The Influence of the Evolution of Sunspot Groups on the Determination of the Solar Velocity Field

Meridional motions and differential rotation of stable recurrent sunspot groups from the Greenwich data set are investigated. Simple and complex, as well as younger and older sunspot groups are treated separately. There is no difference in behavior of the meridional motions for the simple and complex sunspot groups, while complex groups rotate faster than the simple ones. If we attribute the differences of rotational velocities to the errors in position determination, it can be concluded that the rotational velocities determined by using sunspot groups as tracers are slightly overestimated. Both the meridional motions and differential rotation show the same dependence on the age, when simple and complex recurrent sunspot groups are considered. Alexander von Humboldt Research Fellow.     

The causality between the rapid rotation of a sunspot and an X3.4 flare

Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in ac-tive region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neu-tral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field linestwisting in the photosphere. The twist is then transported into the corona and triggers flares.     

Solar rotation measurements at Mount Wilson

Possible sources of systematic error in solar Doppler rotational velocities are examined. Scattered light is shown to affect the Mount Wilson solar rotation results, but this effect is not enough to bring the spectroscopic results in coincidence with the sunspot rotation. Interference fringes at the spectrograph focus at Mount Wilson have in two intervals affected the rotation results. It has been possible to correlate this error with temperature and thus correct for it. A misalignment between the entrance and exit slits is a possible source of error, but for the Mount Wilson slit configuration the amplitude of this effect is negligibly small. Rapid scanning of the solar image also produces no measurable effect.     

Meridional Motions and Reynolds Stress Determined by Using Kanzelhöhe Drawings and White Light Solar Images from 1964 to 2016

Sunspot position data obtained from Kanzelhöhe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images in the period 1964 to 2016 were used to calculate the rotational and meridional velocities of the solar plasma. Velocities were calculated from daily shifts of sunspot groups and an iterative process of calculation of the differential rotation profiles was used to discard outliers. We found a differential rotation profile and meridional motions in agreement with previous studies using sunspots as tracers and conclude that the quality of the KSO data is appropriate for analysis of solar velocity patterns. By analyzing the correlation and covariance of meridional velocities and rotation rate residuals we found that the angular momentum is transported towards the solar equator. The magnitude and latitudinal dependence of the horizontal component of the Reynolds stress tensor calculated is sufficient to maintain the observed solar differential rotation profile. Therefore, our results confirm that the Reynolds stress is the dominant mechanism responsible for transport of angular momentum towards the solar equator.     

Two Populations of Sunspots: Differential Rotation

To investigate the differential rotation of sunspot groups using the Greenwich data, we propose an approach based on a statistical analysis of the histograms of particular longitudinal velocities in different latitude intervals. The general statistical velocity distributions for all such intervals are shown to be described by two rather than one normal distribution, so that two fundamental rotation modes exist simultaneously: fast and slow. The differentiality of rotation for the modes is the same: the coefficient at sin² in Faye’s law is 2.87–2.88 deg/day, while the equatorial rotation rates differ significantly, 0.27 deg/day. On the other hand, an analysis of the longitudinal velocities for the previously revealed two differing populations of sunspot groups has shown that small short-lived groups (SSGs) are associated with the fast rotation mode, while large long-lived groups (LLGs) are associated with both fast and slow modes. The results obtained not only suggest a real physical difference between the two populations of sunspots but also give new empirical data for the development of a dynamo theory, in particular, for the theory of a spatially distributed dynamo.     

Active longitudes of the sun: The rotation period and statistical significance

Using data from the Greenwich catalog, we determined the nonuniformity of the longitudinal distribution of sunspot groups as a function of the rotation period taken for the longitude determination. We estimated the statistical significance of the active longitudes found. A fairly high significance was achieved only for sunspot groups of the Northern Hemisphere and odd activity cycles and only for a synodic rotation period close to 28 days. In this case, one interval of active longitudes was found. The active longitudes are assumed to be associated with the fossil magnetic field frozen in the uniformly rotating radiative zone of the Sun.     

On the existence of prevalent westward shifts in the solar atmosphere

A statistical analysis of the deviations of the sideral angular rotation velocities () of single sunspot groups from the averaged rotation curve , shows that positive deviations tend to be greater than negative ones: we can therefore deduce the existence of prevalent westward shifts in the solar atmosphere. This effect is only partially due to the sunspot group proper motions at the beginning of their evolution, and it could indicate the prevalence of westward currents in the solar photosphere.     

The rotation of sunspots in the solar active region NOAA 10930

The rotation of sunspots in the solar active region NOAA 10930 was investigated on the basis of the data on the longitudinal magnetic field and the Doppler velocities using magnetograms and dopplergrams taken with the Solar Optical Telescope installed aboard the HINODE mission. Under the assumption of axial symmetry, areally-mean vertical, radial, and azimuthal components of the magnetic field and velocity vectors were calculated in both sunspots. The plasma in the sunspots rotated in opposite directions: in the leading sunspot, clockwise, and in the following sunspot, counterclockwise. The magnetic flux tubes that formed sunspots of the active region on the solar surface were twisted in one direction, clockwise. Electric currents generated as a result of the rotation and twisting of magnetic flux tubes were also flowing in one direction. Azimuthal components of magnetic and velocity fields of both sunspot umbrae reached their maximum on December 11, 2006. By the start of the X3.4 flare (December 13, 2006), their values became practically equal to zero.     

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.     

Measurement of Kodaikanal White-Light Images – III. Rotation Rates and Activity Cycle Variations

The Kodaikanal sunspot data set covering the interval 1906–1987 is analyzed for differential rotation of sunspots of different sizes. As is known, smaller sunspots rotate faster than larger sunspots, and this result is verified in the analysis of this data set. These results agree well with the Mount Wilson sunspot results published earlier. The activity cycle dependence of sunspot rotation is studied. An increase in this rate at the minimum phase is seen, which has been reported earlier. It is demonstrated that this cycle variation is seen for sunspots in all size categories, which suggests that it is not a relative increase in the number of the faster-rotating small sunspots that causes the cycle dependence. These results are discussed as they may relate to subsurface dynamic properties of the Sun.     

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.     

Large-Scale Structure of the Sunspot Activity and the Background Magnetic Field Formation

Large-scale distribution of the sunspot activity of the Sun has been analyzed by using a technique worked out previously (Erofeev, 1997) to study long-lived, non-axisymmetric magnetic structures with different periods of rotation. Results of the analysis have been compared with those obtained by analyzing both the solar large-scale magnetic field and large-scale magnetic field simulated by means of the well-known flux transport equation using the sunspot groups as a sole source of new magnetic flux in the photosphere. A 21-year period (1964–1985) has been examined.The rotation spectra calculated for the total time interval of two 11-year cycles indicate that sunspot activity consists of a series of discrete components (modes) with different periods of rotation. The largest-scale component of the sunspot activity reveals modes with 27-day and 28-day periods of rotation situated, correspondingly, in the northern and southern hemispheres of the Sun, and two modes with rotation periods of about 29.7 days situated in both hemispheres. Such a modal structure of the sunspot activity agrees well with that of the large-scale solar magnetic field. Moreover, the magnetic field distribution simulated with the flux transport equation also reveals the same modal structure. However, such an agreement between the large-scale solar magnetic field and both the sunspot activity and simulated magnetic field is unstable in time; so, it is absent in the northern hemisphere of the Sun during solar cycle No. 20. Thus the sources of magnetic flux responsible for formation of the large-scale, rigidly rotating magnetic patterns appear to be closely connected, but are not identical with the discrete modes of the sunspot activity.     

MHD simulations of sunspot rotation and the coronal consequences

A simplified magnetic configuration is used to model some aspects of observations of a rotating sunspot and its overlying coronal loops. In the observations a large sunspot rotates over a few days and two smaller pores spiral into it. The coronal loops become sigmoidal in shape and flares are seen in Yohkoh/SXT and GOES. We have modeled the sunspot, one of the pores and the loops connecting these to a diffuse region of plasma of the opposite polarity. Two sets of MHD simulations are considered: (i) rotation of the sunspot and pore alone and (ii) rotation of the sunspot with inflow of the pore. Rotation alone can trigger the ideal kink instability in the loops but only for a rotation that is much greater than the observed value. There is no build-up of current which is needed for magnetic reconnection to occur. However, when inflow is included a strong build-up of current is seen as the pore merges with the sunspot. Comparing these results from the simulations with the observations, we find that the observed merging of the pores coincides with the timing of the flare. Therefore, we suggest that the merging of the pores with the large sunspot may be responsible for the flaring.     

Solar differential rotation derived from sunspot observations

Sunspot drawings obtained at National Astronomical Observatory of Japan during the years 1954–1986 were used to determine the differential rotation of the Sun. From the limited data set of three solar cycles it was found that three factors (the level of cycle activity, the cycle phase, and sunspot type) affect the solar rotation rate. The differential rotation varies from cycle to cycle in such a way that the rotation velocity in the low activity cycle (cycle 20) is higher than in the high-activity cycle (cycle 19). The equatorial rotation rate shows a systematic variation within each cycle. The rate is higher at the beginning of the cycle and decreases subsequently. Although quite small, the variation of solar differential rotation with respect to Zürich sunspot type was found. The H and J types show the slowest rotation among all the sunspot types.     

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.     

A Standard Law for the Equatorward Drift of the Sunspot Zones

The latitudinal location of the sunspot zones in each hemisphere is determined by calculating the centroid position of sunspot areas for each solar rotation from May 1874 to June 2011. When these centroid positions are plotted and analyzed as functions of time from each sunspot cycle maximum, there appear to be systematic differences in the positions and equatorward drift rates as a function of sunspot cycle amplitude. If, instead, these centroid positions are plotted and analyzed as functions of time from each sunspot cycle minimum, then most of the differences in the positions and equatorward drift rates disappear. The differences that remain disappear entirely if curve fitting is used to determine the starting times (which vary by as much as eight months from the times of minima). The sunspot zone latitudes and equatorward drift measured relative to this starting time follow a standard path for all cycles with no dependence upon cycle strength or hemispheric dominance. Although Cycle 23 was peculiar in its length and the strength of the polar fields it produced, it too shows no significant variation from this standard. This standard law, and the lack of variation with sunspot cycle characteristics, is consistent with dynamo wave mechanisms but not consistent with current flux transport dynamo models for the equatorward drift of the sunspot zones.     

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.     

Long term evolution of solar sector structure

The large-scale structure of the solar magnetic field during the past five sunspot cycles (representing by implication a much longer interval of time) has been investigated using the polarity (toward or away from the Sun) of the interplanetary magnetic field as inferred from polar geomagnetic observations. The polarity of the interplanetary magnetic field has previously been shown to be closely related to the polarity (into or out of the Sun) of the large-scale solar magnetic field. It appears that a solar structure with four sectors per rotation persisted through the past five sunspot cycles with a synodic rotation period near 27.0 days, and a small relative westward drift during the first half of each sunspot cycle and a relative eastward drift during the second half of each cycle. Superposed on this four-sector structure there is another structure with inward field polarity, a width in solar longitude of about 100° and a synodic rotation period of about 28 to 29 days. This 28.5 day structure is usually most prominent during a few years near sunspot maximum. Some preliminary comparisons of these observed solar structures with theoretical considerations are given.     

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.     

Rotation of Plasma in Sunspots

In this paper we present the results of a sunspot rotation study using Abastumani Astrophysical Observatory photoheliogram data for 324 sunspots. The rotation amplitudes vary in theinebreak 2–64° range (with maximum at 12–14°), and the periods around 0–20 days (with maximum atinebreak 4–6 days). It could be concluded that sunspot rotations are rather inhomogeneous and asymmetric, but several types of sunspots are distinguished by their rotational parameters.During solar activity maximum, sunspot average rotation periods and amplitudes slightly increase. This can be affected by the increase of sunspot magnetic flux tube depth. So we can suppose that sunspot formation during solar activity is connected to a rise of magnetic tubes from deeper layers of the solar photosphere, strengthening the processes within the tube and causing variations in rotation.There is a linear relation between tilt-angle oscillation periods and amplitudes, showing higher amplitudes for large periods. The variations of those periods and especially amplitudes have a periodical shape for all types of sunspots and correlate well with the solar activity maxima with a phase delay of about 1–2 years.