronal holes,solar wind streams,and geomagnetic activity during the new sunspot cycle

We have extended our previous study of coronal holes, solar wind streams, and geomagnetic disturbances from the declining phase (1973–1975) of sunspot cycle 20 through sunspot minimum (1976) into the rising phase (1977) of cycle 21. Using daily He I 10830 Å spectroheliograms and photospheric magnetograms, we found the following results:

1. As the magnetic field patterns changed, the solar atmosphere evolved from a structure having a few, large, long-lived, low-latitude coronal holes to one having numerous small, short-lived, high-latitude holes (in addition to the polar holes which persisted throughout this 5-year interval).
2. The high-latitude holes recurred with a synodic rotation period of 28–29 days instead of the 27-day period already known to be characteristic of low-latitude holes.
3. During 1976–1977 many coronal holes were intrinsically ‘weak’ in the sense that their average intensities did not differ greatly from the intensity of their surroundings. Such low-contrast holes were rare during 1973–1975.

An updated Bartels display of the occurrence of holes, wind speed, and geomagnetic activity summarizes the evolution of their characteristics and interrelations as the sunspot cycle has progressed. Long-lived, low-latitude holes have become rare but remain terrestrially effective. The more common high-latitude holes are effective only when the Earth lies at a relatively high heliographic latitude in the same solar hemisphere.     

The use of solar faculae in studies of the sunspot cycle

Comparison of the long-term variation of photospheric faculae areas with that of sunspots shows that studies of faculae provide both complementary and supplementary information on the behaviour of the solar cycle. Detailed studies of the development of sunspots with respect to faculae show that there is a high degree of order over much of a given cycle, but marked differences from cycle to cycle. Within a cycle the relationship between spot and faculae areas appears to be similar for the N and S solar hemispheres, and over the early stages of a cycle it is directly related to the magnitude of the maximum sunspot number subsequently attained in that cycle.This result may well have predictive applications, and formulae are given relating the peak sunspot number to simple parameters derived from this early developmental stage. Full application to the current cycle 21 is denied due to the cessation of the Greenwich daily photoheliographic measurements, but use of the cruder weekly data suggests a maximum smoothed sunspot number of 150 ± 22.The effects of the incompatibility of the spot and faculae data, in that faculae are unobservable over a large fraction of the solar disc and also do not always develop associated spots, have been examined in a detailed study of two cycles and shown not to vitiate the results.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

Solar cycle variations in the growth and decay of sunspot groups

We analysed the combined Greenwich (1874–1976) and Solar Optical Observatories Network (1977–2011) data on sunspot groups. The daily rate of change of the area of a spot group is computed using the differences between the epochs of the spot group observation on any two consecutive days during its life-time and between the corrected whole spot areas of the spot group at these epochs. Positive/negative value of the daily rate of change of the area of a spot group represents the growth/decay rate of the spot group. We found that the total amounts of growth and decay of spot groups whose life times ≥2 days in a given time interval (say one-year) well correlate to the amount of activity in the same interval. We have also found that there exists a reasonably good correlation and an approximate linear relationship between the logarithmic values of the decay rate and area of the spot group at the first day of the corresponding consecutive days, largely suggesting that a large/small area (magnetic flux) decreases in a faster/slower rate. There exists a long-term variation (about 90-year) in the slope of the linear relationship. The solar cycle variation in the decay of spot groups may have a strong relationship with the corresponding variations in solar energetic phenomena such as solar flare activity. The decay of spot groups may also substantially contribute to the coherence relationship between the total solar irradiance and the solar activity variations.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

22-year cycle or 11-year cycle in the latitude drift of sunspot groups?

Some earlier investigations seem to indicate that sunspots show an average drift in latitude which varies sinusoidally with the period of the double sunspot cycle (about 22 years), while the same investigations do not show similar variability with the period of the single sunspot cycle (about 11 years). Other studies, however, show that the drift of sunspots varies with the period of the single sunspot cycle. There seems to be a discrepancy between the two results. The problem is reinvestigated on the basis of long-lived sunspot groups, but treating the material in a way different from that used before. This procedure, which uses central values of the proper motions of the groups instead of their average values, gives an additional proof of the reality of the 11-year period of the drift. It also seems to produce the 22-year period, but there is such a difference between the variabilities of the drift found on the basis of the two methods that the 22-year cycle of the drift is made doubtful.