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.     

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 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.     

Tilt-angle variations of active regions

An examination of the tilt angles of multi-spot sunspot groups and plages shows that on average they tend to rotate toward the average tilt angle in each hemisphere. This average tilt angle is about twice as large for plages as it is for sunspot groups. The larger the deviation from the average tilt angle, the larger, on average, is the rotation of the magnetic axis in the direction of the average tilt angle. The rate of rotation of the magnetic axis is about twice as fast for sunspot groups as it is for plages. Growing plages and spot groups rotate their axes significantly faster than do decaying plages and spot groups. There is a latitude dependence of this effect that follows Joy's law. The fact that these tilt angles move toward the average tilt angle and not toward 0 deg (the east-west orientation), combined with other results presented here, suggest that a commonly accepted view of the origin of active region magnetic flux at the solar surface may have to be re-examined.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

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.     

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.     

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.     

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.     

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 Evolution of the Sun's Open Magnetic Flux – I. A Single Bipole

In this paper the origin and evolution of the Sun's open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis () and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that ge2° the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range –16°<<2° the open flux follows the surface flux and continually decays. Finally, for le–16° the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun's open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses.     

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 concentration of the large-scale solar magnetic field by a meridional surface flow

We calculate analytical and numerical solutions to the magnetic flux transport equation in the absence of new bipolar sources of flux, for several meridional flow profiles and a range of peak flow speeds. We find that a poleward flow with a broad profile and a nominal 10 m s^–1 maximum speed concentrates the large-scale field into very small caps of less than 15° half-angle, with average field strengths of several tens of gauss, contrary to observations. A flow which reaches its peak speed at a relatively low latitude and then decreases rapidly to zero at higher latitudes leads to a large-scale field pattern which is consistent with observations. For such a flow, only lower latitude sunspot groups can contribute to interhemispheric flux annihilation and the resulting decay and reversal of the polar magnetic fields.     

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.     

Results from Kodaikanal synoptic observations

The synoptic observations of Kodaikanal form one of the longest unbroken solar data from the beginning of the 20th century to the present day, and consists of the white light and monochromatic images of the sun. In this review, I shall discuss the results of the investigations in two areas using these data: (i) Tilt angles of the magnetic axes of bipolar spot groups, and (ii) structure and dynamics of large scale unipolar magnetic regions on the solar surface. The observed properties and patterns of behaviour of the tilt angles can be used as effective diagnostics to infer the physical conditions in the subsurface layers of the sun, and thus get an insight into the physical effects that act on the rising magnetic flux tubes during their journey through the convection zone to the surface. The second topic of discussion here, namely, the studies of the dynamics of unipolar regions over several solar cycles, show that the global solar activity has a high latitude component which manifests in the form of polar faculae, in addition to the well known sunspot activity at the middle and low latitudes. This raises the question about the origin of this high latitude component.     

Regularities in the growth of background magnetic fields

The cyclicity in the latitudinal distribution of the growth and decay rates of the total magnetic fluxes for weak magnetic fields is investigated. The synoptic maps of the line-of-sight solar magnetic field strength obtained at the Kitt Peak Observatory (USA) from January 1, 1977, to September 30, 2003, are used as the observational material. The latitudinal distributions of the growth rates of total magnetic fluxes with various strengths constructed from them and their evolution during three solar cycles have been compared with the analogous distribution of the total powers of rotation with various periods as well as the relative sunspot numbers and areas. The results obtained allow a unified picture of the development of solar cycles for weak and strong magnetic fields to be formulated. A new cycle begins with the growth of weak magnetic fields with a strength of 0–200 G at latitudes 20°–25° in both hemispheres. This occurs one year before the activity minimum determined from sunspots. Two years later, the growth rate of the total magnetic flux, which begins to propagate equatorward and poleward, reaches a maximum. This process coincides with the onset of the growth of strong sunspot magnetic fields at the corresponding latitudes and the formation of zones with a stable rotation. Subsequently, a fall-off in growth rate and then a flux decay for weak magnetic fields correspond to the growth of the sunspot areas. In light of the dynamo theory, the results obtained suggest that strong and weak magnetic fields are generated near the bottom of the convection zone, while the observed differences in their behavior are determined by the interaction of emerging magnetic flux tubes of various strengths with turbulent plasma motions inside the Sun.     

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.     

Anchor depths of flux elements and depths of flux sources in relation to the two rotation profiles of the sun's surface magnetic fields

It is known for over two decades now that the rotation of the photospheric magnetic fields determined by two different methods of correlation analysis leads to two vastly differing rotation laws - one the differential and the other rigid rotation. Snodgrass and Smith (2001) reexamining this puzzle show that the averaging of the correlation amplitudes can tilt the final profile in favour of rigid rotation whenever the contribution of the rigidly rotating large-scale magnetic structures (the plumes) to the correlation dominates over that of the differentially rotating small-scale and mesoscale features. We present arguments to show that the large-scale unipolar structures in latitudes >40 deg, which also show rigid rotation (Stenflo, 1989), are formed mainly from the intranetwork magnetic elements (abbreviated as IN elements). We then estimate the anchor depths of the various surface magnetic elements as locations of the Sun's internal plasma layers that rotate at the same rate as the flux elements, using the rotation rates of the internal plasma layers given by helioseismology. We infer that the anchor depths of the flux broken off from the decay of sunspot active regions (the small-scale and mesoscale features that constitute the plumes) are located in the shallow layers close to the solar surface. From a similar comparison with helioseismic rotation rates we infer that the rigid rotation of the large-scale unipolar regions in high latitudes could only be coming from plasma layers at a radial distance of about 0.66–0.68 R _⊙ from the Sun's centre. Using Stenflo's (1991) ‘balloon man’ analogy, we interpret these layers as the source of the magnetic flux of the IN elements. If so, the IN flux elements seem to constitute a fundamental component of solar magnetism.     

Hard X-rays from solar flares — time characteristics in correlation with energy and angular distributions of electrons

Fine time variation of hard X-rays has been explained in terms of a spread in the angle of incidence of the source electrons in non-thermal thick-target model for bremsstrahlung generation. The electron energy and angular distributions have been calculated by combining small angle scatterings using analytical treatment with a large angle collision using Monte Carlo calculations as a function of column density. The incidence angles of electrons are taken as 0, 30, and 60°. Using the Bethe-Heitler cross section and the above calculated electron distributions, the bremsstrahlung flux for different photon energies as a function of column density has been studied. The computed X-ray pulse as a function of column density has been converted into time profile. It corresponds well with the observed fine time structure. The calculated spectra of X-rays at the peak and valley are also consistent with the observations. The variation of photon flux with time has also been computed for photon energies 20, 50, and 100 keV for 90 and 180° observation angles together with the changes in spectral shapes of photon energy spectrum at different times for 90 and 180° observation angles.     

The growth and decay of sunspots: Comparison between the Greenwich and Mount Wilson sunspot data

The complete sample of theGreenwich Photoheliographic Results (GPR) for the years 1874–1976 was used for the investigation of the growth and decay of sunspot groups. The results were compared with similar findings from the Mt. Wilson sunspot data for the years 1917–1985, which were recently published by R. F. Howard. The results of the absolute umbral area changes are about the same for both sets of data. The main difference between the sets of data occurs for the percentage increase of the umbral areas as a function of latitude. The mean values from the Mt. Wilson data are bigger by a factor of 5 to 7 and show a dependence on the latitude, while the increase of the Greenwich data does not depend on the latitude. The decrease of sunspot areas as a function of latitude is only available from the Greenwich data. There occur higher values for the decrease for higher latitudes from 2.5 up to 42.5 deg     

The Evolution of Trailing Plumes from Active Regions

We have studied the evolution of several high-latitude flux `plumes', i.e., unipolar regions, trailing from active regions which emerged near sunspot maximum in cycle 23. The observed patterns are compared with simulations using a simple flux transport equation based on the observed flux for an earlier Carrington rotation. In addition to the long recognized poleward migration and diffusion of flux from active regions, it is found that the evolution of the trailing plumes may be influenced by flux which emerges above latitude 35° over areas of all scales. We describe two cases in which the emerging flux appears in the form of bipolar flux patterns which are not obviously related to sunspots. Further, we find instances in which the observed surface flux decreases or spreads at rates which cannot be explained solely in terms of diffusion using the normally accepted rates. Thus in several cases the poleward migration of flux cannot be described in terms of passive transport by advection and diffusion as considered here, and further investigation of the processes that contribute to the evolution of the polar fields is required.