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The Maunder Minimum was a period with significantly reduced solar activity between 1645 and 1715, approximately. The transition between the low solar activity in the Maunder Minimum and the subsequent "normal" regime of solar activity was gradual. However, there are discrepancies in the solar activity level from sunspot number indices and solar activity proxies in that period. Among the contemporaneous observers, Johann L. Rost and Sebastian Alischer were two key sunspot observers to understand the solar activity in this transition just after the Maunder Minimum. We have revised all their sunspot records, counting the number of groups and individual sunspots to derive reliable data for the solar activity level for the period 1716–1726. We found significant misinterpretations of the sunspot group counting assigned to these astronomers in the existing group number databases. Our new group sunspot counting significantly reduces the number of groups for Rost and Alischer's observations compared to entries in existing databases. Furthermore, our sunspot number estimates (obtained from the active day fraction methodology) of the maximum amplitude of Solar Cycles −3 and −4 are significantly lower than the amplitudes according to the official sunspot number, but they are compatible with sunspot number values obtained from solar activity proxies such as radioisotopes. Our result would imply that solar activity after the Maunder Minimum recovered more gradually and with a lower intensity than previously considered. [ABSTRACT FROM AUTHOR]

Long-term solar activity can be studied using several parameters. Some of the most used are based on the sunspot counting. The active day fraction (ADF) is the simplest index derived from this counting. It is reliable in periods of low solar activity such as the Maunder minimum (MM). In this work, we study the relationship between the ADF and the sunspot number. We have obtained that the optimal fit of that relationship is an exponential function whose exponent is a degree 3 polynomial including all data except those with ADF equal to 100%. Then, we use that fit to estimate the sunspot number during the MM from the ADF calculated from the most recent sunspot group number database. Our estimations of the annual sunspot numbers are below 15, except that for 1656, which is 40.8, whereas our estimations of the triennial sunspot numbers are below 10 from 1648 to 1714. We have found peaks of the solar cycle in the middle of the 1650s, 1670s, 1680s, and 1700s but no clear evidence of solar cycle in the 1660s and 1690s, likely due to the scarcity of the available data. Our results agree with previous works obtaining values significantly higher than those of the group sunspot number derived by Hoyt and Schatten in 1998 but still fully compatible with a grand minimum period. [ABSTRACT FROM AUTHOR]

A sunspot catalog was published by the Madrid Astronomical Observatory from sunspot observations made by Rafael Carrasco and his assistants for the period November 1931 – December 1933. We have digitized this catalog and carried out a quality control to detect inconsistencies. We present a machine-readable version of this sunspot catalog together with an erratum list. Moreover, we compared the Madrid sunspot number and area with other reference series. We found that sunspots in the northern hemisphere were predominant during this period, confirming previous studies. We have also analyzed the group morphological typologies registered in the catalog and show a butterfly diagram drawn with this new information. A comparison with the sunspot catalog by the Royal Greenwich Observatory shows that almost all the groups included in the Carrasco's catalog are also present in the aforementioned catalog. [ABSTRACT FROM AUTHOR]

Jean Tarde and Jan Smogulecki carried out sunspot observations in the 1610s and 1620s at the dawn of the telescopic era. We analysed their original observational records to revise their sunspot-group numbers in the existing database. In this study, we provide a new counting as a basis for future scientific discussions. Furthermore, we compared Smogulecki's sunspot observations with those of Scheiner and Schönberger on the same observation days. We also detected a big sunspot group on 2 – 3 February 1622 in Smogulecki's sunspot drawings and estimated its area to be approximately 1600 millionths of the solar disc. In addition, we measured the sunspot positions in Tarde's and Smogulecki's sunspot drawings to construct a butterfly diagram for this early period. [ABSTRACT FROM AUTHOR]

The Maunder Minimum (MM) was a period of prolonged solar activity minimum between 1645 and 1715. Several works have identified a significant number of problematic spotless days in the MM included in existing data bases. We have found a list of exact spotless (in the second half of 1709) and spot days (January and August 1709) provided by Johann Heinrich Müller. We computed the most probable value and upper/lower limits of the active day fraction (ADF) from Müller's data using the hypergeometrical probability distribution. Our sample is not strictly random because Müller recorded observations in consecutive days when he observed sunspots. Therefore, our result represents an upper threshold of solar activity for 1709. We compared this result with annual values of the ADF calculated for the Dalton Minimum and the most recent solar cycles. We concluded that, although 1709 is one of the most active years in the MM, it was less active than most years both in the Dalton Minimum and in the most recent solar cycles. Therefore, the solar activity level estimated in this work for 1709 represents robust evidence of low solar activity levels in the MM. [ABSTRACT FROM AUTHOR]

Pierre Gassendi (1592 – 1655) carried out sunspot observations during the 1630s. This period is particularly interesting because it occurred a few years before the Maunder Minimum. Gassendi was the second most active sunspot observer in that decade, surpassed only by Christoph Scheiner. Moreover, the sunspot observations made by Gassendi are of interest because most of them were made in days when no other sunspot observations were available. We have analyzed the sunspot drawings included in his Complete Works (Opera Omnia) and the textual reports with sunspot information after translating them from the original Latin. Thus, we have detected mistakes in previous works that studied these observations, such as incorrect dates and incorrect daily number of groups assigned to Gassendi. In addition, we found some observation days recorded by Gassendi not included in the current sunspot-group-number database. In this work, we provide a new account of the number of groups recorded by Gassendi in addition to the translations of his relevant texts on observed sunspots. Our main objective is to include these new recounts into the current sunspot-group-number database, which is the basis of the group-number index, to have a more accurate knowledge of solar activity of the third solar cycle observed with the aid of the telescope. [ABSTRACT FROM AUTHOR]

Naked-eye sunspot observations (NESOs) have been recorded for the past two millennia, approximately. These kinds of records were made around the world, mainly in Asian civilizations, and they are compiled in several catalogs. In this work, we analyze solar activity on days of the 19th century when NESOs were recorded. We found that only more than five sunspot groups were recorded in 39% of days corresponding to these NESO events. Furthermore, regarding the largest groups observed on days when NESOs were reported, we show that the uncorrected areas of these groups were below 200 millionths of solar disk (msd) in 3.2% of total cases, while it is 12.9% for areas between 200 and 499 msd. Thus, NESO records do not necessarily imply high solar activity and big sunspot groups. Therefore, these results contradict the interpretations of recent works that, using the same NESO set, suggest the solar activity level during the Maunder Minimum is still an open question. NESO records support the Maunder Minimum as a very low solar activity period. [ABSTRACT FROM AUTHOR]

We revise the sunspot observations made by Galileo Galilei and Christoph Scheiner in the context of their controversy regarding the nature of sunspots. Those of their sunspot records not included in the current sunspot group database, used as a basis to calculate the sunspot group number, are analysed. Within the documentary sources consulted in this work, we can highlight the sunspot observations by Scheiner included in the letters sent under the pseudonym Apelles to Marcus Welser and the first sunspot observations made by Galileo, which can be consulted in Le opere di Galileo Galilei. These sunspot observations would extend the temporal coverage for these two observers and fill some gaps in the current group database in the earliest period, where the data available are sparse. Moreover, we have detected changes in the quality of the sunspot drawings made by Galileo and Scheiner in their observation series, affecting the number of groups recorded by the two observers. We also compare these records with sunspot observations made by other astronomers of that time. According to this comparison and regarding the same observation days, Scheiner was generally the astronomer who reported more sunspot groups, while Harriot, Cigoli and Galileo recorded a similar number of groups. We conclude that these differences are mainly because of the observational methods used by the observers. [ABSTRACT FROM AUTHOR]

A new software (Soonspot) for the determination of the heliographic coordinates and areas of sunspots from solar images is presented. This program is very user-friendly and the accuracy of its results has been checked by using solar images provided by the Debrecen Photoheliographic Data (DPD). Due to its applicability in the studies of historical solar observations, the program has been used to analyze the solar drawings carried out by Hevelius in the 17th century. [ABSTRACT FROM AUTHOR]

An analysis of the sunspot observations made by Hevelius during 1642–1645 is presented. These records are the only systematic sunspot observations just before the Maunder Minimum (MM). We have studied different phenomena meticulously recorded by Hevelius after translating the original Latin texts. We reevaluate the observations of sunspot groups by Hevelius during this period and obtain an average value 7% greater than that calculated from his observations given in the current group database. Furthermore, the average of the active day fraction obtained in this work from Hevelius's records previous to the MM is significantly greater than the solar activity level obtained from Hevelius's sunspot observations made during the MM (70% versus 30%). We also present the butterfly diagram obtained from the sunspot positions recorded by Hevelius for the period 1642–1645. It can be seen that no hemispheric asymmetry exists during this interval, in contrast with the MM. Hevelius noted a ∼3-month period that appeared to lack sunspots in early 1645 that gave the first hint of the impending MM. Recent studies claim that the MM was not a grand minimum period, speculating that astronomers of that time, due to the Aristotelian ideas, did not record all sunspots that they observed, producing thus an underestimation of the solar activity level. However, we show that the good quality of the sunspot records made by Hevelius indicates that his reports of sunspots were true to the observations. [ABSTRACT FROM AUTHOR]

A revision is presented of the sunspot observations made by Charles Malapert from 1618 to 1626, studying several documentary sources that include those observations. The revised accounting of the group numbers recorded by Malapert for that period shows new information unavailable in the current sunspot group data base. The average solar activity level calculated from these revised records of Malapert is by almost one-third greater than that calculated from his records included in the current group data base. Comparison of the sunspot observations made by Malapert and by other astronomers of that time with regard to the number of recorded groups and sunspot positions on the solar disc shows good agreement. Malapert reported that he only recorded one sunspot group in each sunspot drawing presented in Austriaca Sidera Heliocyclia (the documentary source that includes most of the sunspot records made by Malapert), although he sometimes observed several groups. Therefore, the sunspot counts obtained in this work on Malapert's sunspot observations represent the lower limit of the solar activity level corresponding to those records. [ABSTRACT FROM AUTHOR]

We perform case studies of the sunspot observations by Charles Malapert and William Derham from the point of view of the reconstruction of the solar activity. They made sunspot observations prior and after the deep Maunder Minimum, respectively, being two of the most active sunspot observers of their time. The currently available sunspot group data bases assign one sunspot group for most of observations by Malapert and Derham. However, with documental evidence, we attest that these observers would have sometimes recorded several sunspot groups as only one representative group. Therefore, we conclude that their sunspot group counting should be used with caution for the reconstruction of the solar activity level around the Maunder Minimum. [ABSTRACT FROM AUTHOR]

The use of spotless days to predict future solar activity is revised here based on the new version of the sunspot number index with a 24-month filter. Data from Solar Cycle (SC) 10 are considered because the temporal coverage of the records is 100% for this solar cycle. The interrelationships of the timing characteristics of spotless days and their comparison with sunspot cycle parameters are explored; in some cases, we find very strong correlations. Such is the case for the relationship between the minimum time between spotless days either side of a given solar maximum and the maximum time between spotless days either side of the previous solar minimum, with $r = -0.91$ and a $p\mbox{-value} < 0.001$ . However, the predictions for SCs 24 or 23 made by other authors in previous works using spotless days as a predictor of solar activity are not correct since the predictions have not been fulfilled. Although there seems to be a pattern of strong correlation for some relationships between the parameters that have been studied, a prediction of future solar cycles from these parameters defined as functions of spotless days should be made with caution because the estimated values are sometimes far from the observed ones. Furthermore, SC 23 seems to show a mode change, a break with respect to the behaviour of previous solar cycles and more similar to SCs 10 - 15. [ABSTRACT FROM AUTHOR]

Keywords: errata; addenda; Sun: activity; Sun: general; sunspots EN errata addenda Sun: activity Sun: general sunspots 5715 5716 2 05/09/22 20220601 NES 220601 This is an erratum for our article Carrasco et al. ([1]): 'Strong evidence of low levels of solar activity during the Maunder Minimum'. Sun: activity, Sun: general, sunspots, errata, addenda The annual values of the international sunspot number index (version 2) are available on the website of the Sunspot Index and Long-term Solar Observations (http://www.sidc.be/silso/). [Extracted from the article]

We describe a revised collection of the number of sunspot groups from 1610 to the present. This new collection is based on the work of Hoyt and Schatten ( Solar Phys. 179, 189, 1998). The main changes are the elimination of a considerable number of observations during the Maunder Minimum (hereafter, MM) and the inclusion of several long series of observations. Numerous minor changes are also described. Moreover, we have calculated the active-day percentage during the MM from this new collection as a reliable index of the solar activity. Thus, the level of solar activity obtained in this work is greater than the level obtained using the original Hoyt and Schatten data, although it remains compatible with a grand minimum of solar activity. The new collection is available in digital format. [ABSTRACT FROM AUTHOR]

We revisit several characteristics of the solar cycle using the new version of the sunspot-number index. Thus, we calculated several correlations, including the recent Solar Cycles 23 and 24 in the analysis. We applied two smoothing methods to the sunspot number: i) the usual 13-month running mean and ii) a 24-month Gaussian filter. Each of these methods contains two analyses: on the one hand, we consider all of the solar cycles available, and on the other hand, only those from Solar Cycle 10 onward. It can be seen that this new version improves or yields similar results for the correlations with respect to other works using the old version of the sunspot number, except for the amplitude-descending time effect and the linear fit of the secular trend. However, employing the same methodology in the analysis and considering the same solar cycles, it can be seen that the new sunspot number, in general, does not improve the correlations with respect to the old sunspot number and, moreover, the correlations obtained with the Gaussian filter generally are stronger than those with the 13-month running mean. Furthermore, from a sinusoidal fit to the solar-maximum amplitudes of the whole series, we have obtained a periodicity of the Gleissberg cycle equal to 97.7 years ( ${\approx}\,8.9$ solar cycles) for the 13-month running mean and 99.8 years ( ${\approx}\,9.1$ solar cycles) for the Gaussian filter. Lastly, the Waldmeier effect, the modified Waldmeier effect, the amplitude-period effect, the amplitude-minimum effect, and the even-odd effect are characteristics with high correlation coefficients and significance levels; the sinusoidal fit applied to the solar-maximum amplitudes yields a lower correlation coefficient value but a high significance level; and both the amplitude-descending-time effect and secular trend of the solar activity have weaker correlation coefficients and significance levels. [ABSTRACT FROM AUTHOR]

Aims. The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain because it is based, to a large extent, on historical generic statements of the absence of spots on the Sun. Using a conservative approach, we aim to assess the level and length of solar cycle during the MM on the basis of direct historical records by astronomers of that time. Methods. A database of the active and inactive days (days with and without recorded sunspots on the solar disc) is constructed for three models of different levels of conservatism (loose, optimum, and strict models) regarding generic no-spot records. We used the active day fraction to estimate the group sunspot number during the MM. Results. A clear cyclic variability is found throughout the MM with peaks at around 1655-1657, 1675, 1684, 1705, and possibly 1666, with the active-day fraction not exceeding 0.2, 0.3, or 0.4 during the core MM, for the three models. Estimated sunspot numbers are found to be very low in accordance with a grand minimum of solar activity. Conclusions. For the core MM (1650--1700), we have found that (1) A large portion of no-spot records, which correspond to the solar meridian observations, may be unreliable in the conventional database. (2) The active-day fraction remained low (below 0.3--0.4) throughout the MM, indicating the low level of sunspot activity. (3) The solar cycle appears clearly during the core MM. (4) The length of the solar cycle during the core MM appears for 9 ± 1 years, but this is uncertain. (5) The magnitude of the sunspot cycle during MM is assessed to be below 5-10 in sunspot numbers. A hypothesis of the high solar cycles during the MM is not confirmed. [ABSTRACT FROM AUTHOR]

The solar program of the Astronomical Observatory of Madrid started in 1876. Observations were made in this institution to determine sunspot numbers and areas for ten solar cycles. The program was completed in 1986 and the resulting data have been published in various Spanish scientific publications. Four periods of this program (with different observers and instruments) were identified with the aid of the interesting metadata that has been made available. In the present work, the published data were retrieved and digitized. Their subsequent analysis showed that most of these data could be considered reliable given their very high correlation with reference indices (international sunspot number, group sunspot number, and sunspot area). An abrupt change emerged in the sunspots/groups ratio in 1946, which lasted until 1972. [ABSTRACT FROM AUTHOR]

A simple method to detect inconsistencies in low annual sunspot numbers based on the relationship between these values and the annual number of active days is described. The analysis allowed for the detection of problems in the annual sunspot number series clustered in a few explicit periods, namely: i) before Maunder minimum, ii) the year 1652 during the Maunder minimum, iii) the year 1741 in Solar Cycle −1, and iv) the so-called 'lost' solar cycle in the 1790s and the subsequent onset of the Dalton Minimum. [ABSTRACT FROM AUTHOR]

We present the sunspot ideas and observations of the 18th century Portuguese scholar Teodoro de Almeida (1722 – 1804) and Mexican scientist José Antonio Alzate (1737 – 1799). We describe the implications of dating a single sunspot observation performed by Almeida in the early 1760s, during the maximum of cycle number 1. A possible solar cycle peak in 1760 (instead of 1761) is investigated. We present several observations of sunspots obtained by Alzate during 1769 (partially associated with the Venus and Mercury transits) and also on 20 July 1786. We estimate 100±34 as the Group Sunspot Number for this date. These records were unknown and, therefore, not included in the database compiled by Hoyt and Schatten (1998). [ABSTRACT FROM AUTHOR]

Recently, new estimates of the solar cycle length (SCL) have been calculated using the Zurich Sunspot Number ( R Z) and the Regression-Fourier-Calculus (RFC)-method, a mathematically rigorous method involving multiple regression, Fourier approximation, and analytical expressions for the first derivative. In this short contribution, we show estimates of the solar cycle length using the RFC-method and the Group Sunspot Number ( R G) instead the R Z. Several authors have showed the advantages of R G for the analysis of sunspot activity before 1850. The use of R G solves some doubtful solar cycle length estimates obtained around 1800 using R Z. [ABSTRACT FROM AUTHOR]

In this work, a procedure to elaborate a homogeneous sunspot area series using the Royal Greenwich Observatory/USAFINOAA data (from 1874 to the present) and the De la Rue and co-workers data (from 1832 to 1868) is presented. These two data series correspond to time intervals that do not overlap and a direct comparison between them could not be carried out. We used the International Sunspot Number (Ri) and the Group Sunspot Number (RG) as a link between the two original series. Thus, two homogeneous sunspot area series have been built using a simple mathematic procedure based on linear relations. [ABSTRACT FROM AUTHOR]

In the 19th century De la Rue, Stewart, and Loewy carried out a compilation of drawings and photographs of the solar sunspots corresponding to the interval 1832–1868. Using these drawings and photographs, they determined fortnightly values of the percentage of the solar photosphere covered by the sunspots. In this work, we have performed a spectral analysis of these data in order to determine possible periodic signals. In addition to the 11-year solar cycle, short cycles of about 330 days and 30–50 days have been recovered, lacking the 150–160 days period discovered by other authors using several solar activity indicators. [ABSTRACT FROM AUTHOR]

William Cranch Bond, director of the Harvard College Observatory in mid-19th century, carried out detailed sunspot observations during the period 1847–1849. We highlight Bond was the observer with the highest daily number of sunspot groups observed in Solar Cycle 9 recording 18 groups on 26 December 1848 according to the current sunspot group database. However, we have detected significant mistakes in these counts due to the use of sunspot position tables instead of solar drawings. Therefore, we have revisited the sunspot observations made by Bond, establishing a new group counting. Our new counts of the sunspot groups from Bond's drawings indicate that solar activity was previously overestimated. Moreover, after this new counting, Bond would not be the astronomer who recorded the highest daily group number for Solar Cycle 9 but Schmidt with 16 groups on 14 February 1849. We have also indicated the new highest annual group numbers recorded by any observer for the period 1847–1849 in order to correct those values applied in the "brightest star" method, which is used as a rough indicator of the solar activity level. Furthermore, a comparison between Bond's sunspot records and the sunspot observations made by Schwabe and Wolf is shown. We conclude that the statistics of Wolf and Bond are similar as regards the group count. Additionally, Schwabe was able to observe smaller groups than Bond. [ABSTRACT FROM AUTHOR]

Antonio Colla was a meteorologist and astronomer who made sunspot observations at the Meteorological Observatory of the Parma University (Italy). He carried out his sunspot observations from 1830 to 1843, just after the Dalton Minimum. We have recovered 71 observation days for this observer. Unfortunately, many of these records are qualitative and we could only obtain the number of sunspot groups and/or single sunspots from 25 observations. However, we highlight the importance of these records because Colla is not included in the sunspot group database as an observer and, therefore, neither are his sunspot observations. With regards to the number of groups, the sunspot observations made by Colla are similar to those of several observers of his time. For common observation days, only Stark recorded significantly more groups than Colla. Moreover, we have calculated the sunspot areas and positions from Colla's sunspot drawings concluding that both areas and positions recorded by this observer seem unreal. Therefore, Colla's drawings can be interpreted such as sketches showing reliable information on the number of groups but the information on sunspot areas and positions should not be used for scientific purposes. [ABSTRACT FROM AUTHOR]

A sunspot catalogue was published by the Coimbra Astronomical Observatory (Portugal), which is now called the Geophysical and Astronomical Observatory of the University of Coimbra, for the period 1929 - 1941. We digitalised data included in that catalogue and provide a machine-readable version. We show the reconstructions for the (total and hemispheric) sunspot number index and sunspot area according to this catalogue and compare it with the sunspot number index (version 2) and the Balmaceda sunspot area series (Balmaceda et al. in J. Geophys. Res.114, A07104, 2009). Moreover, we also compared the Coimbra catalogue with records made at the Royal Greenwich Observatory. The results demonstrate that the historical catalogue compiled by the Coimbra Astronomical Observatory contains reliable sunspot data and can therefore be considered for studies about solar activity. [ABSTRACT FROM AUTHOR]

The ratio of penumbral to umbral area of sunspots is an important topic for solar and geophysical studies. Hathaway (Solar Phys.286, 347, 2013) found a curious behaviour in this parameter for small sunspot groups (areas smaller than 100 millionths of solar hemisphere, msh) using records from Royal Greenwich Observatory (RGO). Hathaway showed that the penumbra-umbra ratio decreased smoothly from more than 7 in 1905 to lower than 3 by 1930 and then increased to almost 8 in 1961. Thus, Hathaway proposed the existence of a secular variation in the penumbra-umbra area ratio. In order to confirm that secular variation, we employ data of the sunspot catalogue published by the Coimbra Astronomical Observatory (COI) for the period 1929 - 1941. Our results disagree with the penumbra-umbra ratio found by Hathaway for that period. However, the behaviour of this ratio for large (areas greater or equal than 100 msh) and small groups registered in COI during 1929 - 1941 is similar to data available from RGO for the periods 1874 - 1914 and 1950 - 1976. Nevertheless, while the average values and time evolution of the ratio in large groups are similar those for small groups according to the Coimbra data (1929 - 1941) it is not analogous for RGO data for the same period. We also found that the behaviour of the penumbra-umbra area ratio for smaller groups in both observatories is significantly different. The main difference between the area measurements made in Coimbra and RGO is associated with the umbra measurements. We would like to stress that the two observatories used different methods of observation and while in COI both methodology and instruments did not change during the study period, some changes were carried out in RGO that could have affected measurements of umbra and penumbra. These facts illustrate the importance of the careful recovery of past solar data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]