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.     

On changes of the rotation velocities of stable,recurrent sunspots and their interpretation with a flux tube model

The angular rotation velocities of stable, recurrent sunspots were investigated using data from the Greenwich Photoheliographic Results 1940 until 1968. We found constant rotation velocities during the passages on the solar disk with errors of about ±4 m s^–1. During their lifetime these spots show a decreasing braking of their rotation velocities from 0.8 to 0.3 m s^–1 per day. A plausible interpretation is found by assuming the spots to be coupled to a slowly rising subsurface flux tube and a rotation velocity which increases with depth.Mitteilungen aus dem Kiepenheuer-Institut Nr. 201.     

Stellar differential rotation from direct star-spot tracking

On the Sun, the rotation periods of individual sunspots not only trace the latitude-dependence of the surface rotation rate, but also provide clues as to the amount of subsurface fluid shear. In this paper we present the first measurements of stellar differential rotation made by tracking the rotation of individual star-spots with sizes comparable to the largest sunspots. To achieve this we re-analyse four sequences of densely sampled, high signal-to-noise ratio echelle spectra of AB Doradus spanning several stellar rotations in 1996 December. Using spectral subtraction, least-squares deconvolution and matched-filter analysis, we demonstrate that it is possible to measure directly the velocity amplitudes and rotation periods of large numbers of individual star-spots at low to intermediate latitude. We derive values for the equatorial rotation rate and the magnitude of the surface differential rotation, both of which are in excellent agreement with those obtained by Donati & Collier Cameron from cross-correlation of Doppler images derived a year earlier in 1995 December, and with a re-analysis of the 1996 data by the χ ² landscape method. The differences between the rotation rates of individual spots and the fitted differential rotation law are substantially greater than the observational errors. The smaller spots show a greater scatter about the mean relation than the larger ones, which suggests that buffeting by turbulent supergranular flows could be responsible.     

The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

A method of evolving synoptic maps of the solar magnetic field,II. Comparison with observations of the polar fields

We describe the application of the synoptic transport equation to simulate the temporal evolution of the magnetic flux over the solar surface. This provides a means of predicting each day both the synoptic maps for the Carrington rotation starting the next day and the instantaneous map of the solar flux over the whole solar surface for the next day. The reliability of the predicted synoptic maps is tested by comparing the locations of the zero-flux contour with those of the observed maps produced by the National Solar Observatory, Kitt Peak and with the locations of Hα filaments measured on filtergrams obtained by the Big Bear Solar Observatory. We conclude that the best match at high latitudes is obtained by long-term simulations (over 20 rotations) with flux updates each rotation between latitudes ± 60°. We illustrate the use of the simulations to describe the evolution of the polar fields at the time of the polarity reversals in Cycle 23. The reconstruction of the instantaneous maps is tested by comparison with full-disk magnetograms. The method provides a simple means of estimating the large-scale flux distribution over the whole surface. It does not take account of flux emerging after the central meridian passage each rotation so it is only approximate in the activity belts but provides a reliable map beyond those latitudes.     

Absolute spectroscopic determination of solar rotation

We have made absolute measurements at Kitt Peak of the dependence of solar rotation rate upon latitude during the period 17–20 June 1977. We observed the solar potassium line at 7699 Å using an atomic-beam resonance scattering apparatus. The measured sidereal equatorial rotation rate is 13.5±0.5 deg day^–1. Our results are in agreement with those of Howard and Harvey from 1966–68. We intend to use this technique in a long-term program at Oberlin to monitor the equatorial rotation rate.Visiting Astronomer, Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Measurement of the solar rotation, 1978, from recurrent and non-recurrent sunspots

Results are presented for the solar rotation, 1978, as derived from sunspots by two different methods. Using recurrent spots only, the latitude dependence of the sidereal rotation rate was calculated to be =(14.41±0.05)–(3.13±0.26) sin² . Using recognizable spots, both recurrent and non-recurrent, average rotation rates were obtained for 5-degree intervals of latitude. The results from these two approaches were found to be in agreement with observations made between 1878 and 1951, suggesting that the solar rotation has not changed in the past 100 years.Currently at Northwestern University, Evanston, Ill., U.S.A.     

Differential rotation of cool active stars

The surface differential rotation of active solar‐type stars can be investigated by means of Doppler and Zeeman‐Doppler Imaging, both techniques enabling one to estimate the short‐term temporal evolution of photospheric structures (cools spots or magnetic regions). After describing the main modeling tools recently developed to guarantee a precise analysis of differential rotation in this framework, we detail the main results obtained for a small number of active G and K fast rotating stars. We evoke in particular some preliminary trends that can be derived from this sample, bearing the promise that major advances in this field will be achieved with the new generation of spectropolarimeters (ESPaDOnS/CFHT, NARVAL/TBL). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The rotation of magnetic loop systems in the solar atmosphere

Eclipse photographs indicate that large regions of the inner solar corona are confined in various types of closed magnetic configurations and, as a result, do not participate in the general solar wind expansion. In this paper, the rotation of initially poloidal loop configurations of this type, as influenced by differential rotation of the footpoints, is investigated. The analysis is restricted to axially symmetric fields and it is assumed that the toroidal magnetic field induced by differential rotation is small as compared to the initial poloidal field. This restricts the validity of the analysis to times less than about one month.The most interesting physical situation is that of flux tubes existing in one solar hemisphere only, one end of the tube being fixed in the photosphere at a higher latitude than the other. As a consequence, the lower end of the tube rotates at a faster rate than the upper end. Solution of the pertinent equations reveals that the angular velocity measured along a field line increases monotonically from its value at the poleward footpoint to that at the lower footpoint. The variation of angular velocity along the field depends upon the field geometry only and is not directly related to the variation of angular velocity along the solar surface between the footpoints. Depending upon the field configuration, both outward radial increases and decreases are possible. Using the Newton and Nunn model for the surface differential rotation rate, the angular velocity distribution on two particularly simple types of closed magnetic loop systems is determined analytically. It is shown that the angular velocity increases outward in the polar regions but decreases outward near the equator - leading to a decrease in differential rotation with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

DEPENDENCE OF ROTATION VELOCITY OF INDIVIDUAL SUNSPOTS ON THEIR LIFETIME

By using a large number (452) of individual sunspots or individual sunspots with small spots around them, taken from the Greenwich Photoheliographic Results (GPR) for the years 1964–1976 that cover solar cycle No. 20, it is shown that the rotation velocity of the sunspots varies with their lifetimes. This investigation indicates that at the equator, the rotation rate for the last three days (of the lifetime) is about 1.3% slower than that over the whole lifetime and about 0.5% slower than during the first three days, but this is reversed at high and low latitudes, and the difference is much larger in the northern hemisphere than in the southern hemisphere. These results confirm to the fact that the rotation rate of the solar layers increases with depth.     

The flares associated with the dynamics of the sunspots

In the present study, we consider six years data of spot groups that have well developed leading and following spots obtained from the Kodaikanal Observatory white light pictures and occurrence of Hα flares. From the daily observations, we compute the variations in rotation rates, meridional velocity, the areas and longitudinal separations. We find that among all these variations, the occurrence of abnormal rotation rates (the rotation rates that have greater than 1σ and longitudinal minimum separation during the course of their evolution eventually lead to triggering of flares. We also find that the events of abnormal rotation rates, longitudinal minimum separation and the flares occur mainly during the 50–80% of the sunspots’ life span indicating magnetic reconnection probably below (0.935R⊙) the solar surface. Relevance of these results with the conventional theory of magnetic reconnection is briefly discussed.     

ON THE POSSIBLE CHANGES OF THE SOLAR DIFFERENTIAL ROTATION DURING THE ACTIVITY CYCLE DETERMINED USING MICROWAVE LOW-BRIGHTNESS-TEMPERATURE REGIONS AND Hα FILAMENTS AS TRACERS

The solar rotation rate obtained using the microwave Low-brightness-Temperature Regions (LTRs) as tracers in the heliographic range ± 55° from the years 1979–1980, 1981–1982, 1987–1988, and 1989–1991 varied from 3% to 4% in medium latitudes, and below 1% at the equator. Using H filaments as tracers at higher latitudes from the years 1979, 1980, 1982, 1984, and 1987, the solar rotation rate variation was between 2% and 8%. This represents an upper limit on the rotation rate variation during the solar activity cycle. Such changes could be caused by short-lived, large-scale velocity patterns on the solar surface. The Sun revealed a higher rotation rate on the average during the maxima of the solar activity cycles 21 and 22, i.e., in the periods 1979–1980 and 1989–1991, respectively, which differs from the rotation rates (lower on the average) in some years, 1981–1982 and 1987–1988, between the activity maximum and minimum (LTR data). Simultaneous comparison of rotation rates from LTRs and H filament tracings was possible in very limited time intervals and latitude bands only, and no systematic relationship was found, although the rotation rates determined by LTRs were mostly smaller than the rotation rates determined by H filaments. The errors obtained by applying different fitting procedures of the LTR data were analyzed, as well as the influence of the height correction. Finally, the north–south asymmetry in the rotation rate investigated by LTRs indicates that the southern solar hemisphere rotated slower in the periods under consideration, the difference being about 1%. The reliability of all obtained results is discussed and a comparison with other related studies was performed.     

The 100—year periodic modulation of solar rotation

A periodic long-term modulation of the solar surface rotation with a time scale on the order of 100 years is found in the sunspot data from 1874 to 1992 obtained by combinig the Greenwich Photoheliographic Results from cycle 11 to cycle 20 analysed by Balthasar, Vázquez, and Wöhl and the Mitaka sunspot sketch data from cycle 18 to 22 of the National Astronomical Observatory of Japan which was the Tokyo Astronomical Observatory of the University of Tokyo until 1988. A new index of the solar rotation M defined by integrating the angular momentum density over the whole surface, which we call the angular momentum surface layer density, reached a maximum at solar cycle 14, decreased to a minimum at cycle 17, and then increased to reach another maximum at cycle 21. The increase of M means acceleration of the surface layer as a whole by transport of angular momentum from the deeper layer. This implies an decrease (increase) of the radial gradient of the differential rotation if the basic radial gradient of the differential rotation increases (decreaes) inward. The decrease of M means deceleration of the surface layer and implies an increase (decrease) of the radial gradient. The degree of the equatorial acceleration of the surface differential rotation is also found to have undergone the same 100 year periodic modulation during the same interval, reaching a minimum at cycle 14, a maximum at cycle 17, and a minimum at cycle 21 in antiphase with the modulation of M. Thus both radial and latitudinal gradients of the differential rotation increased and decreased in phase (in anti-phase) if the basic radial gradient increases (decreases) inward.     

Photometric Imaging with Distributive Solar Analogy

The multicolor light curves (UBVRI) of HU Vir have been analyzed to study starspots for epochs 1987 and 1989. The term 'photometric imaging' has been used for predicting cool surface spots by photometric data. Assuming the number of spots and the area are about the same for the two hemispheres, the distributive solar analogy is introduced as a tool to constrain free values of spot parameters into unique values. Therefore, final fitting parameters are claimed unique in a sense that they are independent of free initial guesses. The light and color variations of HU Vir are better explained without polar spots. Finally, the spots are found to be ∼ 1600 K cooler than the T∼ 5000 K of this cool subgiant and cover ∼ %13.9 of the total surface at ±8.0 degrees from the equator for the epoch 1987. The spots at the epoch 1989 are found to be ∼ 2040 K cooler covering ∼ % 12.7 area at ± 27°.7 latitudes. Problems of photometric imaging and possible solutions with distributive solar analogy have been discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Frequency of coronal transients and solar activity

The High Altitude Observatory's white light coronagraph aboard Skylab observed some 110 coronal transients - rapid changes in appearance of the corona - during its 227 days of operation. The longitudes of the origins of these transients were not distributed uniformly around the solar surface (51 of the 100 events observed in seven solar rotations arose from a single quadrant of longitude). Further, the frequency of transient production from each segment of the solar surface was well correlated with the sunspot number and Ca ii plage (area × brightness) index in the segment, rotation by rotation. This correlation implies that transients occur more often above strong photospheric and chromospheric magnetic fields, that is, in regions where the coronal magnetic field is stronger and, perhaps, more variable. This pattern of occurrence is consistent with our belief that the forces propelling transient material outward are, primarily, magnetic. A quantitative relation between transient production from an area and the Zürich sunspot number appropriate to that area is derived, and we speculate that the relation is independent of phase in the solar activity cycle. If true, the Sun may give rise to as many as 100 white light coronal transients per month at solar cycle maximum.Currently at Los Alamos Scientific Laboratory, Los Alamos, N.M., U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

Nonlinear simulations of solar rotation effects in supergranules

Nonlinear calculations for the three-dimensional and time dependent convective flow in a plane parallel layer of fluid are carried out with parameter values appropriate for supergranules on the Sun. A rotation vector is used which is tilted from the vertical to represent various latitudes. For the incompressible fluid used in this model the solar rotation produces turning motions sufficient to completely twist a fluid column in about one day. It is suggested that this effect will be greatly enhanced in a compressible fluid. The tilted rotation vector produces anisotropies and systematic Reynolds stresses which drive mean flows. The resulting flows produce a rotation rate which increases inward and a meridional circulation with poleward flow along the outer surface.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The abundance of 3He in the solar wind - A constraint for models of solar evolution

³He is an intermediate product in the proton-proton chain, and standard models of the Sun predict a large bulge of enhanced ³He abundance near M _r /M ₀ = 0.6 in the contemporary Sun. The relatively low abundance of ³He at the solar surface, which is derived from solar wind observations, poses severe constraints to non-standard solar models.Direct measurements of the ³He abundance in the solar atmosphere are extremely difficult, whereas indirect measurements, e.g., in the solar wind, have been performed with considerable precision. The interpretation of solar wind observations with respect to solar surface abundances has been greatly improved in recent years. Abundance measurements have been performed under a large variety of solar wind conditions and refined models have been developed for the transport processes in the chromosphere and the transition region and for the processes occurring in the solar corona. From these measurements we estimate the present isotopic number ratio ³He/⁴He to be (4.1 ± 1.0) × 10^–4 at the solar surface, corresponding to the weight abundance X ₃ = (9.0 ± 2.4) × 10^–5. The zero-age Main-Sequence abundance of ³He (after burning of D) might have been slightly lower (by about 10 to 20%) than the present-day value.Non-standard solar models involving mild turbulent diffusion (Lebreton and Maeder, 1987) could account for a slow secular increase of the ³He/⁴He ratio in the solar atmosphere. On the other hand it is difficult to reconcile models with severe mass loss as proposed by Guzik, Willson, and Brunish (1987) with this constraint. The slowing down of the solar rotation during the early Main-Sequence evolution was accompanied by stronger differential rotation probably implying a more effective mixing of the inner parts. Again, the surface abundance of ³He imposes severe limits on the evolution of the distribution of momentum within the early Sun.     

On diurnal variations of the solar rotation rate as derived from sunspot tracings

The heliographic positions of more than 100 sunspots were accurately measured several times a day from 1974 until 1979 by means of the computer-controlled tracing method described by Schröter and Wöhl (1975). A striking degree of constancy of the solar rotation rate (about 0.15% or 3 m s^–1) is found, when east-west proper motion components of each individual stable sunspot is considered. However, large differences of the rotation rate are observed (up to 7% or 130 m s^–1) when comparing different sunspots. We found no significant correlation of these fluctuations with characteristics of the sunspots (age, evolution, etc.).Mitteilungen aus dem Kiepenheuer-Institut Nr. 191.     

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.