Systematic Time Delay of Hemispheric Solar Activity

Five solar-activity indices – the monthly-mean sunspot numbers from January 1945 to March 2008, the monthly-mean sunspot areas during the period of May 1874 to March 2008, the monthly numbers of sunspot groups from May 1874 to May 2008, the monthly-mean flare indices from January 1966 to December 2006, and the numbers of solar filaments per Carrington rotation in the time interval of solar rotations 876 to 1823 – have been used to show a systematic time delay between northern and southern hemispheric solar activities in a cycle. It is found that solar activity does not occur synchronously in the northern and southern hemispheres, and there is a systematic time lag or lead (phase shift) between northern and southern hemispheric solar activity in a cycle. About an eight-cycle period is inferred to exist in such phase shifts. The activity on the Sun may be governed by two different and coupled processes, not by a single process.     

Periodicity of Total Solar Irradiance

We investigate the periodicity in the PMOD composite of the daily total solar irradiance (TSI) from 21 September 1978 to 9 June 2009. Besides the Schwabe cycle period (10.32 years), the quasi-rotation period is found to be statistically significant in TSI, whose value is about 32 days, longer than that in sunspot activity (27 days), and it intermittently appears around the sunspot maximum times. The quasi-rotation period in TSI is inferred to be mainly caused by sunspot activity, but to be modulated by bright features as well. It was previously found that variations of TSI over a Schwabe solar cycle mainly come from the combination of the sunspots’ blocking and the intensification due to bright faculae, plages, and network elements, with a slight dominance of the bright-feature effect during the maximum of the Schwabe cycle. For the sunspot-blocking and the bright-feature effect to contribute to TSI over a Schwabe solar cycle, the former is inferred to lead the latter by 29 days at least.     

Study of Multiple Coronal Mass Ejections at Solar Minimum Conditions

Solar activity alternates between active and quiet phases with an average period of 11?years, and this is known as the Schwabe cycle. Additionally, solar activity occasionally falls into a prolonged quiet phase (grand solar minimum), as represented by the Maunder Minimum in the 17th century, when sunspots were almost absent for 70?years and the length of the Schwabe cycle increased to 14?years. To examine the consistency of the cycle length characteristics during the grand solar minima, the carbon-14 contents in single-year tree rings were measured using an accelerator mass spectrometer as an index of the solar variability during the grand solar minimum of the 4th century BC. The signal of the Schwabe cycle was detected with a statistical confidence level of higher than 95?% by wavelet analysis. This is the oldest evidence for the Schwabe cycle at the present time, and the cycle length is considered to have increased to approximately 16?years during the grand solar minimum of the 4th century BC. This result confirms the association between the increase of the Schwabe cycle length and the weakening of solar activity, and indicates the possible prolonged absence of sunspots in the 4th century BC as during the Maunder Minimum. Theoretical implications from solar dynamo theory are discussed in order to identify the trigger of prolonged sunspot absence. A possible association between the long-term solar variation around the 4th century BC and terrestrial cooling in this period is also discussed.     

Starspots, Activity Cycles, and Differential Rotation on Cool Stars

We present the first results of searching for stellar cycles by analysis of stellar spottedness using an algorithm developed at the Crimean Astrophysical Observatory. For more than 35 red spotted stars, we find ten targets which demonstrate cyclic variations of average latitudes and total areas of starspots. Activity cycles detected by this method have a typical cycle length about 4–15 years which are analogous to the 11-year solar Schwabe cycle. Most of the program stars demonstrate a rough analogue with the solar butterfly diagram. They show a tendency for the average starspot latitude lowering when the total spot area grows. At the same time these stars show variations of stellar photometric period (which is traced by starspots) with the starspot latitudinal drift analogously to the solar differential rotation effect. We suspect that the starspot latitudinal drift rate and the differential rotation gradient depend on the stellar spectral type.     

Secular acceleration of solar rotation from 1943 to 1986

The rotation of the surface layer of the Sun is found to have been accelerated secularly from the sunspot data of 1943 to 1986. To represent the overall state of rotation of the differentially rotating Sun, we define an indexM, by integrating the angular momentum density over the whole surface of the Sun, and call it the angular momentum layer density. The indexM increased monotonically or secularly from 1943 to 1986. This period corresponds to solar cycles 18, 19, 20, and 21. The monotonic increase ofM indicates that a net angular momentum must have steadily been coming from the layer down below the surface. The differential rotation latitudinal dependence profile did not change much from cycle 18 to cycle 20, but at cycle 21 the degree of equatorial acceleration dropped. This aspect is discussed in the context of the 55-year grand cycle. Cycle 21 is the start of grand cycle VI. The latitudinal dependence is less steep at cycle 21. The time scale of secular change of the indexM reflects the time scale of change of linkage of the surface and the deep layer in form of the angular momentum transfer, and that the time scale of the profile change of the differential rotation reflects the time scale of the angular momentum transfer within the surface layer.     

Solar Rotation And Cycle Length

A positive correlation is suggested between solar rotation rate and solar cycle length for cycles 12 to 20. This result seems to be opposite to recent observations in solar-type stars and the Sun and yields inverse correlations between cycle lengths and chromospheric activity, but it agrees with previous work with solar-type stars and the Sun suggesting a positive correlation between cycle length and rotation rate. Estimates of solar cycle length for the Maunder minimum suggest a length 17 yr.     

Multi-timescale solar cycles and the possible implications

Based on analysis of the annual averaged relative sunspot number (ASN) during 1700–2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4, respectively since 1700); and 51.5-yr Cycle. From similarities, an extrapolation of forthcoming solar cycles is made, and found that the solar cycle 24 will be a relative long and weak Schwabe cycle, which may reach to its apex around 2012–2014 in the vale between G3 and G4. Additionally, most Schwabe cycles are asymmetric with rapidly rising-phases and slowly decay-phases. The comparisons between ASN and the annual flare numbers with different GOES classes (C-class, M-class, X-class, and super-flare, here super-flare is defined as ≥ X10.0) and the annal averaged radio flux at frequency of 2.84 GHz indicate that solar flares have a tendency: the more powerful of the flare, the later it takes place after the onset of the Schwabe cycle, and most powerful flares take place in the decay phase of Schwabe cycle. Some discussions on the origin of solar cycles are presented.     

A Standard Law for the Equatorward Drift of the Sunspot Zones

The latitudinal location of the sunspot zones in each hemisphere is determined by calculating the centroid position of sunspot areas for each solar rotation from May 1874 to June 2011. When these centroid positions are plotted and analyzed as functions of time from each sunspot cycle maximum, there appear to be systematic differences in the positions and equatorward drift rates as a function of sunspot cycle amplitude. If, instead, these centroid positions are plotted and analyzed as functions of time from each sunspot cycle minimum, then most of the differences in the positions and equatorward drift rates disappear. The differences that remain disappear entirely if curve fitting is used to determine the starting times (which vary by as much as eight months from the times of minima). The sunspot zone latitudes and equatorward drift measured relative to this starting time follow a standard path for all cycles with no dependence upon cycle strength or hemispheric dominance. Although Cycle 23 was peculiar in its length and the strength of the polar fields it produced, it too shows no significant variation from this standard. This standard law, and the lack of variation with sunspot cycle characteristics, is consistent with dynamo wave mechanisms but not consistent with current flux transport dynamo models for the equatorward drift of the sunspot zones.     

Forty years of measurements of the mean magnetic field of the Sun: View from today

During the last 40 years, the Crimean Astrophysical Observatory and five other observatories around the world have carried out more than 18 500 (daily) measurements of the mean magnetic field (MMF) of the Sun as a star. The main MMF periodicity is due to the equatorial rotation of the Sun with a synodic period of 26.92 ± 0.02 day (it was stable for decades, but “bifurcated” in the 23rd cycle). It is shown that (a) the average sidereal period of the equator, 25.122 ± 0.010 day, is in close resonant relations with orbital and axial rotations of Mercury (5: 2 and 5: 3, respectively); (b) the most powerful long period, 1.036 ± 0.007 years, is suspiciously close to the orbital period of the Earth and (c) coincides with the average synodic period of revolution of giant planets 1.036 ± 0.020 years; and (d) MMF reveals a significant period of 1.58 ± 0.02 years, which agrees, within errors, with the synodic period of Venus (1.60 years), and (e) a significant periodicity of 19.8 ± 2.5 years probably related to the 22-year magnetic cycle of the Sun. The nature of all these periodicities is mysterious.The assumption is made that the resonances originated at the early stages of formation of the Solar System, and their existence in the modern epoch is due to the specific features of the structure and dynamics of the central core of our star. It is found that the MMF level averaged over 40 years is practically zero, ?0.018 ± 0.015 G. The anomalous behavior of the 23rd cycle is pointed out; this is expressed in (1) violation of the Gnevyshev-Ohl rule for the pair of cycles 22–23, (2) accelerated rotation of the solar equator by 1.2%, and (3) considerable increase in the cycle duration (not smaller than 11.5 years), as compared to the average cycle duration in the 20th century (11.5 years). The problem of the so called magnetic “monopole” of the Sun is briefly discussed.     

A Relationship Between the Solar Rotation and Activity Analysed by Tracing Sunspot Groups

The sunspot position published in the data bases of the Greenwich Photoheliographic Results (GPR), the US Air Force Solar Optical Observing Network and National Oceanic and Atmospheric Administration (USAF/NOAA), and of the Debrecen Photoheliographic Data (DPD) in the period 1874 to 2016 were used to calculate yearly values of the solar differential-rotation parameters \(A\) and \(B\). These differential-rotation parameters were compared with the solar-activity level. We found that the Sun rotates more differentially at the minimum than at the maximum of activity during the epoch 1977?–?2016. An inverse correlation between equatorial rotation and solar activity was found using the recently revised sunspot number. The secular decrease of the equatorial rotation rate that accompanies the increase in activity stopped in the last part of the twentieth century. It was noted that when a significant peak in equatorial rotation velocity is observed during activity minimum, the next maximum is weaker than the previous one.     

Angular velocity during the cycle deduced using the sunspot group age selection methodology

We have used the “age selection methodology” (ASM) (Zappalá and Zuccarello 1991) to study the variability of the sunspot groups angular velocity during the activity cycle. The ASM allows us to separate the contribution of Young Sunspot Groups (YSG) from that of Recurrent ones (RSG) in the Ω(θ) determination and therefore to evaluate whether the increase in angular velocity during minima (reported in literature using all sunspot groups as tracers), is due to a greater statistical weight of YSG on RSG or whether it reflects a global characteristic of the Sun. The results obtained from the analysis of sunspot groups data collected during the period 1874‐1981 (Greenwich Photoheliographic Results) indicate that during minima, besides the fact that the percentage of RSG drops to ≤ 5%, both YSG and RSG show the same increase in angular velocity, i.e. 0.16 degrees/day. Comparing our results with those reported in literature and taking into account the internal angular velocity as deduced by p‐mode oscillations, it is possible to conclude that the observed higher angular velocity of the Sun during minima concerns several layers of the Sun.     

Non-Axisymmetric Magnetic Fields and Flip-Flops on the Sun and Cool Stars

The modulation of solar activity closely follows the solar rotation period suggesting the existence of long-lived active regions at preferred longitudes. For instance, two preferred active longitudes in both southern and northern hemispheres are found to be persistent at the century time scale. These regions migrate with differential rotation and periodically alternate their activity levels showing a flip-flop cycle. The pattern and behaviour of active longitudes on the Sun is similar to that on cool, rapidly rotating stars with outer convective envelopes. This suggests that the magnetic dynamo, including non-axisymmetric magnetic fields and flip-flop cycles, is also similar in these stars. This allows us to overview the phenomenon of stellar magnetic activity and to study it in detail on the Sun.     

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.     

Determination of the Rotation Periods of Solar Active Longitudes

There are two types of active longitudes (ALs) in terms of the distribution of sunspot areas: long-lived and intra-cyclic ALs. The rotation period of the long-lived ALs has been determined by a new method in this paper. The method is based on the property of ALs to be maintained over several cycles of solar activity. The daily values of sunspot areas for 1878 – 2005 are analyzed. It is shown that the AL positions remain almost constant over a period of about ten cycles, from cycle 13 to cycle 22. The rotation period was found to be 27.965 days during this period. The dispersion in AL positions is about 26° from cycle to cycle, which is half of the dispersion observed in the Carrington system. The ALs in the growth phase of the activity cycle are more stable and pronounced. The excess in solar activity in the ALs over adjacent longitudinal intervals is about 12 – 14%. It is shown that only one long-lived AL can be observed at one time on the Sun, as a rule.     

The 27-Day Cosmic Ray Intensity Variations During Solar Minimum 23/24

We have studied the 27-day variations and their harmonics in Galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components during the recent prolonged solar minimum 23/24. The time evolution of the quasi-periodicity in these parameters connected with the Sun’s rotation reveals that the synodic period of these variations is ≈?26?–?27 days and is stable. This means that the changes in the solar wind speed and the IMF are related to the Sun’s near-equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earth’s orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within ±?7^° in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Sun’s rotation increased up to ≈?33?–?36 days in 2009. This means that the process that drives the 27-day GCR intensity variations takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period (≈?34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Sun’s differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day GCR intensity variations.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

On midrange periodicities in solar radio flux and sunspot areas

Using the Hilbert-Huang transform technique, we investigate the midrange periodicities in solar radio flux at 2800 MHz (F10.7) and sunspot areas (SAs) from February 1, 1947 to September 30, 2016. The following prominent results are found: (1) The quasi-periodic oscillations of both data sets are not identical, such as the rotational cycle, the midrange periodicities, and the Schwabe cycle. In particular, the midrange periodicities ranging from 37.9 days to 297.3 days are related to the magnetic Rossby-type waves; (2) The 1.3-year and 1.7-year fluctuations in solar activity indicators are surface manifestations (from photosphere to corona) of magnetic flux changes generated deep inside the Sun; (3) At the timescale of the Schwabe cycle, the complicated phase relationships in the three intervals (1947–1958, 1959–1988, and 1989–2016) agree with the produced periodicities of the magnetic Rossby-type waves. The findings indicate that the magnetic Rossby-type waves are the possible physical mechanism behind the midrange periodicities of solar activity indicators. Moreover, the significant change in the relationship between photospheric and coronal activity took place after the maximum of solar cycle 22 could be interpreted by the magnetic Rossby-type waves.     

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).     

Magnetic Evolution and the Disappearance of Sun-Like Activity Cycles

After decades of effort, the solar activity cycle is exceptionally well characterized, but it remains poorly understood. Pioneering work at the Mount Wilson Observatory demonstrated that other Sun-like stars also show regular activity cycles, and suggested two possible relationships between the rotation rate and the length of the cycle. Neither of these relationships correctly describes the properties of the Sun, a peculiarity that demands explanation. Recent discoveries have started to shed light on this issue, suggesting that the Sun’s rotation rate and magnetic field are currently in a transitional phase that occurs in all middle-aged stars. Motivated by these developments, we identify the manifestation of this magnetic transition in the best available data on stellar cycles. We propose a reinterpretation of previously published observations to suggest that the solar cycle may be growing longer on stellar evolutionary timescales, and that the cycle might disappear sometime in the next 0.8?–?2.4 Gyr. Future tests of this hypothesis will come from ground-based activity monitoring of Kepler targets that span the magnetic transition, and from asteroseismology with the Transiting Exoplanet Survey Satellite (TESS) mission to determine precise masses and ages for bright stars with known cycles.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.