Active region magnetic fields

The tilt angles of sunspot groups are defined, using the Mount Wilson data set. It is shown that groups with tilt angles greater than or less than the average value (≈ 5 deg) show different latitude dependences. This effect is also seen in synoptic magnetic field data defining plages. The fraction of the total sunspot group area that is found in the leading spots is discussed as a parameter that can be useful in studying the dynamics of sunspot groups. This parameter is larger for low tilt angles, and small for extreme tilt angles in either direction. The daily variations of sunspot group tilt angles are discussed. The result that sunspot tilt angles tend to rotate toward the average value is reviewed. It is suggested that at some depth, perhaps 50 Mm, there is a flow relative to the surface that results from a rotation rate faster than the surface rate by about 60 m/sec and a meridional drift that is slower than the surface rate by about 5 m/sec. This results in a slanted relative flow at that depth that is in the direction of the average tilt angle and may be responsible for the tendency for sunspot groups (and plages) to rotate their magnetic axes in the direction of the average tilt angle.     

Axial tilt angles of active regions

Separate Mount Wilson plage and sunspot group data sets are analyzed in this review to illustrate several interesting aspects of active region axial tilt angles. (1) The distribution of tilt angles differs between plages and sunspot groups in the sense that plages have slightly higher tilt angles, on average, than do spot groups. (2) The distributions of average plage total magnetic flux, or sunspot group area, with tilt angle show a consistent effect: those groups with tilt angles nearest the average values are larger (or have a greater total flux) on average than those farther from the average values. Moreover, the average tilt angles on which these size or flux distributions are centered differ for the two types of objects, and represent closely the actual different average tilt angles for these two features. (3) The polarity separation distances of plages and sunspot groups show a clear relationship to average tilt angles. In the case of each feature, smaller polarity separations are correlated with smaller tilt angles. (4) The dynamics of regions also show a clear relationship with region tilt angles. The spot groups with tilt angles nearest the average value (or perhaps 0-deg tilt angle) have on average a faster rotation rate than those groups with extreme tilt angles.All of these tilt-angle characteristics may be assumed to be related to the physical forces that affect the magnetic flux loop that forms the region. These aspects are discussed in this brief review within the context of our current view of the formation of active region magnetic flux at the solar surface.Dedicated to Cornelis de JagerOperated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

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.     

The rotation of active regions with differing magnetic polarity separations

The separation of the leading and following portions of plages and (multi-spot) sunspot groups is examined as a parameter in the analysis of plage and spot group rotation. The magnetic complexity of plages affects their average properties in such a study because it tends to make the polarity separations of the plages less than they really are (by the definition of polarity separation used here). Correcting for this effect, one finds a clear and very significant dependence of the total magnetic flux of a region on its polarity separation. Extrapolating this relationship to zero total flux leads to an X intercept of about 25 Mm in polarity separation. The average residual rotation rates of regions depend upon the polarity separation in the sense that larger separations correspond to slower rotation rates (except for small values of separation, which are affected by region complexity). In the case of sunspots, the result that smaller individual spots rotate faster than larger spots is confirmed and quantified. It is shown also that smaller spot groups rotate faster than larger groups, but this is a much weaker effect than that for individual spots. It is suggested that the principal effect is for spots, and that this individual spot effect is responsible for much or all of the group effect, including that attributed in the past to group age. Although larger spot groups have larger polarity separations, it is shown that the rotation rate-polarity separation effect is the opposite in groups than one finds in plages: groups with larger polarity separations rotate faster than those with smaller separations. This anomalous effect may be related to the evolution of plages and spot groups, or it may be related to connections with subsurface toroidal flux tubes. It is suggested that the polarity separation is a parameter of solar active regions that may shed some light on their origin and evolution.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

MEASUREMENT OF KODAIKANAL WHITE-LIGHT IMAGES – V. Tilt-Angle and Size Variations of Sunspot Groups

We examine here the variations of tilt angle and polarity separation (as defined in this paper) of multi-spot sunspot groups from the Kodaikanal and Mount Wilson data sets covering many decades. We confirm the tilt-angle change vs tilt-angle result found earlier from the Mount Wilson data alone. Sunspot groups tend on average to rotate their axes toward the average tilt angle. We point out that if we separate groups into those with tilt angles greater than and less than the average value, they show tilt-angle variations that vary systematically with the growth or decay rates of the groups. This result emphasizes again the finding that growing (presumably younger) sunspot groups rotate their magnetic axes more rapidly than do decaying (presumably older) groups. The tilt-angle variation as a function of tilt angle differs for those groups whose leading spots have greater area than their following spots and vice versa. Tilt-angle changes and polarity separation changes show a clear relationship, which has the correct direction and magnitude predicted by the Coriolis force, and this strongly suggests that the Coriolis force is largely responsible for the axial tilts observed in sunspot groups. The distribution of polarity separations shows a double peak. These peaks are perhaps related to super- and meso-granulation dimensions. Groups with polarity separations less than 43 Mm expand on average, while those groups with separations more than this value contract on average. We present evidence that the rotation of the magnetic axes of sunspot groups is about a location closer to the following than to the leading sunspots.     

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.     

Measurement of Kodaikanal white-light images – IV. Axial Tilt Angles of Sunspot Groups

The Kodaikanal sunspot data set, covering the interval 1906–1987, is used in conjunction with the similar Mount Wilson sunspot data set, covering the interval 1917–1985, to examine characteristics of sunspot group axial tilt angles. Good agreement is demonstrated between various results derived from the two independent data sets. In particular, the tendency for sunspot groups near the average tilt angle to be larger than those far from the average tilt angle is confirmed. Similarly the faster residual rotation rate for groups near the average tilt angle is also confirmed. Other confirmations are made for the relationships between latitude drift of sunspot groups and tilt angle, polarity separations, and axial expansion. Evidence is presented that tilt angles averaged over these long time intervals differ between the north and south hemispheres by about 1.4 deg. It is suggested that residual tilt angles show a slight systematic variation with phase in the activity cycle.     

How growth and decay of sunspot groups depend on axial tilt angles

Digitized Mount Wilson sunspot data covering the interval from 1917 to 1985 are analyzed to examine the average growth and decay rates of sunspot groups as a function of the tilt angles of the magnetic axes of the groups. It is found that in absolute terms, both growth and decay rates of groups peak at the average tilt angle of the groups (about +5°). In percentage terms these rates are a minimum near these tilt angles because average group areas are largest at the average tilt angle. The clear peaks at the average tilt angle (rather than at 0°) may be related to the structure or geometry of the subsurface flux loops that form the regions. One suggestion to explain this effect is that this is the angle that represents no twist of these subsurface flux loops. This implies, however, that these loops do not get twisted, on average, during their ascent to the surface by Coriolis forces, as has been suggested in the past. The average percentage growth rates for groups with negative tilt angles show high average values and large dispersions for certain tilt angle intervals, suggesting slower growth rates, for some unknown reason, for many small spot groups in certain tilt angle ranges.     

Some factors affecting the growth and decay of plages

The Mount Wilson coarse array magnetograph data set is analyzed to examine the dependence of growth and decay rates on the tilt angles of the magnetic axes of the regions. It is found that there is a relationship between these quantities which is similar to that found earlier for sunspot groups. Regions near the average tilt angle show larger average (absolute) growth and decay rates. Thepercentage growth and decay rates show minima (in absolute values) at the average tilt angles because the average areas of regions are largest near this angle. This result is similar to that derived earlier for sunspot groups. As in the case of spot groups, this suggests that, for decay, the effect results from the fact that the average tilt angle may represent the simplest subsurface configuration of the flux loop or loops that make up the region. In the case of region growth, it was suggested that the more complicated loop configuration should result in increased magnetic tension in the flux loop, and thus in a slower ascent of the loop to the surface, and thus a slower growth rate. In order to examine this further, the growth and decay rates of plage regions were examined as functions of the magnetic complexity of the regions. In the case of decay, the result was as expected from the model suggested above - that is, the more complex regions decayed more slowly. But for growing regions the effect is the opposite to that expected (more complex regions grow faster, even in terms of percentage growth), so the explanation of the tilt angle effect for growing regions proposed earlier may not be valid.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Nature of Tilt Angles of Sunspot Groups During the 22nd Solar Cycle

Daily white-light images from Kodaikanal Observatory have been utilized to study the nature of tilt angles of sunspot groups during the 22nd solar cycle. 2416 spot groups have been measured to find the tilt angle. An average tilt angle of +4.6 ± 0.4 deg has been obtained for all these spot groups, where the positive sign indicates that the leading part of the group is closer to the equator. It is found that the number of poleward and equatorward spot groups showed an opposite trend as the cycle advanced. The spot groups with positive (equatorward) tilt angles declined in number whereas the spot groups with negative (poleward) tilt angles increased towards the end of the cycle. It is also noticed that the number of spot groups, which changed the sign of tilt angle during their lifetime or passage across the disc, increased during the maximum activity period of the cycle. These findings were confirmed from the analysis of data from the 21st cycle. These results are discussed in this paper along with the daily variation of tilt angles of some of the spot groups from the selected data.     

The magnetic fields of active regions

The Mount Wilson coarse array data set is used to define active regions in the interval 1967 to August, 1988. From the positions of these active regions on consecutive days, rotation rates are derived. The differential rotation of the active regions is calculated and compared with previous magnetic field and plage rates. The agreement is good except for the variation with time. The active region rates are slower by a few percent than the magnetic field or facular rates. The differential rotation rate of active regions with reversed magnetic polarity orientations is calculated. These regions show little or no evidence for differential rotation, although uncertainties in this determination are large. A correlation is found between rotation rate and region size in the sense that larger regions rotate more slowly. A correlation between rotation rate and cycle phase is suggested which is in agreement with earlier sunspot results. Leading and following portions of active regions, unlike leading and following spots, show little or no difference in their rotation rates. The regions with polarity orientations nearest the normal configuration tend to show rotation rates that are nearest the average values. Most of these results generally support the conclusion that old, weaker magnetic fields have evolved different subsurface connections from the time they were a part of sunspots or plages. It seems possible that they are connected at a shallower layer than are sunspot or plage fields.Operated by the Association of Universities for Research in Astronomy, Inc., under Contract with the National Science Foundation.     

Differential Rotation of Stable Recurrent Sunspot Groups

Stable recurrent sunspot groups from the Greenwich data set which were identified in at least two subsequent solar rotations were traced. The solar rotation was determined by the period method from the time difference of the two central meridian passages of each of the 327 identified groups. Sidereal rotation periods were calculated from the synodic ones by a seasonal-dependent procedure taking into account the details of the Earth's motion around the Sun. Growing recurrent sunspot groups rotate on the average faster than decaying recurrent sunspot groups, while sunspot groups of all types taken together rotate faster than both growing and decaying recurrent sunspot groups. A north–south rotational asymmetry and a cycle-dependence of rotational velocity of recurrent sunspot groups were analyzed. Positive rotation velocity deviations are larger, but less numerous than the negative ones. Signatures of torsional oscillations were not found analyzing the rotation velocity residual of recurrent sunspot groups as a function of the distance from the average latitude of activity.     

Measurement of Kodaikanal white-light images – VI. Variation of Rotation Rate with Age of Sunspot Groups

We find from an analysis of the Kodaikanal sunspot group data that the rotation rates of spot groups increase with their age when the rotation rates are computed after sorting the spot groups life-span-wise. We confirm these findings from an analysis of the Mt. Wilson sunspot data set too. We show that this trend is in good agreement with the internal rotation profiles from helioseismology (GONG) observations and is also consistent with the concept that the footpoints of the magnetic loops of spot groups are initially anchored in the deeper layers in the solar interior and rise to shallower layers as the spots age, and that the spots reflect the rotation rates at the respective depths at which their footpoints are temporally located. We project the `first-day rotation rates' and the `daily rotation rates' of spot groups on the rotation profiles from the GONG observations and derive the initial anchoring depths of the footpoints of the magnetic loops of the spot groups and their rates of rise as the spot groups age. Our results of the rotation rates are in antithesis to the results reported by investigators from the Greenwich spot group data that show a deceleration in rotation rates as the spot groups age which are also inconsistent with the rotation profiles from helioseismology observations.     

Asymmetric flux loops in active regions,I

We investigate asymmetries of bipolar sunspot groups. We find that the magnetic field distribution of simple bipolar sunspot groups is significantly asymmetrical: the polarity inversion line is usually nearer to the main following polarity spot than to the main preceding one. This asymmetry grows with the age of the sunspot group. We suggest that this asymmetry has a causal link with two long-established asymmetries- the one in the proper motions of young sunspots, the other in the relative stability of p and f spots.In our view, these asymmetries together indicate that emerging flux loops, making sunspot groups, are not symmetrical but tilted eastward. The tilt is presumably caused by drag forces due to radial differential rotation in subphotospheric layers. In this paper we present observational indications supporting this hypothesis.     

The east-west inclination of magnetic field lines in sunspots

Digitized Mount Wilson sunspot data covering the interval from 1917 to 1985 are analyzed to examine the average areas of individual sunspot umbrae over small zones of central meridian distance. Assuming that systematic, east-west differences in these quantities are due to the inclination of the magnetic fields of the spots, one can calculate average east-west inclination angles for all spots and for subsets of the full data set. It is found from such an analysis that on average spot fields are inclined such as to trail the rotation by a few deg. Leading and following spots may show a tendency to be inclined slightly away from each other, in contrast to the results of an earlier study of plage magnetic fields. Growing spots tend to be inclined much more to the east than decaying spots. This is in the opposite sense to the analogous result derived from plage magnetic fields.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Dynamo saturation in rapidly rotating solar-type stars

The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt angle proportional to the rotation rate are constructed to probe this idea.Two versions of the model- treating the tilt angles globally and using Joy's law for its latitude dependence- are considered. Both models show a saturation of dynamogenerated magnetic flux at high rotation rates. The model with latitude-dependent tilt angles also shows a change in dynamo regime in the saturation region. The new regime combines a cyclic dynamo at low latitudes with an(almost) steady polar dynamo.     

The rotation of calcium plages in the years 1967–1970

An analysis of Ca II spectroheliograms obtained at Catania Observatory in the period 1967–1970 shows that plages rotate - in their first four days of lifetime - with a latitudinal differential rotation profile steeper than for older objects.A closer inspection reveals that plages slow down with age in some latitude strips, and accelerate in some others. That makes the profiles of old and young objects highly different from each other. In particular, the empirical laws of solar rotation usually adopted, appear to be inadequate to describe so complex a phenomenon as the rotation of these magnetic features. A close correspondence has been found between the latitudes at which plages accelerate (slow down) and the latitudes of westward (eastward) streams (Howard and LaBonte, 1980).Some implications of these results, in the light of the theory of a direct coupling of magnetic features to deep layers, are discussed.In the years concerned, Ca-plages of whatever age show differential rotation profiles steeper than in other phases of the solar cycle.     

Common Characteristics of the Active Regions of Strong Proton Flares

Common characteristics of nine active regions with strong proton flares in the 22nd solar activity cycle have been presented. Results show that the typical morphology of these active regions is a -type sunspot with a single multiple structure, in which there are many umbras with different magnetic polarities, packed tightly by a single penumbra. In these active regions, the rotating directions of the sunspot groups are nearly independent of their position on the solar disk. When the angle of rotation approaches the positive or the negative maximum, proton flares may occur in these active regions. After proton flares, sunspot groups rotate in the inverse direction because of the slack in the flux rope.     

Effects of dipole tilt angle on geomagnetic activity

The relationship between the orientation of the interplanetary magnetic field (IMF), represented by the clock angle which is the angle defined by IMF-B_y and -B_z components, and the AL and AU indices is examined at various dipole tilt angles for the period of 1978-1988. We use the IMF data obtained from the IMP 8 satellite, AL and AU indices with corrected seasonal variations, and the dipole tilt angle, which is the dipole magnetic latitude of the subsolar point calculated as a function of the day of year and universal time. For both positive (dipole tilted to the Sun) and negative dipole tilt angles, the values of |AL| and AU decrease as the IMF clock angle moves away from 180^°, becoming more northward. The indices also tend to become smaller for larger dipole tilt angle, either toward or away from the Sun. This dependence on dipole tilt angle enhances the semiannual variation of geomagnetic activity.     

The magnetic fields of active regions

Magnetogram data are analyzed to study east-west magnetic flux differences interpreted as the component of magnetic field line inclination at the photospheric level in a plane parallel to the solar equator. This component is determined by comparing average east-west pairs of flux values at equal distances from the central meridian. The average inclination of a whole region is such as to trail the rotation (incline toward the east) by about 1.9 deg. Leading and following polarities tilt toward each other by about 16 deg. Growing regions are strongly inclined to the west (to lead the rotation) with large differences between leading and following portions. Decaying regions are slightly inclined to the east with more normal differences between leading and following portions. These results concerning growing and decaying regions are seen with greater amplitude for reversed polarity regions. As the activity cycle progresses, the average inclination of the field lines of the following portions of regions varies from about 10 to about 3 deg (leading the rotation), and the average difference in inclination of the leading and following portions of regions decreases monotonically during the cycle from nearly 20 to about 11 deg. A slight difference is seen between the average east-west inclination angles of regions that are rotating faster than average and those that are rotating slower than average in the sense that slower regions are slightly inclined toward the east and faster regions toward the west. Some of these results may be related to the location or nature of the subsurface flux tubes to which the active regions fields are connected and also, perhaps, to the nature of this connection.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.