On the rotation rates of sunspot groups

The analysis of Greenwich sunspot data for cycle No. 18 shows: (1) higher rotation rates for the southern sunspot belt than for the northern belt, (2) lower rotation rates and a tendency to a more rigid rotation for greater sunspot groups, (3) lower rotation rates and a tendency to a more rigid rotation for older sunspot groups, (4) no dependence of rotation rates on the life-time of sunspot groups, (5) a tendency to a more rigid rotation at the activity minimum. Results Nos. 2, 3, and 5 could be interpreted in terms of the evolution and interplay of the active regions, as the regions age. If we assume that the sunspot group life-time is a function of their depth in the solar atmosphere, result No. 4 shows that rotation rates do not depend on the depth.     

Distribution of sunspots 1874–1976

A diagram of the distribution in latitude of sunspot groups during the period 1874–1976 is given. As an indication of sunspot activity, a diagram of the mean total daily sunspot areas for each synodic rotation is also given.     

Axial tilt angles of sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine tilt angles determined from the area-weighted positions of leading and following sunspots. These spot group tilt angles are examined in relation to other group characteristics to give information which may relate to the formation and evolution of sunspot groups and the magnetic connection of groups to subsurface magnetic flux tubes. The average tilt angle of all 24816 (multiple-spot) group observations in this study is found to be + 4.2 ± 0.2 deg, where the positive sign signifies that the leading spots lie equatorward of the following spots. Sunspot group areas are significantly larger on average for groups nearer the average tilt angle, which is similar to a result found earlier for active region plages. Average tilt angles are found to be larger at higher latitudes, confirming earlier results. There is a strong negative correlation between average daily latitudinal motion (plus to poles) and group tilt angle. That is, for groups within about 40 deg of the average tilt angle, smaller tilt angles are associated with more positive (poleward) daily drift. Groups nearest the average tilt angle rotate the fastest, on average, the amplitude differences being between about +0.1 and – 0.1 deg day^–1 for groups near and far from the average tilt angle, respectively. Groups with tilt angles near the average show a negative daily separation change between leading and following spots of close to 4 Mm day^–1 on average. Groups on either side of the average tilt angle show spot separations that are on average more positive. A similar effect is not seen for the daily variations of group areas. These results are discussed in relation to analogous recent results for active region magnetic fields. More evidence is found for a qualitative difference between the magnetic fields of sunspots and of plages, relating, perhaps, to a difference in subsurface connection of the field lines or to different physical mechanisms that may play a role for fields of different field strengths.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Common evolution of adjacent sunspot groups

The evolution of two adjacent bipolar sunspot groups is studied using Debrecen full-disc, white-light photoheliograms and H filtergrams as well as Meudon magnetograms. The proper motions of the principal preceding spots of both groups show quite similar patterns; the spots move along almost parallel tracks and change the direction of their motion on the same day at almost the same heliographic longitude. Also, three simultaneous emergences of magnetic flux were observed in both groups. These observations support the idea that these adjacent sunspot groups were magnetically linked below the photosphere. Matching the extrapolated magnetic field lines with the chromospheric fibril structure appears to be different in the two groups since they indicate quite different model solutions for each group, i.e., a near-potential magnetic field configuration in the older group (1) and a twisted force-free field configuration in the younger group (2). The latter configuration could be created by a considerable twist of the main bunch of flux tubes in Group 2, which is reflected in the relative sunspot motions. It is also showed how this twist contributed to the formation of a filament between the two groups.     

On the dissolution of sunspot groups

The behavior of magnetic fluxes from active regions is investigated for times near sunspot disappearance. It is found that the magnetic fluxes decrease on or near the date the spot vanishes. We investigate this effect, and conclude that it is actually due to changes in the field, rather than through dissipation of the active region fields. This is important in considerations of the large-scale behavior of solar magnetic fields.     

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.     

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.     

The growth and decay of sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine the growth and decay rates of sunspot group umbral areas. These rates are distributed roughly symmetrically about a median rate of decay of a few hemisphere day^-1. Percentage area change rates average 502% day^-1 for growing groups and -45% day^-1 for decaying groups. These values are significantly higher than the comparable rates for plage magnetic fields because spot groups have shorter lifetimes than do plages. The distribution of percentage decay rates also differs from that of plage magnetic fields. Small spot groups grow at faster rates on average than they decay, and large spot groups decay on average at faster rates than they grow. Near solar minimum there is a marked decrease in daily percentage spot area growth rates. This decrease is not related to group area, nor is it due to latitude effects. Sunspot groups with rotation rates close to the average (for each latitude) have markedly slower average rates of daily group growth and decay than do those groups with rotation rates faster or slower than the average. Similarly, sunspot groups with latitude drift rates near zero have markedly slower average rates of daily group growth and decay than do groups with significant latitude drifts in either direction. Both of these findings are similar to results for plage magnetic fields. These various correlations are discussed in the light of our views of the connection of the magnetic fields of spot groups to subsurface magnetic flux tubes. It is suggested that a factor in the rates of growth or decay of spot groups and plages may be the inclination angle to the vertical of the magnetic fields of the spots or plages. Larger inclination angles may result in faster growth and decay rates.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

A twin flare in symmetrical sunspot groups

Two sunspot groups in symmetrical positions relative to the Sun's equator were flaring almost simultaneously. The larger northern group was highly irregular: the two main spots were surrounded by one and the same penumbra, the magnetic polarities were inverted and the inclination of the axis was exceptionally large and of the wrong direction. The larger southern flare consisted of two parallel ribbons that developed into a loop prominence. The two ribbons were moving sideways and upwards, forming a cone. The speed of this motion amounted to 10 km s^–1 at the beginning and decreased to 2 km s^–1 in the course of one hour. The streaming along the slopes of the cone indicates the direction of the magnetic fields.     

A digital method to calculate the true areas of sunspot groups

The areas of sunspots are the most prominent feature of the development of sunspot groups. Since the size of sunspot areas depend on the strength of the magnetic field, accurate measurements of these areas are important. In this study, a method which allows to measure true areas of the sunspots is introduced. A Stonyhurst disk is created by using a computer program and is coincided with solar images. By doing this, an accurate heliographic coordinate system is formed. Then, the true area of the whole sunspot group is calculated in square degrees with the aid of the heliographic coordinates of each picture element forming the image of the sunspot group. This technique’s use is not limited with sunspot areas only. The areas of the flare and filaments observed on the chromospheric disk can also be calculated with the same method. In addition to this, it is possible to calculate the area of any occurrence on the solar disk, whether it is related to an activity or not.     

Note on the asymmetry of bipolar sunspot groups

It is shown that the analytical solution of the equilibrium plasma equation which is a superposition of the axial-symmetric solution and the solution with helical symmetry can describe asymmetry of elements for a bipolar sunspot group.     

On umbral flashes in different sunspot groups

The results of a statistical investigation of the occurrence of umbral flashes for 40 sunspot groups are reported for the period 1966–1983. The following characteristics were chosen for the analysis: (a) position on the solar disk; (b) group area; (c) sunspot area; (d) maximum magnetic field strength of a sunspot; (e) modified Zürich class; (f) sunspot age; (g) magnetic structure; and (h) flare activity of a group. The dependence of umbral flashes on magnetic structure of a sunspot is the most essential feature. The absence of umbral flashes in the umbrae of main sunspots perhaps may be used as one of the predictors of flare activity.     

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.     

Meridional motions of sunspot groups during eleven activity cycles

Greenwich data (1874–1976) are used for a time-dependent analysis of meridional motions of sunspot groups. We obtain the latitude-dependence of meridional motions of sunspot groups with respect to a mean latitude determined for half-year intervals. The daily meridional motions of groups are also given separately for growing and decaying sunspot groups. The development is determined from changes of sunspot areas. Our results are compared with the reductions performed by Howard (1991b) using the Mt. Wilson sunspot data from 1917 until 1985: Although we have smaller errors, we do not find any significant drift. We also do not find different trends in the meridional motions of growing as compared to decreasing sunspots.     

Bright photospheric areas surrounding sunspot groups at 5700 Å

Sunspot groups at various central angles were chosen to study what appears to be an enhanced surrounding area, even at small central angles. The continuous band of observation was 200 Å wide, centered at 5700 Å. The enhancement has been seen before, but only at higher frequencies, as by Jayanthan in the ultraviolet. Four years of sunspot pictures from March 1957 to March 1961, were inspected and no instance of the non-appearance of the enbancement was noted. An attempt to show proof was made by photometry and by high contrast prints of the areas around groups at different central angles. It was shown that more than half of the flux deficit reappears in this enhancement.     

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.     

Flux linkages of bipolar sunspot groups: A computer study

Past studies of the structure of solar magnetic fields have used magnetograph data to compute selected field lines for comparison with the morphology of structures seen in various spectral wavelengths. While those analyses examine one of the integral properties of magnetic fields (field lines), they are not complete since they fail to determine the other important integral property: the boundaries of the flux of field lines of given connectivity. In the present analysis we determine such a system of boundaries, called separatrices, for the current free field of two p-f spot pairs so as to exhibit the line of self-intersection, called the separator. The analysis is compared with previous analytical work. These computer results, confirming earlier studies carried out using iron fillings, show that the separatrix has the form of two intersecting ovoids, defining four flux cells. New features which have emerged from this study include the observation that the projections of the separatrix in a plane perpendicular to the separator at its highest point do not intersect at 90° as has been widely believed, but rather closer to 60° in the case studied. The separator is very nearly circular over most of its length. The two neutral points (B = 0) which appear at the photospheric ends of the separator have the mixed radial-hyperbolic form as expected, a feature requiring every field line lying on the separatrix to connect with at least one of the two neutral points. The rotation of line direction with height (shear) is graphically illustrated in the potential field case studied here. We also exhibit a magnetic arcade.     

On the proper motion of small pores in sunspot groups

The possibility of measuring pore positions and proper motions with high accuracy, using time series of short exposure photographs, is discussed. Preliminary measurements of a series covering a time span of 110 min. show that positions of small pores may be defined, and horizontal velocities determined, to within 0.1, or 30 m s^–1, respectively.Mitteilungen aus dem Kiepenheuer-Institut No. 173.     

Deceleration of the rotational velocities of sunspot groups during their evolution

Using the Greenwich Photoheliographic Results for the years 1874–1976 the daily rotational velocities for 955 recurrent and 13169 non-recurrent sunspot groups from the first day of their appearance and during their evolution have been determined. The rotational velocities were divided in six latitude strips with a width of five degrees and grouped according to the age of the groups. It was established that the rotational velocities of recurrent and non-recurrent sunspot groups decrease with time in all studied latitude strips. At their birth the recurrent spot groups rotate faster by about 0.15° day⁻¹ than the non-recurrent ones and settle, within the errors of measurements, to an about 0.5° day⁻¹ slower velocity value during the second disc passage. A comparison of our results with helioseismology measurements indicates that in the frame of the anchoring hypothesis, the recurrent sunspot groups at their birth could be coupled to the fast rotating layer at about r=0.93 R _⊙.