Digitization of Sunspot Drawings by Staudacher in 1749 – 1796

Original drawings by J.C. Staudacher made in the period of 1749 – 1796 were digitized. The drawings provide information about the size of the sunspots and are therefore useful for analyses sensitive to sunspot area rather than Wolf numbers. The total sunspot area as a function of time is shown for the observing period. The sunspot areas measured do not support the proposition of a weak, “lost” cycle between cycles 4 and 5. We also evaluate the usefulness of the drawings for the determination of sunspot positions for future studies.     

The Butterfly Diagram in the Eighteenth Century

Digitized images of the drawings by J.C. Staudacher were used to determine sunspot positions for the period 1749 – 1796. From the entire set of drawings, 6285 sunspot positions were obtained for a total of 999 days. Various methods have been applied to find the orientation of the solar disk, which is not given for the vast majority of the drawings by Staudacher. Heliographic latitudes and longitudes in the Carrington rotation frame were determined. The resulting butterfly diagram shows a highly-populated Equator during the first two cycles (cycles 0 and 1 in the usual counting since 1749). An intermediate period is cycle 2, whereas cycles 3 and 4 show a typical butterfly shape. A tentative explanation may be the transient dominance of a quadrupolar magnetic field during the first two cycles.     

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.     

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.     

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.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

Sunspot Positions and Areas from Observations by Pierre Gassendi

Solar activity behaviour on the eve of the Maunder minimum may provide important information on the period of further suppression of sunspot population. We analyse sunspot positions and areas in the 1630s extracted from rare drawings published by Pierre Gassendi in Opera Omnia. This work was published in two different editions, the first in Lyon and the second almost 70 years later in Florence. The drawings published in Lyon are found to be slightly different from those published in Florence, which produces a discrepancy in the position of spots of a few degrees, while sunspot group areas may differ by a factor of two. We reveal that the orientation of the drawings in the book is not always the same as might be seen in the telescope. We conjecture that the time of Gassendi’s observations covers the beginning of a new Schwabe cycle in the southern hemisphere. The differential rotation rate in the 1630s is also assessed and discussed.     

Longitudinal and temporal variations of sunspot regions and coronal holes during Cycle 21

The relationship between sunspot activity in heliographic longitude and coronal holes is investigated for the period corresponding to Cycle 21 (Carrington rotations 1623–1779). The major result is that, based on He i 10830 Å data, a strong inverse association is found between the longitudinal positions of sunspot groups and the size and number of coronal holes (especially, the equatorial extensions of polar holes). Frequencies of coincidences in longitude were determined for both types of activity and the evolution of coronal holes over Cycle 21 is depicted in the form of a butterfly diagram displaying their latitudinal and longitudinal extents. A tabular listing identifies average longitude and persistence of sunspot active longitudes.     

Center-to-Limb Variations of the Ca II H and K Lines in Sunspot Umbrae

A comparison of theoretical and observed Caii H and K line profiles in sunspot umbrae has been made for different sunspot positions on the solar disk. Four semi-empirical static umbral models were used in calculations: the SUNSPOT model of Avrett (1981), and the models of Staude (1982), Maltby et al. (1986), and Severino, Gomez, and Caccin (1994). The models suggested by Avrett, Maltby et al., and Severino, Gomez, and Caccin reproduce the center-to-limb evolution of the shape of observed profiles. The best agreement with profile parameters obtained from observations is given by the Severino, Gomez, and Caccin model.     

Distribution of sunspots 1874–1976

A diagram of the distribution in latitude of sunspot groups during the period 1874–1976 is given. As an indication of sunspot activity, a diagram of the mean total daily sunspot areas for each synodic rotation is also given.     

On Short-Term Periodicity of the Solar Radius Measurements

The aim of the present study is to investigate the short-term periodicity in the solar radius measurements and to compare with the short periods in sunspot numbers, sunspot areas and flare index data. The spectral analysis of data sets covering a time interval from 26 February 2000 to 26 October 2007 during Solar Cycle 23 were made by using the Date Compensated Discrete Fourier Transform (DCDFT). The power spectrum of solar radius data corrected for the seeing effect gives an evident peak at 25.7 days with the amplitude of 0.034 arcsec, which is slightly different from the peaks of 26.2 and 26.7 days produced by sunspot numbers and sunspot areas data, respectively. Besides, the main peak of 25.7 days detected in the power spectrum of solar radius data is in agreement with the period of 25.5 days, suggested to be the fundamental period of the Sun by Bai and Sturrock (in Nature 350, 141, 1991).     

Sunspot Observations Made by Hallaschka During the Dalton Minimum

We present and analyse the sunspot observations performed by Franz I.C. Hallaschka in 1814 and 1816. These solar observations were carried out during the so-called Dalton minimum, around the maximum phase of Solar Cycle 6. These records are very valuable because they allow us to complete observational gaps in the collection of sunspot group numbers, improving the coverage for this epoch. We have analysed and compared the observations made by Hallaschka with the records made by other contemporary observers. Unfortunately, the analysis of the sunspot areas and positions showed that they are too inaccurate for scientific use. We conclude, however, that the sunspot counts made by Hallaschka are similar to those made by other astronomers of that time. The observations by Hallaschka confirm a low level of solar activity during the Dalton minimum.     

The Greenwich Photo-heliographic Results (1874 – 1976): Initial Corrections to the Printed Publications

A new sunspot and faculae digital dataset for the interval 1874?–?1955 has been prepared under the auspices of the NOAA National Geophysical Data Center (NGDC). This digital dataset contains measurements of the positions and areas of both sunspots and faculae published initially by the Royal Observatory, Greenwich, and subsequently by the Royal Greenwich Observatory (RGO), under the title Greenwich Photo-heliographic Results (GPR), 1874?–?1976. Quality control (QC) procedures based on logical consistency have been used to identify the more obvious errors in the RGO publications. Typical examples of identifiable errors are North versus South errors in specifying heliographic latitude, errors in specifying heliographic (Carrington) longitude, errors in the dates and times, errors in sunspot group numbers, arithmetic errors in the summation process, and the occasional omission of solar ephemerides. Although the number of errors in the RGO publications is remarkably small, an initial table of necessary corrections is provided for the interval 1874?–?1917. Moreover, as noted in the preceding companion papers, the existence of two independently prepared digital datasets, which both contain information on sunspot positions and areas, makes it possible to outline a preliminary strategy for the development of an even more accurate digital dataset. Further work is in progress to generate an extremely reliable sunspot digital dataset, based on the long programme of solar observations supported first by the Royal Observatory, Greenwich, and then by the Royal Greenwich Observatory.     

The Clustering Properties of Active Regions During the First Part of Solar Cycle 23

In this paper we study the longitudinal distribution of solar magnetic regions, using the synoptic magnetic maps from Kitt Peak National Observatory, the active region data from Solar Geophysical Data and the Hobservations from Prairie View Solar Observatory. The clusters of activity were identified by comparing the positions of sunspot groups between successive Carrington rotations. We have found that a large percentage of active regions was involved in the clustering process (40–50%, if we only take into account clusters with a minimum lifetime of 4 rotations). The nests followed the differential rotation of the solar surface, within an intrinsic spread. A remarkable feature of sunspot nests detected in our study is their high degree of complexity, with a large number of nests being organized in diverging, converging, or parallel structures. Of the flares which occurred during the time interval of interest, the great majority originated from the sunspot nests; the distribution of the flares between these nests was not uniform, revealing active and quiet nests. A high flaring rate was recorded at the intersection points of diverging or converging nests, suggesting that these points represent violent interactions of magnetic fluxes. The complexes were in continuous interaction, which impacts their properties and future evolution. The behavior of the nests indicate that they are maintained by repeated injection of magnetic flux rather than by the evolution of the surface magnetic fields.     

Statistical Properties Of Sunspots In 1996–2004: I. Detection, North–South Asymmetry And Area Distribution

The first statistical results in sunspot distributions in 1996–2004 obtained from the Solar Feature Catalogues (SFC) are presented. A novel robust technique is developed for automated identification of sunspots on SOHO/MDI white-light (WL) full-disk solar images. The technique applies image standardization procedures for elimination of the limb darkening and non-circular image shape, uses edge-detection methods to find the sunspot candidates and their edges and morphological operations to smooth the features and fill in gaps. The detected sunspots are verified with the SOHO/MDI magnetograms by strong magnetic fields being present in sunspots. A number of physical and geometrical parameters of the detected sunspot features are extracted and stored in the relational SFC database including umbra/penumbra masks in the form of run-length data encoding of sunspot bounding rectangles. The detection results are verified by comparison with the manual daily detection results in Meudon and Locarno Observatories in 2002 and by correlation (about 96%) with the 4 year sunspot areas produced manually at NOAA. Using the SFC data, sunspot area distributions are presented in different phases of the solar cycle and hemispheres which reveals a periodicity of the north–south asymmetry with a period of about 7–8 years. The number of sunspots increases exponentially with the area decrease with the index slightly increasing from −1.15 (1997) to −1.34 (2001).     

Solar activity in the sixteenth and seventeenth centuries (a revision)

Maximum relative sunspot numbers for the 16th and 17th century were computed by means of the dependence of the maximum relative sunspot numbers on the solar cycle rise time and on the cycle asymmetry. In these dependencies four separate modes of relations, two for odd and two for even cycles, were identified. These modes are coupled two and two in even-odd cycle pairs. The rise times and the asymmetries of solar cycles in the 16th and 17th centuries were taken from cycle extreme estimates by Schove (1979), from auroral and telescopic sunspot observations during this period, but with some necessary corrections. Annual relative sunspot numbers and decade averages were estimated from the cycle maxima and the epochs of extremes. In addition, the efficiency of auroral records in latitudes lower than 55 deg was computed for the time interval 1500–1868. For this purpose the dependence of occurrence numbers of aurorae on the cycle and decade means of the relative sunspot numbers was derived.     

An Analysis of the Sunspot Groups and Flares of Solar Cycle 23

Designing a statistical solar flare forecasting technique can benefit greatly from knowledge of the flare frequency of occurrence with respect to sunspot groups. This study analyzed sunspot groups and Hα and X-ray flares reported for the period 1997 – 2007. Annual catalogs were constructed, listing the days that numbered sunspot groups were observed (designated sunspot group-days, SSG-Ds) and for each day a record for each associated Hα flare of importance category one or greater and normal or bright brightness and for each X-ray flare of intensity C 5 or higher. The catalogs were then analyzed to produce frequency distributions of SSG-Ds by year, sunspot group class, likelihood of producing at least one flare overall and by sunspot group class, and frequency of occurrence of numbers of flares per day and flare intensity category. Only 3% of SSG-Ds produced a substantial Hα flare and 7% had a significant X-ray flare. We found that mature, complex sunspot groups were more likely than simple sunspot groups to produce a flare, but the latter were more prevalent than the former. More than half of the SSG-Ds with flares had a maximum intensity flare greater than the lowest category (C-class of intensity five and higher). The fact that certain sunspot group classes had flaring probabilities significantly higher than the combined probabilities of the intensity categories when all SSG-Ds were considered suggest that it might be best to first predict the flaring probability. For sunspot groups found likely to flare, a separate diagnosis of maximum flare intensity category appears feasible.     

Long-Period Oscillations of Sunspots Observed by SOHO/MDI

We processed magnetograms that were obtained with the Michaelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). The results confirm the basic properties of long-period oscillations of sunspots that have previously been established and also reveal new properties. We show that the limiting (lowest) eigenmode of low-frequency oscillations of a sunspot as a whole is the mode with a period of 10?–?12 up to 32?–?35 hours (depending on the sunspot’s magnetic-field strength). This mode is observed consistently throughout an observation period of 5?–?7 days, but its amplitude is subject to quasi-cyclic changes, which are separated by about 1.5?–?2 days. As a result, the lower mode with a period of about 35?–?48 hours appears in the power spectrum of sunspot oscillations. But this lowest mode is apparently not an eigenmode of a sunspot because its period does not depend on the magnetic field of the sunspot. Perhaps the mode reflects the quasi-periodic sunspot perturbations caused by supergranulation cells that surround it. We also analyzed SOHO/MDI artifacts, which may affect the low-frequency power spectra of sunspots.     

Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.