On time variations of the solar differential rotation law and asymmetry of the global distribution of the solar activity

The relation between the systematic time variations of the solar differential rotation at middle latitudes and the asymmetry of global distribution of the solar activity is discussed in connection with the study of the maintenance of the solar differential rotation. The systematic variations at middle latitudes are inferred from a peculiar correlation in the time variations of the solar differential rotation which is shown in this paper to be implied in the data of Howard and Harvey (1970) of spectroscopic measurements of rotational velocities. If we adopt the working hypothesis of the solar equatorial acceleration maintained by the angular momentum transport due to the very large scale convection, the two phenomena are related through the concurrent presence of the neighboring modes with the presumed dominant mode of the very large scale convection.     

N–S asymmetry in the differential rotation of the sun and its variation with the solar activity cycles

Peculiarities in the characteristics of the solar differential rotation are investigated using hydrogen filaments as tracers. The existence of North–South (N–S) asymmetry in hydrogen filaments rotation is confirmed statistically. The connection of asymmetry with the solar activity cycles is established. It is found that the northern hemisphere rotates faster during the even cycles (Cycles 20 and 22) while the rotation of southern hemisphere dominates in odd one (Cycle 21). The mechanism of the solar activity should be responsible for the N–S asymmetry of the solar differential rotation.     

Solar rotation and the giant cells

Departures from the mean solar differential rotation rate as a function of latitude, longitude, and epoch of the solar cycle, together with variations in the rotation rate as determined by spectroscopic and tracer measurements are reviewed. It is shown that, if giant convection cells do exist as predicted, real variations in the subsurface rotation rate should occur and that this may be responsible for the observed surface anomalies.In terms of this hypothesis, a simple account is given for the anomalous rotation rates of sunspots. Furthermore, the torsional oscillations are identified as a modulation of the differential rotation produced by a system of toroidal convective rolls generated near the poles and propagating towards the equator. It is suggested that, as these rolls progress through lower latitudes, they break up into a system of cells which are the long sought for giant cells of the convection zone. Thus the torsional oscillations are identified as direct surface evidence for the existence of these cells.Solar Cycle Workshop Paper.     

N–S Asymmetry in the Solar Differential Rotation During 1957–1993

The properties of the differential rotation of the Sun are investigated by using H filaments as tracers. Annual average angular velocities of 716 quiescent filaments are determined from H photoheliograms of the Abastumani Astrophysical Observatory film collection for the years 1957–1993. The existence of north-south (N–S) asymmetry in H filaments rotation is confirmed statistically. The connection of asymmetry with the solar activity cycles is established. It is found that the northern hemisphere rotates faster during the even cycles (20 and 22) while the rotation of southern hemisphere dominates in odd ones (cycles 19 and 21). The mechanism of the solar activity should be responsible for the N–S asymmetry of the solar differential rotation. A theoretical explanation for the N–S asymmetry in the Suns rotation is offered. It is suggested that the asymmetry in the rotation of the two hemispheres of the Sun is balanced by the dynamo mechanism, which acts in parallel to the mechanism offered here. It is concluded that the N–S asymmetry of the solar rotation should cause a difference in activity level between the northern and southern hemispheres.     

Radial variation of differential rotation in the solar electron corona

Long-lived brightness structures in the solar electron corona persist over many solar rotation periods and permit an observational determination of coronal magnetic tracer rotation as a function of latitude and height in the solar atmosphere. For observations over 1964–1976 spanning solar cycle 20, we compare the latitude dependence of rotation at two heights in the corona. Comparison of rotation rates from East and West limbs and from independent computational procedures is used to estimate uncertainty. Time-averaged rotation rates based on three methods of analysis demonstrate that, on average, coronal differential rotation decreases with height from 1.125 to 1.5 R _S. The observed radial variation of differential rotation implies a scale height of approximately 0.7 R _S for coronal differential rotation.Model calculations for a simple MHD loop show that magnetic connections between high and low latitudes may produce the observed radial variations of magnetic tracer rotation. If the observed tracer rotation represents the rotation of open magnetic field lines as well as that of closed loops, the small scale height for differential rotation suggests that the rotation of solar magnetic fields at the base of the solar wind may be only weakly latitude dependent. If, instead, closed loops account completely for the radial gradients of rotation, outward extrapolation of electron coronal rotation may not describe magnetic field rotation at the solar wind source. Inward extrapolations of observed rotation rates suggest that magnetic field and plasma are coupled a few hundredths of a solar radius beneath the photosphere.     

Statistical Weights and Selective Height Corrections in the Determination of the Solar Rotation Velocity

Observations of the Sun performed at 37 GHz with the 14-m radio telescope of the Metsähovi Radio Observatory were analyzed. Rotation velocities were determined, tracing Low Temperature Regions (LTRs) in the years 1979–1980, 1981–1982, 1987–1988, and 1989–1991. Statistical weights were ascribed to the determined rotation velocities of LTRs, according to the number of tracing days. Measured changes of the rotation velocity during the solar activity cycle, as well as a north–south rotation asymmetry, are discussed. The results obtained with and without the statistical weights procedure are compared, and it was found that the statistical significance of the solar differential rotation parameters' changes is higher when the statistical weights procedure is applied. A selective application of the height correction on LTR's positions has not removed the cycle-related changes nor the north–south asymmetry of the solar rotation measured tracing LTRs. So, projection effects cannot explain these changes. The differential rotation of LTRs is more rigid than the differential rotation obtained tracing magnetic features and measuring Doppler shifts, which can be explained by the association rate of the LTRs' positions with rigidly rotating `pivot points'. The observed cycle-related changes and the north–south asymmetry of the rotation velocity of LTRs are consistent with the cycle-related changes and the north–south asymmetry of the association rate between LTRs and pivot points.     

Signature of differential rotation in solar disk‐integrated chromospheric line emission

UARS SOLSTICE data have been subjected to Fourier and wavelet analyses in order to search for the signature of the solar rotation law in the disk‐integrated irradiance of UV lines. Lyman‐α, Mg II, and Ca II data show a different behaviour. In the SOLSTICE data there are significant temporal variations of the rotation rate of the UV tracers over 5—6 years. Often several distinct rotation periods appear almost simultaneously. Beside the basic period around 27 days there are signals at 32—35 days corresponding to the rotation rate at very high latitudes. For more than 5 years during another period of the solar cycle the rotational behaviour is quite different; there is an indication of differential rotation of active regions in these Ca II ground‐based data. The data contain a wealth of information about the solar differential rotation, but it proves difficult to disentangle the effects of the different emitting sources.     

Solar rotation during the Maunder Minimum

We have measured solar surface rotation from sunspot drawings made in a.d. 1642–1644 and find probable differences from present-day rates. The 17th century sunspots rotated faster near the equator by 3 or 4%, and the differential rotation between 0 and ±20° latitude was enhanced by about a factor 3. These differences are consistent features in both spots and groups of spots and in both northern and southern hemispheres. We presume that this apparent change in surface rotation was related to the ensuing dearth of solar activity (the Maunder Minimum) which persisted until about 1715.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.     

Large-scale flows excited by magnetic fields in the solar convective zone

Observations demonstrate a nearly 22-year periodic zonal flow superimposed on general solar differential rotation (LaBonte and Howard, 1982) and some meridional motions (e.g., Tuominen, Tuominen, and Kyrolänen, 1983). Such flows can be excited by the magnetic wave generated by the dynamo in the solar convective zone.An approximate analytical solution for the zonal and meridional flows for a given magnetic wave is constructed. This approach is justified by the fact that the magnetic field is generated by differential rotation and mean helicity, and the magnetic field in the time interval under consideration does not affect much this main flow; it can, however, strongly influence the perturbations of this flow.The density gradient in the convective zone is taken into account as an essential point in the solution construction. The solution agreed well with observational features and, in particular, it gives a phase shift between the rotational (zonal) wave and solar activity. A polar branch of the rotational wave can be described as an effect created by a poleward moving dynamo wave.Secular variations in the symmetrical part of the differential rotation and in the asymmetry between the north and south hemispheres are predicted.The alternative approaches to the explanation of the origin of the observed large-scale flows are discussed.     

On the Long-Term Modulation of Solar Differential Rotation

Long-term modulation of solar differential rotation was studied with data from Mt. Wilson and our original observations during Solar Cycles 16 through 23. The results are that i) the global B-value (i.e. latitudinal gradient of differential rotation) is modulated with a period of about six or seven solar cycles, ii) the B-values of the northern and southern hemispheres are also modulated with a period similar to the global one, but iii) they show quasi-oscillatory behavior with a phase shift between them. We examined the yearly fluctuations of the B-values in every solar cycle with reference to the phase of the sunspot cycle and found that the B-values in the sunspot-minimum years show large and erratic variations, while those in the sunspot-maximum years show small fluctuations. Positive correlation between the former B-values and the latter was found. We discuss the independent long-term behavior of solar differential rotation between the northern and southern solar hemispheres and the implication for the solar dynamo.     

Solar rotation studies using sunspot data (1967–1974)

The solar rotation rate during 1967–1974 was measured from photographic observations of sunspots. The rates derived from isolated single spots and from bipolar groups were 14.38 ±0.02 and 14.71±0.05 deg per day equatorial sidereal, respectively. Year-to-year fluctuations in the bipolar group rates correlate with fluctuations in the Mt. Wilson spectroscopic rotation rates, while the isolated single spots show smaller, uncorrelated variations. A possible explanation for the fluctuations in the bipolar rates is year-to-year changes in the separation rates of the bipolar groups, rather than changes in the global solar rotation rate. The latter interpretation requires caution because (1) the sunspot rotation rates were derived from a limited amount of data (one month per year), and (2) the rotation rates were reduced to equatorial values assuming a differential rotation law {ie205-01}.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Center-to-limb profiles of the aluminum autoionization lines in the solar spectrum

The rotation of the solar corona has been studied using recurrence properties of the green coronal line (5303 Å) for the interval 1947–1970. Short-lived coronal activity is found to show the same differential rotation as short-lived photospheric magnetic field features. Long-lived recurrences show rigid rotation in the latitude interval ±57°.5. It is proposed that at least part of the variability of rotational properties of the solar atmosphere may be understood as a consequence of coexistence of differential and rigid solar rotation.On leave from Torino University, Italy, as an ESRO-NASA Fellow.     

Rotation of solar structures in the upper chromosphere. II. Time variations in the latitudinal distribution of the rotation of active regions and coronal holes

The time variations in the latitudinal distribution of the rotation of active regions and coronal holes are investigated. The synoptic maps obtained from observations in the He I 1083 nm line at Kitt Peak Observatory over almost three solar cycles are used as observational data. A Fourier analysis of the time series constructed from synoptic maps has yielded the following results. The rotation of active regions differs significantly from the rotation of coronal holes in all parameters: the set of the most significant rotation periods, their latitudinal distribution, and time variations. The rotation of active regions and coronal holes is characterized by variations from cycle to cycle, a time-varying north-south asymmetry. The power spectra for consecutive cycles of solar activity differ significantly for both epochs of high activity and minima. Analysis of the total power of the spectra within four selected intervals of periods from 21 to 33 days has shown that the total power is highest in the intervals of periods 24–27 and 27–30 days. This is valid for both active regions and coronal holes. The correlation between the total powers in the above intervals of periods changes noticeably with time. Long-lived or successively appearing active regions with rotation periods in the range 24–30 days are typical of the time of a sharp decrease in the total equivalent width of active regions. This includes not only the decline time of the 11-year cycles, but also the minima between recurrent activity maxima during one cycle. A predominance of long-lived coronal holes as their total equivalent width decreases is noticeable for coronal holes with rotation periods in the interval 30–33 days. All of the above results suggest that the rotation of solar structures is determined mainly by the subphotospheric sources of specific structures, not by the rotation of the main volumes of solar plasma of the quiet Sun.     

Statistical study of the north–south asymmetry of the solar differential rotation based on various solar structures during 1966–1985

The time variation and latitude dependence of the solar rotation are found using observational data on Hα filaments and compact magnetic features with different polarities during solar activity cycles 20 and 21 (1966–1985). Statistical analysis of the observational data shows that there is a north–south asymmetry in the rotation, both for the Hα filaments and for compact magnetic features (structures) with negative and positive polarities. The N-S asymmetry in the differential rotation of the Hα filaments and the compact magnetic features with both polarities shows up quite distinctly in solar activity cycles 20 and 21, but the asymmetry for the compact magnetic features with positive polarity is comparatively lower in cycle 21. The confidence level is lower the compact magnetic features with positive polarity than for the compact magnetic features with negative polarity.     

On the characteristics of the basic framework of solar active regions and the magnetohydrodynamical structure of the convection zone

The characteristics of the basic framework of structure and development of solar active regions are interpreted as good indicators of the magnetohydrodynamical structure of the convection zone, the magnetic field lines of which are twisted and are made wave-like by the action of the very large scale non-axisymmetric convection, called here the global convection. The characteristics discussed in this paper are: (i) the preponderance of preceding spots of bipolar sunspot groups in strength and life time relative to the following spots of the groups, (ii) the tilt of bipolar axes of the sunspot groups to the local parallels of latitude, (iii) the forward inclination of normal axes of sunspots inferred from the east-west asymmetry of the appearance and total area of sunspots, (iv) the faster rotation of sunspots than the averaged fluid rotation, and (v) the association of the characteristics of an active region with the presence of an older active region in its vicinity and with the relative disposition of the two active regions.     

An anticorrelation between polar and equatorial rotation of the solar photosphere

Published spectroscopic measurements of solar rotation are analyzed to show that when the rotation velocity increases at high latitudes it tends to decrease at low latitudes, and conversely. The high latitude velocities typically vary over only 20% of the range of those near the equator and the smallest variations of all occurred near latitude 60° during the rising portion of the previous solar cycle. The anticorrelation is consistent with a recent suggestion that differential rotation on the sun arises from photospheric wind systems whose strength is determined, ultimately, by oscillations within the Sun.     

A statistical study of the spiral spots on the solar disc

After adding the data observed in the years from 1979 to 1982 to those obtained earlier (Ding et al., 1981), we re-examine the previous results and conclude:

1. The longitudinal distribution of spiral spots on the solar disc is generally the same as that of sunspot groups with areas of S _p ≥ 400, but their active longitudes seem to be more concentrated.
2. The distribution of spiral patterns in the southern and northern hemispheres shows that the differential rotation may be a fundamental solar dynamo for the formation of the spiral spots.
3. The statistical directions of the emerging twisted magnetic vectors in the active regions in the southern and northern hemispheres are synchronously inverse with a period of about two years. This period seems to be detected in other solar observations.

     

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.     

Starspot modelling of the RS CVn binary HK lacertae

Investigating more than 270 nightly mean magnitudes of the long-period RS CVn binary HK Lac, we can draw some conclusions about the nature of its complicated light variations. The mean brightness, the apparent photometric period, and the shape of the light curve all show strong variations. Analysis with a starspot model, assuming two large spots and a general uniform spottedness, indicates two comparably large spots which appear to have maintained their separate identities for the last 15 yr and drifted in longitude separation from each other smoothly by only about 45°. The phase of the two spots indicates both are rotating very nearly synchronously with the orbital motion, one slightly (0.025%) faster and the other slightly (0.080%) slower. the latitudes of the two spots, one farther above the equator and one closer to the equator, are consistent with solar-type differential rotation and yield an estimate of 25±12° for the co-rotating latitude. A correlation between mean spot latitude and instantaneous photometric period yields another estimate of 31±2°, in agreement with the first.