22-year variations of the solar rotation and solar activity cycles

We have performed a comparative analysis of the results of our study of the 22-year rotation variations obtained from data on large-scale magnetic fields in the Hα line, magnetographic observations, and spectral-corona observations. All these types of data suggest that the rotation rate at low latitudes slows down at an epoch close to the maximum of odd activity cycles. The 22-year waves of rotation-rate deviation from the mean values drift from high latitudes toward the equator in a time comparable to the magnetic-cycle duration. We discuss the possibility of the generation of a solar magnetic cycle by the interaction of 22-year torsional oscillations with the slowly changing or relic magnetic field. We consider the generation mechanisms of the high-latitude magnetic field through a superposition of the magnetic fields produced by the decay and dissipation of bipolar groups and the relic or slowly changing magnetic field and a superposition of the activity wave from the next activity cycle at high latitudes.     

Solar radiation and solar differential rotation

Areas of sunspots and their positions taken from the Greenwich Photoheliographic Results (1874–1976) and typical intensities of the umbrae and penumbrae are used to calculate daily values of the solar flux at a wavelength of about 500 nm. Using overlapping time series of 512 days each solar rotation periods are determined by Fourier transformation. The periods found depend on the phase of the solar activity cycle, as expected from the solar differential rotation. This method may be used for solar type stars to determine relations between activity and rotation too. The problems of errors - e.g. by faculae or the variation of the umbral intensity within the activity cycle - are explained.Mitteilungen aus dem Kiepenheuer-Institut Nr. 284     

Spots,activity cycles,and differential rotation on cool stars

The first results are reported from a search for activity cycles in stars similar to the sun based on modelling their spotting with an algorithm developed at the Crimean Astrophysical Observatory. Of the more than thirty program stars, 10 manifested a cyclical variation in their central latitudes and total starspot area. The observed cycles have durations of 4–15 years, i.e., analogous to the 11 year Schwabe sunspot cycle. Most of the stars have a rough analog of the solar butterfly pattern, with a reduction in the average latitude of the spots as their area increases. A flip-flop effect during the epoch of the maximum average latitude is noted in a number of these objects (e.g., the analog LQ Hya of the young sun or the RS CVn-type variable V711 Tau), as well as a reduction in the photometric rotation period of a star as the spots drift toward the equator, an analog of the differential rotation effect in the sun. Unlike in the sun, the observed spot formation cycles do not correlate uniquely with other indicators of activity— chromospheric emission in the CaII HK lines (Be Cet, EK Dra, Dx Leo), H line emission (LQ Hya, VY Ari, EV Lac), or cyclical flare activity (EV Lac). In V833 Tau, BY Dra, EK Dra, and VY Ari short Schwabe cycles coexist with long cycles that are analogous to the Gleissberg solar cycle, in which the spotted area can approach half the entire area of the star.Translated from Astrofizika, Vol. 48, No. 1, pp. 29–43 (February 2005).     

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.     

Rotating convection and the solar differential rotation

We discuss the implication of a numerical experiment on rotating convection and its relevance to the construction of a model for the solar differential rotation.     

Solar proton events during solar cycles 19, 20, and 21

Solar proton events have been studied for over thirty years and a great deal of lore has grown around them. It is the purpose of this paper to test some of this lore against the actual data. Data on solar proton events now exist for the period from 1956 to 1985 during which time 140 events took place in which the event integrated fluxes for protons of energy > 30 MeV was larger than 10⁵ particles cm^-2. We have studied statistical properties of event integrated fluxes for particles with energy > 10 MeV and for particles with energy > 30 MeV. Earlier studies based on a single solar cycle had resulted in a sharp division of events into ordinary and anomalously large events.Two such entirely separate distributions imply two entirely separate acceleration mechanisms, one common and the other very rare. We find that the sharp division is neither required nor justified by this larger sample. Instead the event intensity forms a smooth distribution for intensities up to the largest observed implying that any second acceleration mechanism cannot be rare. We have also studied the relation of event sizes to the sunspot number and the solar cycle phase. We find a clear bimodal variation of annual integrated flux with solar cycle phase but no statistically significant tendency for the large events to avoid sunspot maximum. We show there is almost no relation between the maximum sunspot number in a solar cycle and the solar cycle integrated flux. We also find that for annual sunspot numbers greater than 35 (i.e., non-minimum solar cycle conditions) there is no relation whatsoever between the annual sunspot numbers and annual integrated flux.     

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)     

On the differential rotation with height in the solar atmosphere

Spectroscopic measurements of solar rotation having good height discrimination show no change in angular velocity through the photosphere layers but an increase of 8% for the Hα chromosphere (epoch 1968.9). Spectroscopic results in general are compared with measures made with tracers, i.e. sunspots, filaments, etc., and it is seen that the spectroscopic method always shows increased differential rotation with height, while tracers indicate none. A westward flowing wind is proposed that increases in velocity with height, but produces negligible movement to magnetic regions associated with tracers. Kitt Peak National Observatory Contribution No. 450. Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Ten cycles of solar and geomagnetic activity

Series of 110 years of sunspot numbers and indices of geomagnetic activity are used with 17 years of solar wind data in order to study through solar cycles both stream and shock event solar activity. According to their patterns on Bartels diagrams of geomagnetic indices, stable wind streams and transient solar activities are separated from each other. Two classes of stable streams are identified: equatorial streams occurring sporadically, for several months, during the main phase of sunspot cycles and both polar streams established, for several years, at each cycle, before sunspot minimum. Polar streams are the first activity of solar cycles. For study of the relationship between transient geomagnetic phenomena and sunspot activity, we raise the importance of the contribution, at high spot number, of severe storms and, at low spot number, of short lived and unstable streams. Solar wind data are used to check and complete the above results. As a conclusion, we suggest a unified scheme of solar activity evolution with a starting point every eleventh year, a total duration of 17 years and an overlapping of 6 years between the first and the last phase of both successive series of phenomena: first, from polar field reversal to sunspot minimum, a phase of polar wind activity of the beginning cycle is superimposed on the weak contribution of shock events of the ending cycle; secondly, an equatorial phase mostly of shock events is superimposed on a variable contribution of short lived and sporadic stable equatorial stream activities; and thirdly a phase of low latitude shock events is superimposed on the polar stream interval of the following cycle.     

Solar soft X-rays and solar activity

Soft solar X-rays (8 gl 12 Å) were observed from OSO-III. An analysis of the X-ray enhancements associated with 165 solar flares revealed that there is a tendency for a weak soft X-ray enhancement to precede the cm- burst and H flare. The peak soft X-ray flux follows the cm- peak by about 4 min, on the average. Additionally, it was found that flare-rich active centers tend to produce flares which are stronger X-ray and cm- emitters than are flares which take place in flare-poor active centers.     

Solar soft X-rays and solar activity

Flare-associated soft X-ray bursts (8–12 Å) are examined for 283 events observed by OSO-III. These bursts are shown to be predominantly thermal in nature. Their time-profiles are roughly similar to those of the associated H flares, although the X-ray burst begins about two minutes earlier, on the average. The strength of the soft X-ray burst is directly related to the area and brilliance of the flare, the age and flare-richness of the associated plage, and the general level of solar activity at the time of the burst. The peak enhancements in the soft X-ray and H emission rates during flares are of the same order of magnitude, as are the total flare energies radiated at these wavelengths. We estimate that soft X-radiation accounts for up to 10% of a flare's total electromagnetic emission.NRC/NAS Resident Research Associate.     

Solar soft X-rays and solar activity

Peak fluxes of flare-associated 8–12 Å X-ray bursts occur at or near the time of the maximum energy content of the soft X-ray source volume. The amplitudes of flare-associated bursts may thus be used as a measure of the energy deposited in the source volume by non-thermal electrons and other processes. In the mean, the soft X-ray burst amplitude is apparently independent of the occurrence of a type III event. This is interpreted to indicate that electrons accelerated by the type III process do not directly participate in establishing the soft X-ray source volume.     

A joined model for solar dynamo and differential rotation

A model for the solar dynamo, consistent in global flow and numerical method employed with the differential rotation model, is developed. The magnetic turbulent diffusivity is expressed in terms of the entropy gradient, which is controlled by the model equations. The magnetic Prandtl number and latitudinal profile of the alpha-effect are specified by fitting the computed period of the activity cycle and the equatorial symmetry of magnetic fields to observations. Then, the instants of polar field reversals and time-latitude diagrams of the fields also come into agreement with observations. The poloidal field has a maximum amplitude of about 10 Gs in the polar regions. The toroidal field of several thousand Gauss concentrates near the base of the convection zone and is transported towards the equator by the meridional flow. The model predicts a value of about 10³⁷ erg for the total magnetic energy of large-scale fields in the solar convection zone.     

The solar differential rotation and ‘Rossby-type’ waves

It has been suggested that the solar differential rotation might be maintained by nearly horizontal non-spherical convective circulation called the Rossby-type waves (the wave motions characterized by the close balance of the Coriolis force and pressure gradient in horizontal motions). In this paper, such Rossby-type waves which could be excited in the upper solar convection zone are considered, and the possibility of maintenance of the solar differential rotation by such waves is examined. A numerical estimate, in terms of the rate of conversion of the kinetic energy of such wave motions into the mean rotational motion, indicates this possibility. The implications and limitations of the results are also discussed.Visiting Scientist to the High Altitude Observatory on leave of absence from the Department of Astronomy, University of Tokyo, Japan.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Long-term cyclic variations of prominences, green and red coronae over solar cycles

Long-term cyclic variations in the distribution of prominences and intensities of green (530.3 nm) and red (637.4 nm) coronal emission lines over solar cycles 18–23 are presented. Polar prominence branches will reach the poles at different epochs in cycle 23: the north branch at the beginning in 2002 and the south branch a year later (2003), respectively. The local maxima of intensities in the green line show both poleward- and equatorward-migrating branches. The poleward branches will reach the poles around cycle maxima like prominences, while the equatorward branches show a duration of 18 years and will end in cycle minima (2007). The red corona shows mostly equatorward branches. The possibility that these branches begin to develop at high latitudes in the preceding cycles cannot be excluded.     

Observation of solar differential rotation with the aid of magnetic tracers

We tried to search for the manifestation of differential rotation in the distribution of weak remnants of magnetic fields measured with a very low resolution. We found that, during the periods of low solar activity and in parts of the solar photosphere with smaller density of new magnetic flux sources, it was possible to observe the distribution of magnetic tracers in the form of differential rotation parabolas which increase their curvature from one rotation to the next. The obtained differential rotation rates are not far from those given by highly averaged sunspot data or by the daily magnetic fields. The characteristic differential rotation parabolas as well as specific cellular-like features disturbing their smooth patterns are always formed from fields of one main polarity, the sign of which depends on the phase of the activity cycle.Solar Cycle Workshop Paper.     

Short-time variations of solar neutrinos and solar activity cycle

It is shown from the statistical analysis of the sunspot data and solar neutrino data that both the data exhibits 5, 10, 15, 20, 25, and 30 months period and these periods may be g-mode oscillation of the core associated with the solar activity.     

Periodicities in the solar differential rotation,surface magnetic field and planetary configurations

Using Greenwich data on sunspot groups during 1874–1976, we have studied the temporal variations in the differential rotation parametersA andB by determining their values during moving time intervals of lengths 1–5 yr successively displaced by 1 yr. FFT analysis of the temporal variations ofB (orB/A) shows periodicities 18.3 ± 3 yr, 8.5 ± 1 yr, 3.9 ± 0.5 yr, 3.1 ± 0.2 yr, and 2.6 ± 0.2 yr at levels 2. This analysis also shows five more periodicities at levels 1–2. The maximum entropy method is used to set narrower limits on the values of these periods. The reality of the existence of all these periodicities ofB (orB/A ) except the one at 2.8 yr is confirmed by analyzing the simulated time series ofB andB/A with values ofA andB randomly distributed within the limits of their respective uncertainties. Four of the prominent periods ofB agree, within their uncertainties, with the known periods in the the large-scale photospheric magnetic field. The deviations from the average differential rotation are larger near the sunspot minima. On longer time scales, the variations in the amount of sunspot activity per unit time are well correlated to the variations in the amplitudes of the torsional oscillation represented by the 22-yr periodicity inB. All the periods inB found here are in good agreement with the synodic periods of two or more consecutive planets. The possibility of planetary configurations providing perturbations needed for the Sun's MHD torsional oscillations is speculated upon and briefly discussed.     

On the negative correlation between solar activity and solar rotation rate

An increase in solar activity is shown to be accompanied by a decrease in solar rotation rate. This effect has been established from various indices; it manifests itself as cyclic and secular variations in the global magnetic field, in the observations of the magnetic field of the Sun as a star, and in the observations of the solar corona. Some possible explanations of this effect are discussed.     

Solar neutrino flux,cosmic rays,and the solar activity cycle

It is suggested that the experimental data on the solar neutrino flux as measured by Davis and his collaborators from 1970 to 1982 vary with the solar activity cycle to a very high level of statistical significance for all the available tests of the hypothesis (e.g., (t-test, ²-test, run test, Wilcoxon-Mann-Whitney test) when the solar neutrino flux data are computed from the weighted moving averages of order 5. The above tests have also been applied to the data that have been generated by the Monte Carlo simulation with production rate and background rate parameters that are typical of those in the actual experiment. It is shown that the Monte Carlo simulated data do not indicate a variation within the solar cycle. Thus the moving average data strongly favours the variation within the solar activity cycle.