Long-term variations in sunspot characteristics

Relative variations in the number of sunspots and sunspot groups in activity cycles have been analyzed based on data from the Kislovodsk Mountain Astronomical Station and international indices. The following regularities have been established: (1) The relative fraction of small sunspots decreases linearly and that of large sunspots increase with increasing activity cycle amplitude. (2) The variation in the average number of sunspots in one group has a trend, and this number decreased from ～12 in cycle 19 to ～7.5 in cycle 24. (3) The ratio of the sunspot index (Ri) to the sunspot group number index (G _gr) varies with a period of about 100 years. (4) An analysis of the sunspot group number index (G _gr) from 1610 indicates that the Gnevyshev-Ohl rule reverses at the minimums of secular activity cycles. (5) Ratio of the total area to area of Ssp/Sum nuclei has long-term variation with a period approximately 8 cycles. Minimum ratio falls on 16–17 cycles of activity. (6) It has been indicated that the magnetic field intensity and sunspot area in the current cycle are related to the amplitude of the next activity cycle.     

Synchronism of long-period oscillations of the magnetic field in sunspots

It is shown that long-period (T = 10?C20 h) oscillations of the magnetic field in sunspots, combined in bipolar groups, are excited synchronously in the main and tail spots of a group. At the same time, there is no correlation between long-period oscillations of the field of sunspots which are in different active regions, i.e., spaced sunspots oscillate independently. This fact eliminates the question about the apparatus nature of the oscillations of interest (if there is an artifact, oscillations of all sunspots on the visible solar hemisphere would be synchronous!). High-resolution (0.5 angular seconds per pixel) MDI(SOHO) data show a high correlation between long-period oscillations of the magnetic field at isolated points of the sunspot shadow. This points to the fact that the sunspot shadow participates in long-period oscillations as a quite integral physical formation.     

Prediction of cycle 24 based on information about solar activity during the last 10 000 years

The average and maximal numbers of sunspot groups in the approaching solar cycle (cycle 24) have been predicted using paleoastrophysical information about solar activity during the last more than 10000 years. The linear and nonlinear prediction methods have been applied. It has been indicated that, from the standpoint of solar paleoastrophysics, the next cycle will most probably be average: the number of sunspot groups at a maximum will reach 68–101. The probability that cycle 24 will be powerful (more than 160 sunspot groups), which was predicted by some researchers, is low (not higher than 2%).     

Latitude and Power Characteristics of Solar Activity at the End of the Maunder Minimum

Two important sources of information about sunspots in the Maunder minimum are the Spörer catalog (Spörer, 1889) and observations of the Paris observatory (Ribes and Nesme-Ribes, 1993), which cover in total the last quarter of the 17th and the first two decades of the 18th century. These data, in particular, contain information about sunspot latitudes. As we showed in (Ivanov et al., 2011; Ivanov and Miletsky, 2016), dispersions of sunspot latitude distributions are tightly related to sunspot indices, and we can estimate the level of solar activity in the past using a method which is not based on direct calculation of sunspots and weakly affected by loss of observational data. The latitude distributions of sunspots in the time of transition from the Maunder minimum to the regular regime of solar activity proved to be wide enough. It gives evidences in favor of, first, not very low cycle no.–3 (1712–1723) with the Wolf number in maximum W = 100 ± 50, and, second, nonzero activity in the maximum of cycle no.–4 (1700–1711) W = 60 ± 45. Therefore, the latitude distributions in the end of the Maunder minimum are in better agreement with the traditional Wolf numbers and new revisited indices of activity SN and GN (Clette et al., 2014; Svalgaard and Schatten, 2016) than with the GSN (Hoyt and Schatten, 1998); the latter provide much lower level of activity in this epoch.     

Magnetic field variations in the umbra of single sunspots during their passage across the solar disk

Temporal variations of the maximum (B _max) and average (〈B〉) magnetic inductions, minimum (α _min) and average (〈α〉) inclination angles of the field lines to the radial direction from the center of the Sun, and areas of the sunspot umbra S in the umbra of single sunspots during their passage across the solar disk are investigated. The variation of the properties of single sunspots has been considered at different stages of their existence, i.e., during formation, the “quiet” period, and the disappearance stage. It has been found that, for the majority of the selected single sunspots, there is a positive correlation between B _max and S and between 〈B〉 and S defined at different times during the passage of sunspots across the solar disk. It is shown in this case that the nature of the dependence between the parameters α _min and B _max, α _min and S, as well as between 〈α〉 and 〈B〉, 〈α〉 and S, can vary from sunspot to sunspot, but for many sunspots the inclination angle of the field lines decreases on average with the growth of the sunspot umbra area and the field strength.     

Asymmetry in the form of solar spots

We have analyzed the geometric characteristics of sunspots. The form of sunspots has been studied by sunspot image normalization to obtain the average profile of spots and the profile relative to the position of cores. The deviation of the sunspot form from the axisymmetric configuration has been studied. We have found that the spots of leading and trailing polarities have a drop shape. The cores of leading and trailing sunspots are shifted toward the western and eastern edges of the photosphere–penumbra boundary, respectively. The strength of the magnetic field of the cores of leading spots in the eastern hemisphere exceeds the field strength in the western hemisphere. We considered the tilt of the form of sunspots as a function of size. The form of spots of a large area (S > 1000 ppm of solar hemisphere) is elongated along the magnetic axis of the bipole of a group of sunspots.     

The spatial relationship between active regions and coronal holes and the occurrence of intense geomagnetic storms throughout the solar activity cycle

We study the annual frequency of occurrence of intense geomagnetic storms (Dst < –100 nT) throughout the solar activity cycle for the last three cycles and find that it shows different structures. In cycles 20 and 22 it peaks during the ascending phase, near sunspot maximum. During cycle 21, however, there is one peak in the ascending phase and a second, higher, peak in the descending phase separated by a minimum of storm occurrence during 1980, the sunspot maximum. We compare the solar cycle distribution of storms with the corresponding evolution of coronal mass ejections and flares. We find that, as the frequency of occurrence of coronal mass ejections seems to follow very closely the evolution of the sunspot number, it does not reproduce the storm profiles. The temporal distribution of flares varies from that of sunspots and is more in agreement with the distribution of intense geomagnetic storms, but flares show a maximum at every sunspot maximum and cannot then explain the small number of intense storms in 1980. In a previous study we demonstrated that, in most cases, the occurrence of intense geomagnetic storms is associated with a flaring event in an active region located near a coronal hole. In this work we study the spatial relationship between active regions and coronal holes for solar cycles 21 and 22 and find that it also shows different temporal evolution in each cycle in accordance with the occurrence of strong geomagnetic storms; although there were many active regions during 1980, most of the time they were far from coronal holes. We analyse in detail the situation for the intense geomagnetic storms in 1980 and show that, in every case, they were associated with a flare in one of the few active regions adjacent to a coronal hole.     

Changed relation between sunspot numbers,solar UV/EUV radiation and TSI during the declining phase of solar cycle 23

We study the mutual relation of sunspot numbers and several proxies of solar UV/EUV radiation, such as the F10.7 radio flux, the HeI 1083 nm equivalent width and the solar MgII core-to-wing ratio. It has been noted earlier that the relation between these solar activity parameters changed in 2001/2002, during a large enhancement of solar activity in the early declining phase of solar cycle 23. This enhancement (the secondary peak after the Gnevyshev gap) forms the maximum of solar UV/EUV parameters during solar cycle 23. We note that the changed mutual relation between sunspot numbers and UV/EUV proxies continues systematically during the whole declining phase of solar cycle 23, with the UV/EUV proxies attaining relatively larger values for the same sunspot number than during the several decennia prior to this time. We have also verified this evolution using the indirect solar UV/EUV proxy given by a globally averaged f₀(F2) frequency of the ionospheric F2 layer. We also note of a simultaneous, systematic change in the relation between the sunspot numbers and the total solar irradiance, which follow an exceptionally steep relation leading to a new minimum. Our results suggest that the reduction of sunspot magnetic fields (probably photospheric fields in general), started quite abruptly in 2001/2002. While these changes do not similarly affect the chromospheric UV/EUV emissions, the TSI suffers an even more dramatic reduction, which cannot be understood in terms of the photospheric field reduction only. However, the changes in TSI are seen to be simultaneous to those in sunspots, so most likely being due to the same ultimate cause.     

Relations of latitudinal characteristics of sunspot groups to the 11-year cycle amplitude at different phases

Using sunspot data for cycles 12 to 23, we have investigated relations of some latitude characteristics of sunspot groups to the 11-year cycle amplitude at different phases. We have revealed a high correlation (with correlation coefficients >0.9) between the middle latitude of sunspot groups at phases of rise, maximum, and decay, on the one hand, and the amplitude of the corresponding cycle, on the other hand. We have shown that the maxima of the velocity of the motion of the sunspot formation zone to the equator have a special physical meaning: the rise phase of the 11-year cycle is characterized by significant correlations between the cycle amplitude and the maximum for the lowest boundary, and the cycle decay phase is characterized by the same maximum for the highest boundary. We have built equations allowing one to determine the amplitude of the 11-year cycle on the basis of data on the given latitudinal characteristics of sunspots groups.     

The sunspot cycle and solar and lunar daily variations inH

Summary Results of sunspot cycle influence on solar and lunar ranges at a low latitude station, Alibag, outside the equatorial electrojet belt, show that the sunspot cycle association in solar ranges is three times that of the lunar ranges in thed- andj-seasons. This is in general agreement with the earlier results for non-polar latitude stations. The association with sunspot number of individual lunar amplitudes is greatest for lunar semidiurnal harmonic in thej-season. During this season, the sunspot cycle influence on lunar variations is more than that on solar variations, thereby indicating that the lunar current is situated at a level more favourable for sunspot cycle influence than the level of the current associated with solar variations. With the increase in solar activity a shift appears in the times of maxima of semidiurnal lunar variation towards a later lunar hour ine- andj-seasons and in the year.     

第二十二太阳黑子周特征值预报

太阳活动对地球的影响是人们关心的重要研究课题。太阳黑子相对数作为描述太阳活动的一个参量,虽然不如射电流量密度等参量具有明确的物理意义,但是由于它有较长的观测历史以及在统计上可较好地反映太阳活动的变化,因此在较长期的太阳活动预报等工作中仍是个常用的参量,为有关部门所使用。 将上一个太阳周即第21周的种种预报极值与实际极值165.3比较,可知:一般说     

HSUNSPOTS: A tool for the analysis of historical sunspot drawings

Valuable information about the evolution of solar activity is recorded in early sunspot drawings, especially during 17th–19th centuries. In this context, we have developed a computer program to analyze historical drawings showing the trajectories of sunspots across the solar disk. As an example, we have analysed the drawings published in the book De heliometri structura et usu by Zucconi (1760). These drawings span the period from April 1754 to June 1760. We present the Butterfly diagram for those years. The ending of solar cycle 0 and the beginning of solar cycle 1 are clearly noted in this diagram.     

Transition of solar cycle length in association with the occurrence of grand solar minima indicated by radiocarbon content in tree-rings

In this paper, we review the variation of the 11-year solar cycle since the 15th century revealed by the measurement of radiocarbon content in single-year tree-rings of Japanese cedar trees. Measurements of radiocarbon content in absolutely dated tree-rings provide a calibration curve for accurate dating of archaeological matters, but at the same time, enable us to examine the variations of solar magnetic activity in the pre-historical period. The Sun holds several long-term quasi-cyclic variations in addition to the fundamental 11-year sunspot activity cycle and the 22-year polarity reversal cycle, and it is speculated that the property of the 11-year and the 22-year solar cycle varies in association with such long-term quasi-cycles. It is essential to reveal the details of solar variations around the transition time of solar dynamo for illuminating the mechanisms of the long-term solar variations. We therefore have investigated the property of the 11-year and 22-year cycles around the two grand solar minima; the Maunder Minimum (1645–1715 AD) and the Spoerer Minimum (1415–1534 AD), the periods of prolonged sunspot minima. As a result, slight stretching of the “11-year” and the “22-year” solar cycles was found during these two grand solar activity minima; continuously during the Maunder Minimum and only intermittently during the Spoerer Minimum. On the contrary, normal or slightly shortened 11-year cycles were detected during the interval period of these two minima. It suggests the inverse correlation between the solar cycle length and solar magnetic activity level, and also the change of meridional flow during the grand solar activity minima. Further measurements for the beginning of the grand solar minima will provide a clue to the occurrence of such prolonged sunspot disappearance. We also discuss the effect of solar variations to radiocarbon dating.     

Properties of the sunspot latitudinal distribution skewness

The properties of the sunspot latitudinal distributions related to skewness have been studied based on the data of the extended Greenwich catalog for 1874–2011. The results of the performed analysis indicate that a significant skewness is present in most annual latitudinal distributions of the sunspot index. In this case, the distribution skewness increases near the 11-year cycle maximum phase. An increase in the sunspot group number is also accompanied by an increase in skewness. In particular, when the sunspot index is large, the number of groups located below midlatitudes is mostly larger than the number of groups above these latitudes and this imbalance increases with increasing total sunspot activity level. In medium and large 11-year cycles, the average distribution skewness for a cycle is always positive and its value is related to the cycle amplitude. This results agree with the theoretical models of the 11-year cycle, where the specific features of the low-latitude meridional circulation are related to the sunspot activity level.     

Solar dynamo and geomagnetic activity

The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity peaks are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field and back. We find that in the last 12 cycles the solar surface meridional circulation varied between 5 and 20 m/s (averaged over latitude and over the sunspot cycle), the deep circulation varied between 2.5 and 5.5 m/s, and the diffusivity in the whole of the convection zone was ～10⁸ m²/s. In the last 12 cycles solar dynamo has been operating in moderately diffusion dominated regime in the bulk of the convection zone. This means that a part of the poloidal field generated at the surface is advected by the meridional circulation all the way to the poles, down to the tachocline and equatorward to sunspot latitudes, while another part is diffused directly to the tachocline at midlatitudes, “short-circuiting” the meridional circulation. The sunspot maximum is the superposition of the two surges of toroidal field generated by these two parts of the poloidal field, which is the explanation of the double peaks and the Gnevyshev gap in sunspot maximum. Near the tachocline, dynamo has been operating in diffusion dominated regime in which diffusion is more important than advection, so with increasing speed of the deep circulation the time for diffusive decay of the poloidal field decreases, and more toroidal field is generated leading to a higher sunspot maximum. During the Maunder minimum the dynamo was operating in advection dominated regime near the tachocline, with the transition from diffusion dominated to advection dominated regime caused by a sharp drop in the surface meridional circulation which is in general the most important factor modulating the amplitude of the sunspot cycle.     

Prediction of sunspot number amplitude and solar cycle length for cycles 24 and 25

The prediction of solar activity strength for solar cycles 24 and 25 is made on the basis of extrapolation of sunspot number spectral components. Monthly sunspot number data during the 1850–2007 interval (solar cycles 9–23) are decomposed into several levels and searched for periodicities by iterative regression in each level. For solar cycle 24, the peak is predicted in November 2013 with a sunspot number of 113.3. The cycle is expected to be weak, with a length of 133 mo (months) or 11.1 yr. The sunspot number maximum in cycle 25 is predicted to occur in April 2023 with a sunspot number 132.1 and a solar cycle length of 118 mo or 9.8 yr. Thus, solar cycle 24 is predicted to have an intensity 23% lower than cycle 23, and cycle 25 will be 5% lower than cycle 23.     

An attempt to the explanation and to the prediction of the eleven-year cycle of solar activity

Summary According to the author the reason of the subsistence of the 11 years' sunspot cycle is to be found in the conjunction of the planets. As a result of the investigations it has been stated that from among the nine planets the joint tidal effect of Venus-Jupiter-Earth is a decisive factor in the variations of sunspot activity. The above three planets are every 10.4 years and 12.0 years respectively, in a close conjunction. The mean value (11.2 years) is in an almost full accordance with the average cycle-period. The fluctuations of the period of the cycle come from the fact that the planets' getting into approximately one line takes a different time within each cycle. This time delay is the cause of the stronger or weaker sunspot activity, and of the shorter or longer cycles.     

强磁暴的时间分布特性

对比分析1957--2008年间Dst≤-100nT的强磁暴数与太阳黑子数的变化趋势,发现太阳黑子数和Dst≤-100nT的强磁暴数的变化趋势有很好的一致性。进一步统计强磁暴在太阳周不同阶段的分布后发现,同一太阳周内60％以上的强磁暴出现在下降年,但从太阳周各个阶段的平均磁暴年发生率来看,强磁暴平均年发生率最高的年份仍然是太阳活动极大年。     

The sunspot cycle, the QBO, and the total ozone over Northeastern Europe: a connection through the dynamics of stratospheric circulation

The interaction between the factors of the quasi-biennial oscillation (QBO) and the 11-year solar cycle is considered as an separate factor influencing the interannual January–March variations of total ozone over Northeastern Europe. Linear correlation analysis and the running correlation method are used to examine possible connections between ozone and solar activity at simultaneous moment the QBO phase. Statistically significant correlations between the variations of total ozone in February and, partially, in March, and the sunspot numbers during the different phases of QBO are found. The running correlation method between the ozone and the equatorial zonal wind demonstrates a clear modulation of 11-y solar signal for February and March. Modulation is clearer if the QBO phases are defined at the level of 50 hPa rather than at 30 hPa. The same statistical analyses are conducted also for possible connections between the index of stratospheric circulation C₁ and sunspot numbers considering the QBO phase. Statistically significant connections are found for February. The running correlations between the index C₁ and the equatorial zonal wind show the clear modulation of 11-y solar signal for February and March. Based on the obtained correlations between the interannual variations of ozone and index C₁, it may be concluded that a connection between solar cycle – QBO – ozone occurs through the dynamics of stratospheric circulation.     

Manifestation of 22-year solar magnetic cycle in the imbalance between positive and negative photospheric magnetic fluxes

Time variations in strong and weak photospheric magnetic fields have been considered based on synoptic maps from the Kitt Peak observatory for 1976?C2003. The magnetic fields of positive and negative polarities of the Northern and Southern hemispheres of the Sun and their imbalance were studied. It has been indicated that different groups of magnetic fields vary with 11-or 22-year periods depending on their values. The difference between positive and negative fluxes for each hemisphere always varies with a 22-year period. For weak fields, the 22-year cycle is related to the manifestation of the global solar magnetic field. For strong fields, the imbalance between positive and negative fluxes reflects the predominant role of leading sunspots in a given solar hemisphere. It has been detected that the total magnetic flux over the entire solar disk varies with an 11-year period in antiphase with the solar activity cycle for the weakest magnetic fields (0?C5 G).