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\"A history of the controversy over sunspots with translations of the letters contained in Galileo's Istoria e dimostrazioni intorno alle macchie solari e loro accidenti. The material that was added during the printing of the Istoria, the dedication, preface, laudatory poems, and the note from the printer to introduce Scheiner's tracts, have been added in an appendix\"-- Provided by publisher.

Historical sunspot records and the construction of a comprehensive database are among the most sought after research activities in solar physics. Here, we revisit the issues and remaining questions on the reconstruction of the so-called group sunspot numbers (GSN) that was pioneered by D. Hoyt and colleagues. We use the modern tools of artificial intelligence (AI) by applying various algorithms based on machine learning (ML) to GSN records. The goal is to offer a new vision in the reconstruction of sunspot activity variations, i.e. a Bayesian reconstruction, in order to obtain a complete probabilistic GSN record from 1610 to 2020. This new GSN reconstruction is consistent with the historical GSN records. In addition, we perform a comparison between our new probabilistic GSN record and the most recent GSN reconstructions produced by several solar researchers under various assumptions and constraints. Our AI algorithms are able to reveal various new underlying patterns and channels of variations that can fully account for the complete GSN time variability, including intervals with extremely low or weak sunspot activity like the Maunder Minimum from 1645 – 1715. Our results show that the GSN records are not strictly represented by the 11-year cycles alone, but that other important timescales for a fuller reconstruction of GSN activity history are the 5.5-year, 22-year, 30-year, 60-year, and 120-year oscillations. The comprehensive GSN reconstruction by AI/ML is able to shed new insights on the nature and characteristics of not only the underlying 11-year-like sunspot cycles but also on the 22-year Hale’s polarity cycles during the Maunder Minimum, among other results previously hidden so far. In the early 1850s, Wolf multiplied his original sunspot number reconstruction by a factor of 1.25 to arrive at the canonical Wolf sunspot numbers (WSN). Removing this multiplicative factor, we find that the GSN and WSN differ by only a few percent for the period 1700 to 1879. In a comparison to the international sunspot number (ISN) recently recommended by Clette et al. (Space Sci. Rev. 186 , 35, 2014 ), several differences are found and discussed. More sunspot observations are still required. Our article points to observers that are not yet included in the GSN database.

Johann Georg Locher wrote Disquisitiones Mathematicae (Mathematical Disquisitions) in 1614, about astronomy and the sun. Galileo replied, through Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican, in 1632.

We study the long-term behaviour of the sunspot penumbra to umbra area ratio by analysing recently digitised Kodaikanal white-light data (1923 – 2011). We implement an automatic umbra extraction method and compute the ratio over eight solar cycles (Cycles 16 – 23). Although the average ratio does not show any variation with spot latitudes, cycle phases and strengths, it increases from 5.5 to 6 as the sunspot size increases from 100 μhem to 2000 μhem. Interestingly, our analysis also reveals that this ratio for smaller sunspots (area < 100  μhem) does not have any long-term systematic trend as was earlier reported from the photographic results of the Royal Observatory, Greenwich (RGO). To verify the same, we apply our automated extraction technique to Solar and Heliospheric Observatory (SOHO)/ Michelson Doppler Imager (MDI) continuum images (1996 – 2010). Results from this data not only confirm our previous findings, but they also show the robustness of our analysis method.

Sunspot observations are available in fairly good numbers since 1610, after the invention of the telescope. This review is concerned with those sunspot observations of which longer records and drawings in particular are available. Those records bear information beyond the classical sunspot numbers or group sunspot numbers. We begin with a brief summary on naked-eye sunspot observations, in particular those with drawings. They are followed by the records of drawings from 1610 to about 1900. The review is not a compilation of all known historical sunspot information. Some records contributing substantially to the sunspot number time series may therefore be absent. We also glance at the evolution of the understanding of what sunspots actually are, from 1610 to the 19th century. The final part of the review illuminates the physical quantities that can be derived from historical drawings.

We demonstrate that the radial magnetic-field component at the outer boundary of the sunspot penumbra is about 550 Mx cm −2 independent of the sunspot area and the maximum magnetic field in the umbra. The mean magnetic-field intensity in sunspots grows slightly as the sunspot area increases up to 500 – 1000 millionth of visual hemisphere (m.v.h.) and may reach about 900 – 2000 Mx cm −2 . The total magnetic flux weakly depends on the maximum field strength in a sunspot and is determined by the spottedness, i.e. the sunspot number and the total sunspot area; however, the relation between the total flux and the sunspot area is substantially nonlinear. We suggest an explicit parametrization for this relation. The contribution of the magnetic flux associated with sunspots to the total magnetic flux is small, not achieving more than 20% even at the maximum of the solar activity.

Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described by Clette et al. ( Space Sci. Rev. 186 , 35, 2014 ), we now assembled all separately derived corrections to produce a new standard version of the reference sunspot-number time series. We explain here the three main corrections and the criteria used to choose a final optimal version of each correction factor or function, given the available information and published analyses. We then discuss the differences between the new corrected series and the original sunspot number, including the disappearance of any significant rising secular trend in the solar-cycle amplitudes after this recalibration. We also introduce the new version management scheme now implemented at the World Data Center Sunspot Index and Long-term Solar Observations (WDC-SILSO), which reflects a major conceptual transition: beyond the rescaled numbers, this first revision of the sunspot number also transforms the former static data archive into a living observational series open to future improvements.

With recent advances in the field of machine learning, the use of deep neural networks for time series forecasting has become more prevalent. The quasi-periodic nature of the solar cycle makes it a good candidate for applying time series forecasting methods. We employ a combination of WaveNet and Long Short-Term Memory neural networks to forecast the sunspot number using the years 1749 to 2019 and total sunspot area using the years 1874 to 2019 time series data for the upcoming Solar Cycle 25. Three other models involving the use of LSTMs and 1D ConvNets are also compared with our best model. Our analysis shows that the WaveNet and LSTM model is able to better capture the overall trend and learn the inherent long and short term dependencies in time series data. Using this method we forecast 11 years of monthly averaged data for Solar Cycle 25. Our forecasts show that the upcoming Solar Cycle 25 will have a maximum sunspot number around 106 ± 19.75 and maximum total sunspot area around 1771 ± 381.17. This indicates that the cycle would be slightly weaker than Solar Cycle 24.

We study the geomagnetic activity Ap-index in relation to sunspot number and area for the interval covering Solar Cycles 17 to 24 (1932 – 2019), in view of the availability of data for the Ap-index from 1932 on, in order to predict the amplitude of Sunspot Cycle 25. We examine the statistical relationship between sunspot-maximum amplitude and Ap-index, and similarly that between sunspot area and Ap-index. We apply the χ 2 -test for the best fit between two parameters and obtain the correlation coefficient. We also derive the standard deviation for the error limits in the predicted results. Our study reveals that the amplitude of the Sunspot Cycle 25 is likely to be ≈ 100.21 ± 15.06 and it may peak in April 2025 ± 6.5 months. On the other hand, the sunspot area will have maximum amplitude ≈ 1110.62 ± 186.87  μ Hem and may peak in February 2025 ± 5.8  months, which implies that Solar Cycle 25 will be weaker than or comparable to Solar Cycle 24. In view of our results as well as those of other investigators, we propose that the Sun is perhaps approaching a global minimum.

We study the latitudinal distribution and evolution of sunspot areas of Solar Cycles 12 – 23 (SC12–23) and sunspot groups of Solar Cycles 8 – 23 (SC8–23) for even and odd cycles. The Rician distribution is the best-fit function for both even and odd sunspots group latitudinal occurrence. The mean and variance for even northern/southern butterfly wing sunspots are 14.94/14.76 and 58.62/56.08, respectively, and the mean and variance for odd northern/southern wing sunspots are 15.52/15.58 and 61.77/58.00, respectively. Sunspot groups of even cycle wings are thus at somewhat lower latitudes on average than sunspot groups of the odd cycle wings, i.e. about 0.6 degrees for northern hemisphere wings and 0.8 degrees for southern hemisphere wings. The spatial analysis of sunspot areas between SC12–23 shows that the small sunspots are at lower solar latitudes of the Sun than the large sunspots for both odd and even cycles, and also for both hemispheres. Temporal evolution of sunspot areas shows a lack of large sunspots after four years (exactly between 4.2 – 4.5 years), i.e. about 40% after the start of the cycle, especially for even cycles. This is related to the Gnevyshev gap and is occurring at the time when the evolution of the average sunspot latitudes crosses about 15 degrees. The gap is, however, clearer for even cycles than odd ones. Gnevyshev gap divides the cycle into two disparate parts: the ascending phase/cycle maximum and the declining phase of the sunspot cycle.