Meridional Motions and Reynolds Stress Determined by Using Kanzelhöhe Drawings and White Light Solar Images from 1964 to 2016

Sunspot position data obtained from Kanzelhöhe Observatory for Solar and Environmental Research (KSO) sunspot drawings and white light images in the period 1964 to 2016 were used to calculate the rotational and meridional velocities of the solar plasma. Velocities were calculated from daily shifts of sunspot groups and an iterative process of calculation of the differential rotation profiles was used to discard outliers. We found a differential rotation profile and meridional motions in agreement with previous studies using sunspots as tracers and conclude that the quality of the KSO data is appropriate for analysis of solar velocity patterns. By analyzing the correlation and covariance of meridional velocities and rotation rate residuals we found that the angular momentum is transported towards the solar equator. The magnitude and latitudinal dependence of the horizontal component of the Reynolds stress tensor calculated is sufficient to maintain the observed solar differential rotation profile. Therefore, our results confirm that the Reynolds stress is the dominant mechanism responsible for transport of angular momentum towards the solar equator.     

Meridional Motion and Reynolds Stress from Debrecen Photoheliographic Data

The Debrecen Photoheliographic Data catalogue is a continuation of the Greenwich Photoheliographic Results providing daily positions of sunspots and sunspot groups. We analyse the data for sunspot groups focussing on meridional motions and transfer of angular momentum towards the solar equator. Velocities are calculated with a daily shift method including an automatic iterative process of removing the outliers. Apart from the standard differential rotation profile, we find meridional motion directed towards the zone of solar activity. The difference in measured meridional flow in comparison to Doppler measurements and some other tracer measurements is interpreted as a consequence of different flow patterns inside and outside of active regions. We also find a statistically significant dependence of meridional motion on rotation velocity residuals confirming the transfer of angular momentum towards the equator. Analysis of horizontal Reynolds stress reveals that the transfer of angular momentum is stronger with increasing latitude up to about \(40^{\circ}\), where there is a possible maximum in absolute value.     

Solar Variability Induced in a Dynamo Code by Realistic Meridional Circulation Variations

In this work we use an already-published method to infer a variation profile for the solar meridional circulation over the last 250 years. We feed this variation profile into a numerical dynamo code, and we reconstruct a sunspot time series that acts as a proxy for solar cycle activity. We perform three simulations with slightly different parameters, and the results are compared with the observational data. The medium and large correlation coefficients between reconstructed and observational time series seem to indicate that variations in meridional circulation play an important role in the modulation of solar activity.     

Meridional motions of sunspot groups during eleven activity cycles

Greenwich data (1874–1976) are used for a time-dependent analysis of meridional motions of sunspot groups. We obtain the latitude-dependence of meridional motions of sunspot groups with respect to a mean latitude determined for half-year intervals. The daily meridional motions of groups are also given separately for growing and decaying sunspot groups. The development is determined from changes of sunspot areas. Our results are compared with the reductions performed by Howard (1991b) using the Mt. Wilson sunspot data from 1917 until 1985: Although we have smaller errors, we do not find any significant drift. We also do not find different trends in the meridional motions of growing as compared to decreasing sunspots.     

Differential Rotation of Stable Recurrent Sunspot Groups

Stable recurrent sunspot groups from the Greenwich data set which were identified in at least two subsequent solar rotations were traced. The solar rotation was determined by the period method from the time difference of the two central meridian passages of each of the 327 identified groups. Sidereal rotation periods were calculated from the synodic ones by a seasonal-dependent procedure taking into account the details of the Earth's motion around the Sun. Growing recurrent sunspot groups rotate on the average faster than decaying recurrent sunspot groups, while sunspot groups of all types taken together rotate faster than both growing and decaying recurrent sunspot groups. A north–south rotational asymmetry and a cycle-dependence of rotational velocity of recurrent sunspot groups were analyzed. Positive rotation velocity deviations are larger, but less numerous than the negative ones. Signatures of torsional oscillations were not found analyzing the rotation velocity residual of recurrent sunspot groups as a function of the distance from the average latitude of activity.     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

Double maxima of 11-year solar cycles

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ?ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ?ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ?ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.     

Prograde and Retrograde Waves in Sunspot Eruption Patterns with Longitudinal Velocities of ∼30 – 75 m s−1

Sunspots are discrete objects in the background magnetic activity on the Sun. Their individual proper motions are partially influenced by both the differential rotation of the Sun’s outer envelope and the meridional flows toward the equator and poles, but their collective behavior is more complex, suggesting other forces at work. Previous examinations of long-term sunspot patterns revealed longitudinal clusters (nests) with apparent stability over a few Carrington rotations (CRs) but with drifts, 180° shifts, and apparent standing-wave patterns over longer periods. Evidence is presented in this report that slowly moving prograde and retrograde waves characterize the eruption patterns of sunspot groups over a several-year period in the middle of each 11-year sunspot cycle. Making use of modified stackplots with the dimensions of longitude and time, the sunspot eruptions that occur in both hemispheres within the same windows of latitude, longitude, and CR are selected for examination. A convolution method, based on an adaptive function, is developed to enhance and display the trajectories occurring through space and time. Examples are provided from different solar cycles to demonstrate the general nature of the phenomenon. A linear relationship is observed between wave velocity and maximum magnitude of the sunspot index of the past 12 solar cycles. Overall, the trajectories suggest longitudinal traveling waves that appear to interact in a manner similar to solitons, suggesting that they originate from nonlinear dynamics affecting the appearance of flux tubes at the solar surface. These bidirectional traveling waves, and their collisions, also explain the recently described evidence for standing waves observed in surface spherical harmonic analysis of sunspot patterns.     

The Influence of the Evolution of Sunspot Groups on the Determination of the Solar Velocity Field

Meridional motions and differential rotation of stable recurrent sunspot groups from the Greenwich data set are investigated. Simple and complex, as well as younger and older sunspot groups are treated separately. There is no difference in behavior of the meridional motions for the simple and complex sunspot groups, while complex groups rotate faster than the simple ones. If we attribute the differences of rotational velocities to the errors in position determination, it can be concluded that the rotational velocities determined by using sunspot groups as tracers are slightly overestimated. Both the meridional motions and differential rotation show the same dependence on the age, when simple and complex recurrent sunspot groups are considered. Alexander von Humboldt Research Fellow.     

22周上升相日面各经度带的活动规律

本文回顾了１９８３年以来一些对太阳活动的谱分析结果。大致可分为两种规律：在太阳活动１１年周期的上升相一般呈现８０天左右的周期。下降相呈现１５０天左右的周期。这些规律均是由太阳全日面总体活动指数得到的谱分析结果。文中将第２２周上升段（１９８７．１．１—１９８８．７．３１）的太阳黑子群和Ｘ射线耀斑按经度带作了极大熵谱估计。结果表明，各经度带的活动规律不同，同一经度带内，太阳黑子群和Ｘ射线耀斑的出现规律也不尽相同。这种将事件按经度带分布得到的活动规律对事件本身的中期预报将会有实际应用价值。     

One Possible Reason for Double-Peaked Maxima in Solar Cycles: Is a Second Maximum of Solar Cycle 24 Expected?

We investigate solar activity by focusing on double maxima in solar cycles and try to estimate the shape of the current solar cycle (Cycle 24) during its maximum. We analyzed data for Solar Cycle 24 by using Learmonth Solar Observatory sunspot-group data collected since 2008. All sunspot groups (SGs) recorded during this time interval were separated into two groups: The first group includes small SGs [A, B, C, and H classes according to the Zurich classification], the second group consists of large SGs [D, E, and F]. We then calculated how many small and large sunspot groups occurred, their sunspot numbers [SSN], and the Zurich numbers [Rz] from their daily mean numbers as observed on the solar disk during a given month. We found that the temporal variations for these three different separations behave similarly. We also analyzed the general shape of solar cycles from Cycle 1 to 23 by using monthly International Sunspot Number [ISSN] data and found that the durations of maxima were about 2.9 years. Finally, we used the ascending time and SSN relationship and found that the maximum of Solar Cycle 24 is expected to occur later than 2011. Thus, we conclude that i) one possible reason for a double maximum in solar cycles is the different behavior of large and small sunspot groups, and ii) a double maximum is expected for Solar Cycle 24.     

A new interpretation of Christian Horrebow''s sunspot observations from 1761 to 1777

Christian Horrebow and his colleagues of Copenhagen, Denmark, actively observed sunspots from 1761 to 1777. These observations were examined by Thiele in 1859 and by d'Arrest in 1873 with markedly different conclusions. Thiele reported nearly twice as many sunspot groups as d'Arrest. To resolve this discrepancy, we have reexamined Horrebow's original notebooks. We find slightly more sunspot groups then did d'Arrest. Thiele apparently called individual sunspots sunspot groups, so he would call a bipolar group two groups. d'Arrest seems to have missed counting some of the smaller sunspot groups. A correct interpretation of Horrebow's observations is required in efforts to reconstruct solar activity. Wolf gave a sunspot number for 1769 of 106.1. On the basis of our re-examination of Horrebow's drawings and other observers, we deduce a sunspot number of about 80.5 for 1769.     

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.     

Sunspot Positions and Areas from Observations by Galileo Galilei

Sunspot records in the seventeenth century provide important information on the solar activity before the Maunder minimum, yielding reliable sunspot indices and the solar butterfly diagram. Galilei’s letters to Cardinal Francesco Barberini and Marcus Welser contain daily solar observations on 3?–?11 May, 2 June?–?8 July, and 19?–?21 August 1612. These historical archives do not provide the time of observation, which results in uncertainty in the sunspot coordinates. To obtain them, we present a method that minimizes the discrepancy between the sunspot latitudes. We provide areas and heliographic coordinates of 82 sunspot groups. In contrast to Sheiner’s butterfly diagram, we found only one sunspot group near the Equator. This provides a higher reliability of Galilei’s drawings. Large sunspot groups are found to emerge at the same longitude in the northern hemisphere from 3 May to 21 August, which indicates an active longitude.     

Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavelet Analysis of the Schwabe Cycle Properties in Solar Activity

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14-year. We make the comparison of 11-year‘s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.     

Automatic Detection of Sunspots and Extractionof Their Feature Parameters

Sunspots are solar features located in active regions of the Sun, whose number is an indicator of the Sun's magnetic activity. With a substantial increase in the quantity of solar image data, the automated detection and verification of various solar features have become increasingly important for the accurate and timely forecasts of solar activity and space weather. In order to use the high time-cadence SDO/HMI data to extract the main sunspot features for forecasting solar activities, we have established an automatic detection method of sunspots based on mathematical morphology, and calculated the sunspot group area and sunspot number. By comparing our results with those obtained from the Solar Region Summary compiled by NOAA/SWPC, it is found that the sunspot group areas and sunspot numbers computed with our algorithm are in good agreement with the active region values released by SWPC, and the corresponding correlation coefficients for the sunspot group area and sunspot number are 0.77 and 0.79, respectively. By using the method of this paper, the high time-cadence feature parameters can be obtained from the HMI data to provide the timely and accurate inputs for the solar activity forecast.     

太阳活动区活动性的模糊预测

运用模糊数学的理论和方法对太阳活动区的活动性进行了预测。为了综合评估和预测活动区的活动性，根据耀斑与黑子群特征因子间的关系，构造了隶属函数。通过数据处理与分析，得到了对活动区活动性较好的预测结果，预测的准确性＞95%。已成功编制了太阳活动预报的数据处理实用软件，根据黑子群的特征因子值，即刻就能得到活动区活动性的预报结果，预测结果表明模糊综合评估方法能很好地预报太阳活动。     

Statistical behavior of sunspot groups on the solar disk

In the present study we have produced a diagram of the latitude distribution of sunspot groups from the year 1874 through 1999 and examined statistical characteristics of the mean latitude of sunspot groups. The reliability of the observed data set prior to solar cycle 19 is found quite low as compared with that of the data set observed after cycle 19. A correlation is found between maximum latitude at which first sunspot groups of a new cycle appear and the maximum solar activity of the cycle. It is inferred that solar magnetic activity during the early part of an extended solar cycle may contain some information about the strength of forthcoming solar cycle. A formula is given to describe latitude change of sunspot groups with time during an extended solar cycle. The latitude-migration velocity is found to be largest at the beginning of solar cycle and decreases with time as the cycle progresses with a mean migration velocity of about 1.61° per year.     

New Evidence for Long-Term Persistence in the Sun's Activity

Possible persistence of sunspot activity was studied using rescaled range and detrended fluctuation analyses. In addition to actual Wolf numbers (1700–2000 A.D.), two solar proxies were used in this research, viz., an annual sunspot proxy obtained for 1090–1700 A.D. and sunspot numbers reconstructed from the decadal radiocarbon series (8005 B.C. – 1895 A.D). The reconstruction was made using a five-box carbon exchange model. Analyses showed that in all cases the scaling exponent is significantly higher than 0.5 in the range of scales from 25 yr up to 3000 yr. This indicates the existence of a long-term memory in solar activity, in agreement with results obtained for other solar indices.