Long-Term Variations in the Solar Differential Rotation

Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs). The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s⁻¹. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s⁻¹ and from cycle 21 to cycle 22 by about 0.016 μrad s⁻¹. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years (Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s<sup>−1</sup> around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s⁻¹ around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass of the solar system.     

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.     

Solar Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

Periodic variation of the north-south asymmetry of solar activity phenomena

We report here a study of various solar activity phenomena occurring in both north and south hemispheres of the Sun during solar cycles 8&amp;#x2013;23. In the study we have used sunspot data for the period 1832&amp;#x2013;1976, flare index data for the period 1936-1993, H&amp;#x03B1; flare data 1993&amp;#x2013;1998 and solar active prominences data for the period 1957&amp;#x2013;1998. Earlier Verma reported long-term cyclic period in N-S asymmetry and also that the N-S asymmetry of solar activity phenomena during solar cycles 21, 22, 23 and 24 will be south dominated and the N-S asymmetry will shift to north hemisphere in solar cycle 25. The present study shows that the N-S asymmetry during solar cycles 22 and 23 are southern dominated as suggested by Verma.     

Power Spectrum of Cosmic-ray Fluctuations During Consecutive Solar Minimum and Maximum Periods

Power spectral analysis of cosmic-ray intensity recorded by eight stations was carried out over a wide range of frequencies from 2.3 × 10^–8 Hz to 5.8 × 10^–6 Hz (2–500 days) during the period 1964–1995. Spectrum results of large-scale fluctuations have revealed the existence of a broad peak near 250–285 days and a narrower peak at 45–50 days during the studied epochs as a stable feature in all neutron monitors covering a wide rigidity range. The cosmic-ray power spectrum displayed significant peaks of varying amplitude with the solar rotation period (changed inversely with the particle rigidities) and its harmonics. The amplitudes of 27-day and 13.5-day fluctuations are greater during the positive-polarity epochs of the interplanetary magnetic field (qA>0) than during the qA<0 epochs. The comparison of cosmic-ray power spectra during the four successive solar activity minima have indicated that at the low-rigidity particles the spectrum differences between the qA>0 and qA<0 epochs are significantly large. Furthermore, the spectrum for even solar maximum years are higher and much harder than the odd years. There are significant differences in the individual spectra of solar maxima for different cycles.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

The slender solar tachocline: a magnetic model

A model for the sharp transition from differential rotation in the solar convection zone to rigid rotation in the radiative interior is presented. Differential rotation in the radiative zone is shown to be quenched efficiently by an internal magnetic field. The poloidal field amplitude, B₀, is the input parameter for our model which determines the transition layer thickness and the toroidal field strength. It is illustrated analytically and confirmed numerically that a rather small field, B₀ = 10⁻⁴ Gauss, suffices to satisfy the helioseismological restrictions on the depth of the differential rotation penetration below the convection zone. The transition layer thickness decreases further with increasing B₀. The toroidal field amplitude B ≃ 200 Gauss is almost independent of B₀.     

The peculiarities of rotation of the solar polar regions

The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s^–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s^–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s^–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator.     

Hurst analysis of Mt. Wilson rotation measurements

I study the temporal variation of the solar rotation on time scales shorter than the 11-year cycle by analyzing the daily Mt. Wilson Doppler measurements from 1967 to 1992. The differential rotation is represented by the three coefficients,A, B, andC, of the following expansion: =A +B sin²() +C sin⁴(). TheA, B, andC time series show clearly the 11-year solar cycle and they also show high-frequency fluctuations. The Hurst analysis of these time series shows that a Gaussian random process such as observational noise can only account for fluctuations on time scales shorter than 20 days. For time scales from 20 days to 11 years, the variations of A give rise to a Hurst exponent ofH = 0.83, i.e., the variations ofA are persistent. The temporal variations ofB show the same behavior asC, which is different fromA. From one to 11 years, theB andC variations are dominated by the 11-year cycle, while for time lags shorter than about 250 days, theB andC fluctuations give rise to a Hurst exponent ofH = 0.66, which lies betweenH = 1/2, of a Gaussian random process, and the exponent of the persistent process shown byA. An analysis of the equivalent coefficients of the first three even Legendre polynomials, computed usingA, B, andC, provides additional information. For time scales between 100 and 1000 days, the ranges,R/S, of Legendre polynomial coefficients decrease with increasing order of the polynomials which suggests that the persistent process operates mainly on large spatial scales. The Hurst exponent ofH = 0.83 for variations inA is the same asH for monthly sunspot numbers with time scales between 6 months and 200 years and for¹⁴C radiocarbon data with time scales between 120 years and 3000 years, previously analyzed by other authors. The combined results imply that the underlying solar process shows the same persistent behavior for time scales as short as about 20 days up to time scales of a few thousand years.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Photometry of the spotted flare star by dra during 1985-1991

Spot photometry in theUBV was obtained for the flare star BY Dra during 1985-1991 at the Bulgarian National Astronomical Observatory. Light curves are presented for 1986, 1987, 1988, and 1991. There are significant variations of the amplitudes of the light curves implying changes of the spot distribution. The phases of the light minima are variable, indicating possible latitudinal migration of the spot and differential rotation. Rough estimate of the corresponding latitudinal shear is in the range 3 × 10^–11 –5 × 10^–10 rad s^–1 deg^–1. The photometric behaviour of BY Dra since 1960 shows no compeling evidence for existence of stellar cycles. This is in contradiction with previous studies. During 1985-1991 a total of 38.47 hours of monitoring in theU-filter were obtained. Analysis of the flare activity of BY Dra shows no significant changes from previous studies.     

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.     

Mid Pleistocene climate instability in the subtropical northwestern Atlantic

We present Globigerinoides ruber, G. sacculifer and Neogloboquadrina dutertrei oxygen isotope records from northwestern subtropical Atlantic Site 1058 spanning the mid Pleistocene ( 600 to 400 ka). The high temporal resolution of these records ( 800 yr) allows us to compare millennial-scale climate signals during one of the most extreme glacial periods of the Pleistocene (Marine Isotope Stage (MIS) 12) to an earlier, less extreme glacial (MIS 14), as well as to two full interglacial intervals (MIS 13 and MIS 15). We observe excellent agreement in the timing and amplitude of variations between the surface-most dwelling species G. ruber and Northern Hemisphere insolation during the two interglacial periods. There is some expression of Northern Hemisphere insolation during glacial MIS 14; however, during the more extreme glacial MIS 12 Northern Hemisphere insolation patterns are not apparent in any of the planktonic foraminiferal δ¹⁸O records. Insolation remains relatively high, but δ¹⁸O values increase toward the characteristic δ¹⁸O maximum of MIS 12 in all three of the records. On the millennial-scale, all three species display their highest amplitude δ¹⁸O variations (with a period between 4–6 kyr) during glacial MIS 12. Suborbital-scale variability is also statistically significant during glacial MIS 14, but the amplitude is smaller. These results support hypotheses linking millennial-scale climate fluctuations to the extent of continental glaciation. We propose that the relatively high degree of sea surface instability during one of the most extreme glacial periods of the Pleistocene arises from the competing effects of strong atmospheric winds related to the presence of a large ice sheet to the north and persistently high incident solar radiation during this interval of time.     

Solar rotation as determined from OSO-4 EUV spectroheliograms

Spectroheliograms obtained in extreme ultraviolet (EUV) lines and the Lyman continuum are used to determine the rotation rate of the solar chromosphere, transition region, and corona. A cross-correlation analysis of the observations indicates the presence of differential rotation through the chromosphere and transition region. The rotation rate does not vary with height. The average sidereal rotation rate is given by (deg day^–1) = 13.46 - 2.99 sin² B where B is the solar latitude. This rate agrees with spectroscopic determinations of the photospheric rotation rate, but is slower by 1 deg day^–1) = 13.46 - 2.99 sin² than rates determined from the apparent motion of photospheric magnetic fields and from the brightest points of active regions observed in the EUV. The corona does not clearly show differential rotation as do the chromosphere and transition region.     

Solar wind variation with the cycle

The cyclic evolution of the heliospheric plasma parameters is related to the time-dependent boundary conditions in the solar corona. &amp;#x201C;Minimal&amp;#x201D; coronal configurations correspond to the regular appearance of the tenuous, but hot and fast plasma streams from the large polar coronal holes. The denser, but cooler and slower solar wind is adjacent to coronal streamers. Irregular dynamic manifestations are present in the corona and the solar wind everywhere and always. They follow the solar activity cycle rather well. Because of this, the direct and indirect solar wind measurements demonstrate clear variations in space and time according to the minimal, intermediate and maximal conditions of the cycles. The average solar wind density, velocity and temperature measured at the Earth&amp;#x2019;s orbit show specific decadal variations and trends, which are of the order of the first tens per cent during the last three solar cycles. Statistical, spectral and correlation characteristics of the solar wind are reviewed with the emphasis on the cycles.     

Polar magnetic field reversals of the Sun in Maunder Minimum

A possible scenario of polar magnetic field reversal of the Sun during the Maunder Minimum (1645&amp;#x2013;1715) is discussed using data of magnetic field reversals of the Sun for 1880&amp;#x2013;1991 and the¹⁴ C content variations in the bi-annual rings of the pine-trees in 1600&amp;#x2013;1730 yrs.     

The Relationship Between Solar Activity and the Large-Scale Axisymmetric Magnetic Field

To investigate the relationship between solar activity and the large-scale axisymmetric magnetic field of the Sun, we inferred from sunspot data over the period 1964–1985 a latitude–time distribution of magnetic field associated with active regions. This has been done allowing for both bipolar structure of the active regions and inclination of their axes to parallels of latitude, so the inferred magnetic field characterizes latitudinal separation of magnetic polarities which might be related to the large-scale magnetic field of the Sun according to the Babcock–Leighton model. The inferred magnetic field, A _z, is compared with the longitude-averaged (zonal) magnetic field of the Sun, B _z, derived from series of magnetograms obtained at Mount Wilson Observatory in the years 1964–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. The inferred magnetic field, A _z, exhibits a complex structure distribution of magnetic polarities with respect to latitude and time. Apart from concentration of the different polarity magnetic fields inside the high- and low-latitude portions of the sunspot belts, bipolar active regions produce an intensive, shorter-scale component of the magnetic field which varies on the time scale of about 2 years. Such a short-term variation of A _z reveals substantial correlation with the short-term component of B _z which has the form of the poleward-drifting streams of magnetic field. Most significant correlation takes place between the short-term variations of A _z occurring at latitudes below 20° and those of the large-scale magnetic fields occurring at middle latitudes of 40–50°. Moreover we analyze harmonic coefficients a _l and b _l obtained by expanding A _z and B _z into series in terms of the spherical harmonics. Power spectra of the time-dependent harmonic coefficients indicate that both A _z and B _z reveal a number of resonant modes which oscillate either with the 22-year period in the case of the anti-symmetric (odd-l) modes or with periods of about 2 years in the case of the symmetric (even-l) modes, but the resonant modes of A _z have significantly larger values of the spherical harmonic degree l (and, hence, smaller spatial scales) as compared to those of B _z. It is found that there is a close relationship between the harmonic coefficients b _l and a _m for which either m–l16 (even l=4,...,10) or m–l=4 (odd l=5,...,15).     

The two components in the distribution of sunspot groups with respect to their maximum areas

From an analysis of the distribution of sunspot groups with respect to their maximum areas we find that this distribution consists of two distinct components. One component contributes to spot groups of all possible values of A_* with a distribution density varying as ∼ exp (b₁ á _* ^1/2 ) with b₁ nearly constant from cycleto cycle and having a mean value ∼10^-4 km^-1. The other component is predominantly responsible for spot groups withA* ≲, 30 *10^-6 hemisphere but may provide a few spot groups even above 50 * l0^-6 hemisphere. This component may follow a distribution density ∼ exp (-b₂ A_*). We also determine the widths of the latitude zones over which spot groups in various intervals of A_* appear and study their variation with time. These widths and their variations indicate that the two statistical samples of spot groups may be produced by two families of flux-tube clusters as suggested earlier in a phenomenological model. Very thin flux-tube clusters in the statistical samples seem to be related to the ephemeral active regions and X-ray bright points.     

Variations of 14C around AD 775 and AD 1795 – due to solar activity

The motivation for our study is the disputed cause for the strong variation of ¹⁴C around AD 775. Our method is to compare the ¹⁴C variation around AD 775 with other periods of strong variability. Our results are: (a) We see three periods, where 14C varied over 200 yr in a special way showing a certain pattern of strong secular variation: after a Grand Minimum with strongly increasing ¹⁴C, there is a series of strong short‐term drop(s), rise(s), and again drop(s) within 60 yr, ending up to 200 yr after the start of the Grand Minimum. These three periods include the strong rises around BC 671, AD 775, and AD 1795. (b) We show with several solar activity proxies (radioisotopes, sunspots, and aurorae) for the AD 770s and 1790s that such intense rapid ¹⁴C increases can be explained by strong rapid decreases in solar activity and, hence, wind, so that the decrease in solar modulation potential leads to an increase in radioisotope production. (c) The strong rises around AD 775 and 1795 are due to three effects, (i) very strong activity in the previous cycles (i.e. very low ¹⁴C level), (ii) the declining phase of a very strong Schwabe cycle, and (iii) a phase of very weak activity after the strong ¹⁴C rise – very short and/or weak cycle(s) like the suddenly starting Dalton minimum. (d) Furthermore, we can show that the strong change at AD 1795 happened after a pair of two packages of four Schwabe cycles with certain hemispheric leadership (each package consists of two Gnevyshev‐Ohl pairs, respectively two Hale‐Babcock pairs). We show with several additional arguments that the rise around AD 775 was not that special. We conclude that such large, short‐term rises in ¹⁴C (around BC 671, AD 775, and 1795) do not need to be explained by highly unlikely solar super‐flares nor other rare events, but by extra‐solar cosmic rays modulated due to solar activity variations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Very short-term behaviour of the flare star EV Lac

Sinusoidal variations in Johnson'sB-band of the flare star EV Lac have been confirmed at its quiet state luminosity. The cycle lengths are more than one hour and less than two hours with amplitudes varying from 0 _. ^m 105 to 0 _. ^m 306. These registered cycles have agreed with cycles detected by Mavridis and Varvoglis (1990) and Mavridis (1990). In the same time, the cycles have confirmed the light variation detection in Johnson'sV-band in the same flare star by Pettersen (1980) with a cyclic period equals about 4 _. ^d 378 and an amplitude of about 0 _. ^m 07. Our net results confirm, to some extent, the presence of active region(s) as an origin of stellar flare phenomenon of UV Ceti type flare stars. We can cautiously say that the solar and stellar flare phenomenon have a similar origin.