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.     

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 _⊙.     

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.     

Differential rotation in the solar atmosphere inferred from optical,radio, and interplanetary data

Autocorrelation analysis of sunspot number, solar radio flux, and interplanetary field in the period 1967 to 1970 yields new information concerning solar atmospheric rotation. The upper chromosphere and the lower corona are rotating on the average about 5 to 8 % faster than is either the photosphere or the upper corona. In addition, short-lived features in the chromosphere and lower corona are found to rotate sometimes as much as 10% faster than relatively long-lived features at the same height. Coronal and photospheric features are found to rotate more or less synchronously. Analysis of yearly data has indicated a considerable change in rotation periods from one year to another.     

Differential rotation of solar filaments

The latitudinal component of solar differential rotation and the possibility of a radial component are discussed and compared to the observed rotational velocities of solar filaments. Our values of rotational rate versus heliographic latitude for 100 points in the solar atmosphere derived from 17 quiescent filaments are comparable to the rates found by d'Azambuja and d'Azambuja (1948). The filament rate is significantly greater than the spot rate (Newton and Nunn, 1951); the difference cannot be accounted for by the poleward migration of filaments and seems to reflect a true radial gradient of rotational velocity in the Sun. We show that filaments in closer proximity to active regions usually exhibit no differential rotation, while those far from active regions generally show it clearly. Comparison with Mt. Wilson photospheric Doppler measurements shows that filaments rotate faster than the general photosphere and that, as is well known, the spot rate exceeds that for the general photosphere.     

Meridional Motions 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 and meridional motions were determined from the two central meridian passages. In total, 327 meridional velocities were calculated and the results for the northern and the southern solar hemisphere were compared. A dependence of the solar meridional velocity vectors on the development status, latitude and position respectively to the activity belt of sunspots is investigated. The results indicate that sunspot groups are moving on the average away from the center of activity. This was found for sunspot groups growing and decreasing in area.     

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.     

Rotational Modulation of Microwave Solar Flux

Time series data of 10.7 cm solar flux for one solar cycle (1985–1995 years) was processed through autocorrelation. Rotation modulation with varying persistence and period was quite evident. The persistence of modulation seems to have no relation with sunspot numbers. The persistence of modulation is more noticeable during 1985–1986, 1989–1990, and 1990–1991. In other years the modulation is seen, but its persistence is less. The sidereal rotation period varies from 24.07 days to 26.44 days with no systematic relation with sunspot numbers. The results indicate that the solar corona rotates slightly faster than photospheric features. The solar flux was split into two parts, i.e., background emission which remains unaffected by solar rotation and the localized emission which produces the observed rotational modulation. Both these parts show a direct relation with the sunspot numbers. The magnitude of localized emission almost diminishes during the period of low sunspot number, whereas background emission remains at a 33% level even when almost no sunspots may be present. The localized regions appear to shift on the solar surface in heliolongitudes.     

Rotation cycles of the sector structure of the solar magnetic field and its activity

We study the rotation of the sector structure of the solar magnetic field by using Stanford magnetographic observations from 1975 until 2000 and magnetic synoptic Hα-maps obtained from 1904 until 2000. The two independent series of observations yielded the same rotation periods of the two-sector (26.86 days) and four-sector (13.64 days) structures. We introduce a new index of the solar rotation, SSPM(t). The spectral power density of the sector structure of the magnetic field is shown to exhibit a 22-year cyclicity. The two-and four-sector structures of the magnetic field rotate faster at the maxima of even 11-year sunspot cycles. This phenomenon may be called the Gnevyshev-Ohl rule for the solar rotation. The 11-year sector-structure activity cycles are shown to lead the 11-year sunspot cycles (Wolf numbers) by 5.5 years. A 55-year component with the slowest rotation in the 18th cycle (1945–1955) was distinguished in the sector-structure rotation.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Temporal Variations of the Solar Rotation Determined by Sunspot Groups

The extended Greenwich data set consisting of positions of sunspot groups is used for the investigation of cycle-related variations of the solar rotation in the years 1874–1981. Applying the residual method, which yields a single number for each year describing the average deviation from the mean value of the solar rotation, the dependence of the rotation velocity residual on the phase of the solar cycle is investigated. A secular deceleration of the solar rotation was found: the slope being statistically significant at the 3σ level. Periods of 33, 22, 11, 5.2, and 3.5 years can be identified in the power spectra. The rotation velocity residuals were averaged for all years with the same solar cycle phase relative to the nearest preceding sunspot minimum. The variation pattern reveals a higher than average rotation velocity in the minimum of activity and, to a lesser extent, also around the maximum of activity. The analysis was repeated with several changes in the reduction method, such as elimination of the secular trend, application of statistical weights, different cutoffs of the central meridian distance, division of the latitude into subregions and treating data from the years of activity minima separately. The results obtained are compared with those from the literature, and an interpretation of the observed phenomena is proposed.     

Evidence for Long-term Retrograde Motions of Sunspot Patterns and Indications of Coupled g-mode Rotation Rates

Solar g-modes are global oscillations that would exist primarily in the radiative zone (RZ) and would be excited by either convective overshoot or nuclear burning in the core. Wolff and O’Donovan (Astrophys. J. 661, 568, 2007) proposed a non-linear coupling of g-modes into groups that share the same harmonic degree ℓ. Each group (denoted set(ℓ)) exhibits a unique retrograde rotation rate with respect to the RZ that depends mainly on ℓ. The coupling yields a standing wave (nearly stationary in longitude) that has two angularly defined hot spots offset from the equator on opposite sides of the Sun that would deposit energy asymmetrically in the lower convective envelope (CE). It is anticipated that when two or more groups overlap in longitude, an increase in local heating would influence the distribution of sunspots. In this paper, we scanned a multitude of rotational reference frames for sunspot clustering to test for frames that are concordant with the rotation of these g-modes sets. To achieve this, spherical harmonic filtering of sunspot synoptic maps was used to extract patterns consistent with coalesced g-modes. The latitude band, with minimal differential rotation, was sampled from each filtered synoptic map and layered into a stackplot. This was progressively shifted, line-by-line, into different rotational reference frames. We have detected long-lived longitudinal alignments, spanning 90 years of solar cycles, which are consistent with the rotation rate of the deep solar interior as well as other rotational frames predicted by the coupled g-mode model. Their sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2 and 430.0 nHz correspond, respectively, to coupled g-modes for ℓ = 2 through 7 and G, where G is a set with high ℓ values or a group of such sets (unresolved) that rotate almost as fast as the RZ. While the clustering in these reference frames offers new approaches for studying the longitudinal behavior of solar activity, it tentatively leads to the more profound conclusion that a portion of the driving force for sunspot occurrence is linked to energy extracted from the solar core and deposited at the top of the RZ by solar g-modes.     

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.     

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.     

Velocity Characteristics of Rotating Sunspots

A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J. 646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h⁻¹. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.     

Properties of space and time distribution of solar coronal holes

The space and time distribution properties of solar coronal holes (CH) are investigated. The data of the catalogue UAG-102, supplemented up to 1995, and synoptic H-charts of Solar Geophysical Data are used. It was found that both the polar and equatorial CH can be divided into two subclasses. The properties of time classes are discerned. Statistical weights of the recurrent CH are accounted, which allow to determine the character of rotation of the different classes of CH with more accuracy. It was shown that the equatorial CH with long lifetimes possess differential rotation that is similar to sunspot groups, and the long-living polar CH rotate as a rigid body. A conclusion about the existence of two types of large-scale solar magnetic fields is made.     

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.     

On the determination of heliographic positions and rotation velocities of sunspots

In an earlier paper of this series it was shown how the Wilson depression influences the determination of sunspot rotation velocities. Using this finding and the fact that stable recurrent sunspots show a very constant rotation velocity it is possible to determine the effect of wrong solar image radii on the determination of sunspot rotation velocities and correct them.Mitteilungen aus dem Kiepenheuer-Institut Nr. 238.     

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.     

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.