Revisiting Christoph Scheiner’s Sunspot Records: A New Perspective on Solar Activity of the Early Telescopic Era

Christoph Scheiner was one of the most outstanding astronomers in the history of sunspot observations. His book, Rosa Ursina, is the reference work regarding the study of the earliest sunspot records. The sunspot observations compiled by Scheiner in Rosa Ursina and Prodomus, including records made by other observers, forms one of the main references of the observations known for that period—particularly around the 1620s. Thus, his work is crucial to determine the solar activity level of the first solar cycles of the telescopic era. The number of sunspot groups recorded in Scheiner’s documentary sources has been included in the existing sunspot group number databases. However, we have detected significant errors in the number of groups currently assigned to Scheiner’s records. In this work, we reanalyze the information in Scheiner’s source documents. Consequently, the standard 11 yr solar cycle shape for the second solar cycle of the telescopic era, which is not clear in previous studies, now becomes evident. In addition, the highest daily number of groups recorded during this cycle (eight groups) is 20% less than in the one included in the existing sunspot group number databases. Using the hypergeometrical probability distribution, we find that solar minima in 2008–2009 and 2018–2019 are comparable to the most probable solar activity level of the minimum around 1632. In particular, the estimated lower limit for the solar activity in 1632 is even comparable with the solar activity level in 2008 and 2018.

Sunspot observations were recorded more systematically when telescopes started to be used as an astronomical instrument; that is, since 1610 (Muñoz-Jaramillo & Vaquero 2019; Arlt & Vaquero 2020;Vokhmyanin et al. 2020). A complete daily observational coverage of sunspot records is roughly available since the mid-nineteenth century (Hoyt & Schatten 1998;Clette et al. 2014;Vaquero et al. 2016). Nowadays, more than 400 yr later, sunspot counts constitute the longest direct observation set of solar activity. Moreover, it is considered to be the longest-lived running "experiment" in the world (Owens 2013).
Galileo and Scheiner disputed who was the first to discover sunspots (Galilei & Scheiner 2010). However, the first welldated sunspot observations by telescope that are available in the current sunspot group number database (Vaquero et al. 2016, hereafter V16) were recorded by Harriot in 1610 December and Fabricius in 1611 March (Herr 1978;Chapman 1995;Neuhäuser & Neuhäuser 2016;Vokhmyanin et al. 2020). Other astronomers who recorded sunspot observations in that time were Malapert, Jungius, and Mögling. Several works have recently been published using these early observations, which shed light on solar activity during the first years of the telescopic era. For example, Carrasco et al. (2020) identified a significant number of sunspot observations made by Galileo and Scheiner that are not included in V16. Moreover, these authors showed how the observation method by projection that was invented by Castelli (a student of Galileo) and used by Galileo from 1612 May 3 had an important impact on the number of groups recorded by this astronomer. Arlt et al. (2016, hereafter A16) and Vokhmyanin & Zolotova (2018a) derived the positions and group number of sunspots recorded by Scheiner (1630) and Galileo in their drawings, respectively. Neuhäuser & Neuhäuser (2016) revised some of the early sunspot observations that were made by several astronomers, such as Marius and Saxonius. Meanwhile, Carrasco et al. (2019b) pointed out some problematic groups that were included in V16 due to misinterpretations of Malapert's sunspot observations. Moreover, Carrasco et al. (2019a) found the standard shape of the 11 yr solar cycle in the solar cycle around 1620s using Malapert's data, in addition to a reduction of the number of groups assigned to this observer in V16. Hayakawa et al. (2021) analyzed Mögling's original manuscripts to revise his sunspot group number and derive sunspot positions, revising Schickard and Hortensius' sunspot group number. We also note the work carried out by Vokhmyanin & Zolotova (2018b) and Carrasco et al. (2021a) on the group number, sunspot positions and areas recorded by Gassendi in the 1630s. Carrasco et al. (2019c) analyzed the sunspot observations made by Hevelius just before the Maunder Minimum and obtained that the solar activity level computed from those Hevelius' sunspot observations is significantly greater than that according to the sunspot records made by Hevelius during the Maunder Minimum. In addition, Hevelius recorded a period of around three months without sunspots at the end of 1644 and early-1645 (Carrasco et al. 2019c), which provides an indication of the possible start of the Maunder Minimum (Eddy 1976;Usoskin et al. 2015).
However, despite the latest efforts to improve our knowledge of solar activity in the first part of the telescopic era, further improvements are still required: the observational coverage for the two first solar cycles of the telescopic era is currently around 20% of the days. It is also important to study these early sunspot observations to understand how the transition of solar activity changed from a normal regime to a grand minimum period (Vaquero et al. 2011). Considering these objectives, we revise the sunspot observations published by Scheiner in Rosa Ursina (Scheiner 1630) and Prodomus (Scheiner 1651) after detecting some misinterpretations and missing information in previous works on these sources (Hoyt & Schatten 1998;Arlt et al. 2016;Vaquero et al. 2016). We provide some notes about Scheiner and their previously mentioned documentary sources in Section 2. We analyze and discuss the new sunspot group counting made in this work from Scheiner's sunspot observations in Section 3. In Section 4, we show a comparison between modern minima and the solar activity level of the solar minimum around 1632, computed from the active day fraction. Finally, the main conclusions are given in Section 5.

Scheiner, Rosa Ursina, and Prodomus
Christoph Scheiner was born in Walda (Germany) in 1573. He joined the Jesuit order at Lansberg in 1595 and studied Mathematics at Ingolstadt (Mitchell 1916;Daxecker 2004 (Scheiner 1651). He lived at Vienna in 1633 and definitely returned to Niesse in 1637, where he passed away in 1650. In addition to the works previously mentioned, he also performed studies in mathematics and sundials.
Because of the Aristotelian ideas of that time, Scheiner first attempted to explain his sunspot observations assuming the perfection of the Sun. Thus, he postulated that sunspots were celestial bodies orbiting the Sun. He sent three letters under the pseudonym of Apelles explaining his work to Marcus Welser, who published them under the title Tres epistolae de maculis solaribus. Galileo refuted these arguments, which led to one of the famous debates in the history of astronomy between Galileo and Scheiner (Shea 1970). Although Scheiner was initially wrong on the nature of sunspots, he was nevertheless a great scientist and a superb observer. His sunspot observations were rigorous and of good quality, particularly those made in the 1620s. Scheiner continued observing sunspots for approximately two decades. Scheiner designed and built many different telescopes, including one with convex lenses that improved the solar image in his observations of the 1620s (Arlt et al. 2016). Moreover, he also modified the observation method by projection, which was used for the first time by Castelli and Galileo in 1612 (Galilei & Scheiner 2010;Carrasco et al. 2020), by adding to the helioscope, which is the earliest known equatorial mount. Scheiner named this instrument the "heliotropic telescope." These two innovations significantly improved the quality of his sunspot observations. Figure 1 depicts two examples of sunspot drawings recorded by Scheiner before and after using the new methodology with improved instruments (Scheiner 1630). Note that the first sunspot observations made by Scheiner were made through the telescope using a colored glass.
Scheiner's two documentary sources that are analyzed in this work are Rosa Ursina (Scheiner 1630) and Prodomus (1651). Rosa Ursina is divided into four parts. The first part discusses the question of the discovery of the sunspots and it also includes Scheiner's admission that his previous conclusions on the nature of sunspots were wrong, in addition to his sunspot observations made in 1611. The second part includes descriptions of the telescopes and the observational method that he used. The third part collects sunspot observations made from 1618 to 1627. The fourth and last part deals with sunspots, the solar rotation, and the inclination of its rotational axis. Scheiner used his sunspot observations to demonstrate the inclination by 7°of the solar equator with respect to the ecliptic.
The second book, Prodomus, was posthumously published in 1651. This book collects several years of Scheiner's work and it includes his effort to refute the heliocentric theory. It also includes a criticism to Galileo because of his work published in 1632 "Dialogo" (Drake 1967). Prodomus contains several drawings published by Scheiner (1630), in addition to new sunspot observations made until the end of 1632.

Analysis and Discussion of Scheiner's Sunspot Observations
The sunspot observations published by Scheiner (1630Scheiner ( , 1651 were previously analyzed by Wolf (1859) for the creation of the sunspot number index. Hoyt & Schatten (1998) used observations from these two books to extend the group sunspot number to the beginning of the seventeenth century, among other records, pointing out that Elizabeth Nesme-Ribes also re-examined Rosa Ursina to get group counts. V16 incorporated data from Hoyt & Schatten (1998) to a consolidated sunspot group number database. Furthermore, A16 used observations from these books to classify sunspot groups and calculate sunspot positions, areas, and group tilt angles for 1611-1631.
These sources contain observations made in 1611 and also for the period 1618-1632. Most of Rosa Ursinaʼs and Prodomus' observations are contained in sunspot drawings, although other observations form part of the textual reports. Figure 2 (top panel) shows the number of sunspot groups included in V16 for the period 1610-1649. Red color shows the 882 daily sunspot records attributed to Scheiner in V16 during the periods 1611-1640. However, we have detected several mistakes in the way that sunspots were recorded by Scheiner in Rosa Ursina and Prodomus, which were counted because of significant misinterpretations of the observations. Some of these have been already reported by Carrasco (2019), such as those observations made on 1622 February 27 and 1625 January 16.

Errors Detected in Previous Works
The first kind of error is that the number of groups recorded by other observers is assigned to Scheiner. Scheiner's record (1630, 1651 includes the observations made by six different astronomers. In Section Totius operis notatu dignoria, Scheiner (1630) specifically points out that he also shows drawings from observations made by Grünberger at Rome (Italy), Malapert at Douai (nowadays France), and Schönberger at Freiburg and Ingolstadt (Germany). Scheiner (1630, p. 257) mentions that Georg Schönberger, who was Scheiner's student and successor in the University of Freiburg, attributes the observations made at Ingolstadt from 1625 August 4 to 11 to another observer (whose name is not mentioned). Scheiner (1651) also included observations made in Vienna (Austria) by Johann Baptist Cysat -a Jesuit astronomer who was born in Luzern (Switzerland). Neither V16 nor A16 provided the observers responsible for each observation, whereas we have indicated that the sunspot observations published in those sources were made by multiple astronomers (Figure 2). An example of this problem occurs in the period of 1625 January 14-17. According to V16, Scheiner reported six groups on the January 14 and 15 and seven groups on the 1625 January 16-17. However, Scheiner only recorded three groups each day for January 14-15 and four groups both on January 16 and 17 (Scheiner 1630, p. 169 and 171). In the same period, Schönberger recorded three groups each day for the period 1625 January 14-17 (Scheiner 1630, p. 173). Counting both observers' results in the reported number of groups (mistakenly attributed to Scheiner) gives six groups for January 14-15 and seven for January 16-17. These observations are included in Figure 3. As an example, groups observed by Scheiner and Schönberger on 1625 January 16 are illustrated by green squares.
The second kind of error that is found in V16 relates to double counting of groups drawn twice in a single day. We note that the group counting by Arlt et al. (2016) is free of this error. One striking example of this kind of error is the highest number of sunspot groups included in V16 in the 1620s. According to V16, Scheiner recorded 10 groups on 1625 July 4. However, in reality these numbers reflect the double counting groups that were drawn in two separate drawings made on the same day ( Figure 4): drawing XXX (Scheiner 1630, p. 235) and drawing XXXI (Scheiner 1630, p. 237). Scheiner frequently recorded groups observed on the same dates in different drawings because of the lack of space to include new groups in the drawing. All of the solar phenomena (sunspots and faculae) recorded by Scheiner on 1625 July 4 are identified in Figure 4 by squares. There are five sunspot groups recorded by Scheiner in Figure 4(A) and six groups in Figure 4(B). Note that the solar phenomenon "l" furthest to the left-hand side in the red squares ( Figure 4(B)) is a solar facula and not a sunspot group. Nevertheless, five groups identified by red squares in Figure 4(B) are the same groups as those recorded in Figure 4(A). Thus, it is incorrect to include the five groups in red squares to determine the group counting because they are the same groups that were already counted in Figure 4(A). This means that the real number of groups recorded by Scheiner on 1625 July 4 is not the sum of all of the groups recorded in Figure 4. Only the six groups identified by blue squares in Figure 4 count.
Finally, we noticed that Scheiner may have omitted some groups in his drawings given that these groups were observed in previous and subsequent days to the date when they were not recorded. For example, a great group composed by sunspots "b" and "c" according to Scheiner (1630, p. 185) from 1625 February 9 to 22 was not recorded on February 13, 16, and 18, even though Scheiner had made observations in these dates (Figure 3(D)). Given its size, this large group should have been visible to Scheiner on the February 13, 16, and 18 (as in previous and subsequent days). We found this kind of possible error on another 14 observation days. We hypothesize that this is likely to have been caused by a lack of drawing space. Carrasco (2019) found a report of this problem in the Latin translation of Scheiner (1630, p. 195) according to Malapert's observations from 1625 March 24 to April 2. There, Scheiner indicated that not all sunspots were recorded in the drawings due to the space limitation on the paper. We can find another example comparing the sunspot observations recorded by Scheiner for the period 1625 February 1-7, which is divided into two drawings (Scheiner 1630, p. 177 and 183), with those made by Schönberger (Scheiner 1630, p. 179) and Malapert (Scheiner 1630, p. 181) for the same dates. The great sunspot "a" recorded by Scheiner (1630, p. 183) from 1625 February 1 to 13 is not included in the drawings by Schönberger and Malapert. Because of the significant size of the sunspot "a," it is very probable that both astronomers observed this spot. This could suggest that Scheiner had a particular interest in comparing the trajectories of the groups recorded only in the drawing VIII (Scheiner 1630, p. 177) with those equivalent groups observed by Malapert and Schönberger. In fact, this group is included in another drawing by Schönberger (Scheiner 1630, p. 199) but is never included by Malapert.

A Recount of Group Numbers
We recounted the number of sunspot groups in 1083 observations for the period 1611-1632 from Scheiner (1630Scheiner ( , 1651. These records correspond to 928 different observation days. Scheiner is the observer with the highest number of daily records (814) regarding the observations included in those documentary sources followed by Schönberger (166), Malapert (62), Cysat (22), Grünberger (13), and the anonymous astronomer cited above (6). We recounted the number of groups recorded in their sunspot observations according to the modern classification of sunspot groups (McIntosh 1990). We highlight that no additional group was added to the group counting on those days when an evident omission of some group was detected, except in the case showed by Carrasco (2019) (Scheiner 1630, p. 185), where it can be seen that the big group defined by Scheiner as "b" and "c" was omitted in the drawing on February 13, 16, and 18, although Scheiner observed on those dates. Panels (E) and (F) include the sunspot groups (green squares) recorded by Scheiner on 1625 October 12. 1621-1625 were omitted in Figure 2 (middle and bottom panel) because the number of groups included in V16 according to this observer are wrong due to misinterpretations of the observations (Carrasco et al. 2021b), (ii) we incorporate 108 additional observation days not included in V16 according to Scheiner (1630Scheiner ( , 1651, and (iii) we also find that 44 observation days in V16 from Scheiner (1630Scheiner ( , 1651 are wrong because no observation was made on those dates. The highest daily number of sunspot groups recorded by any observer for the second solar cycle of the telescopic era was 10, according to V16. This record would have been made by Scheiner on 1625 July 4. However, we have shown that this is wrong because of the misinterpretation of the groups recorded in the drawings (Figure 4). The highest number of groups recorded in that period, according to this new counting, is that made by Scheiner on 1625 October 12, when he recorded eight groups (Figure 3, panels (E) and (F)). These groups are recorded in drawings XLIII and XLIV in Scheiner (1630, p. 265 and 267). This implies a decrease of 20% in the maximum amplitude for that solar cycle with respect to the previous knowledge.
Between 1616 and 1624, no sunspot records have a number of groups greater than one according to V16. However, the number of groups from this new counting is up to three in that period. Now, the ascending phase of that solar cycle has a more standard shape and there is no abrupt change from the minimum to maximum (see for example Figure 30 in Svalgaard & Schatten 2016). A similar behavior happens in the declining phase. We have counted up to five groups recorded by Scheiner in 1629 (September 12), whereas it was only one in V16. This results in a more gradual decrease of solar activity in the declining phase. Thus, the minima of this solar cycle would be around 1620, the maximum amplitude would be around 1625, and the following minimum would be around 1632. This result agrees with the standard solar cycle shape found by Carrasco et al. (2019a) and Hayakawa et al. (2021) for the same solar cycle from a revision of Malapert's and Mögling's data.
The solar activity level resulting from our recount of Scheiner's observations at the end of 1611 is significantly greater than that from V16. The average number of groups calculated from V16ʼs Scheiner's observations for the period 1611 October 21-December 14 is equal to 3.8, while in our recount it is 5.0 (i.e., around 33% higher). Regarding the sunspot observations published by Scheiner (1630, 1651) from 1618 to 1629, the average of the number of groups computed from this work is 2.3, which is very similar to that from V16 (22); even though the maximum amplitude of this solar cycle is 20% lower in our recount.
We also compared our group counts with the number of groups defined by A16 from Scheiner's observations published in Rosa Ursina and Prodomus (Figure 2). The group counts made in both studies are similar on each observation day. However, some differences can be found due to the way that some sunspot groups are counted (especially in the first sunspot observations by Scheiner). The daily average of the group number corresponding to the sunspot observations published by Scheiner for the period 1611 October 21-December 14 computed from A16 is 5.8 and it is 5.1 from our group counting using the same observations days as A16. Moreover, the daily group average according to this work and A16, regarding the same observation days for the period 1611-1631, is 2.5 and 2.7, respectively. Note that on the days in which observations from different astronomers are available, we only chosen Scheiner's sunspot records to perform the previous calculations. The highest number of groups counted by A16 was: (i) 12 groups in the first solar cycle of the telescopic era on 1625 November 7, and (ii) nine groups in the second solar cycle for 1625 October 8-12. We counted up to eight groups in both solar cycles: 1611 November 1-2 for the first solar cycle and 1625 October 12 for the second solar cycle. Occasionally, it is not straightforward to define groups in the first sunspot drawings made by Scheiner, such as the drawing corresponding to 1611 November 7. The way in which several groups included in that sunspot drawing are defined is the main reason for the significant difference in the highest number of groups counted by A16 and this work. Regarding the highest number of groups in the second solar cycle (1625 October 12), we consider that the sunspots named by Scheiner as "b," "f," and "g" are the same group (see Figure 3, panel (E)), while A16 counted them as different groups. Moreover, we provide 332 observations in 177 observation days not included in A16. Note that we recover the spotless days recorded by Scheiner (1630Scheiner ( , 1651, whereas A16 did not consider them. There are a few isolated significant differences according to the group counts made in A16 and this work. A difference between group counting made in both studies larger than three is only found on five observation days: 1611 November 7 and 8, 1625 May 28, 1625 June 8, 1626 March 7. Scheiner published more sunspot records in addition to the observations studied in this work. For example, his sunspot observations made from 1611 mid-December to the beginning of 1613 were studied by Carrasco et al. (2020). Moreover, V16 assigned spotless days to Scheiner on 1616 November 13-15 and 22-23. The description of these records can be consulted in Scheiner (1617, p. 63 and 65-66). However, after translating the original Latin text, we conclude that Scheiner is not describing sunspots in these observations. One example of this fact can be found in the annotation made by Scheiner on 1616 November 22: (English translation) "The Sun moderately came out calm. It was seen that spots [maculae] had appeared and then the Sun rose over the horizon. When the Sun touched the horizon, the entire periphery could be seen not very torn, and the Sun was cut in half by a stretch of clouds." Thus, Scheiner mentions the term "spots" (maculae) to likely describe the meteorological conditions or the state of the atmosphere just before seeing the Sun over the horizon. This discards the view that Scheiner recorded a sunspot observation on that date. Thus, these observations should be removed in future versions of the sunspot group number databases. In addition, V16 included from Hoyt & Schatten (1998) two sunspot observations made by Scheiner on 1640 August 21 and 22. However, we did not find the information corresponding to those observations made in 1640. Thus, more research on these records should be done in the future.

Scheiner, Schönberger, and Malapert: A Comparison
Some of the sunspot records made by other observers that were published by Scheiner (1630Scheiner ( , 1651 were carried out on dates that Scheiner also observed. Thus, we can perform a direct comparison between the observations of several astronomers. Figure 5 represents the daily number of groups recorded by Schönberger (top panel) and Malapert (bottom panel) against those made by Scheiner on the same dates. Schönberger and Scheiner made observations on 97 common dates from 1625 January 14 to September 15. In all those days, Scheiner recorded more groups than Schönberger in 41 observations days and Schönberger only in nine days more than Scheiner. The average of the number of groups recorded by Schönberger in those days is 2.1 while it is 2.6 in the case of Scheiner. Malapert and Scheiner recorded observations on 18 common dates. The average of the number of groups computed from Malapert's observations in those days is 2.3. In the case of Scheiner, the average is equal to 2.8. Given that Malapert only recorded more groups than Scheiner on one of those 18 days, we can say that Scheiner systematically recorded more groups than Schönberger and Malapert.
We also carried out a comparison between observations by other observers with a lower number of common observations days. For example, Scheiner and Cysat recorded observations on 15 common dates during the periods 1629 August 11-22 and September 10-19, also including one spotless day (1624 December 21). The average of the number of groups obtained from Scheiner's records is 1.9. This is similar to that from Cysat's data for those dates, which is 1.7. Furthermore, Schönberger and Malapert recorded a similar number of groups in their common observation days-they observed on 12 common dates. The average of the number of groups calculated from Schönberger on those days is 2.3 and it is 2.1 according to Malapert's data.

Active Day Fraction Around the Minimum of the 1630s
Scheiner (1651) recorded a large number of quiet days (days without any spot on the Sun) for the period 1630-1632. He also indicated another significant set of days when he observed sunspots in the same period but without specifying the number of groups or single sunspots. We consider these days as active days (i.e., days with at least one sunspot on the visible solar disk). In particular, Scheiner provided information on active and quiet days in the following periods (Scheiner 1651, p. 53-56) Scheiner observed the Sun almost every day for the period 1630 September 12-1631 June 22. In this period, Scheiner (1651) recorded 269 observations days with 65 quiet days and 204 active days. There are only 15 days without observation for that whole period. Thus, the active day fraction in this period is equal to 75.8%. If we suppose that those 15 days were active, then the active day fraction would be of 77.1% and 71.8% in case those 15 days were quiet. This solar activity level is similar to that found from sunspot data provided by the sunspot Index and Long-term Solar Observations (SILSO, http://sidc.be/silso/) for 2006 (82.2%) and 2017 (73.7%), both in the last part of the declining phases of the modern Solar Cycle 23 and 24, respectively. Note that according to sunspot number index provided by SILSO, the minima of Solar Cycle 24 and 25 were in 2008 and 2019 December, respectively.
The solar minimum of the third solar cycle regarding the telescopic observations from 1610 was likely to be in 1632. Several comments made by Scheiner (1651, p. 55-56) point to the prolonged absence of sunspots in that year. The only period of active days recorded by Scheiner in 1632 when he provided specific dates of observation were from May 10 to 20. Furthermore, according to Scheiner (1651, p. 55), although no sunspot was observed for the most part of January, "some insignificant sunspots, which were not valid for our purpose" were observed in that month. We also note that from April 12 to the end of the month, "there was hardly any very small sunspot." As a general comment, he pointed out that February was even less active than January and March, and April did not bring an increase in activity. In total, Scheiner recorded 63 quiet days and 11 active days for the period 1632 February 26-December 13. We can use the hypergeometrical probability distribution to estimate the solar activity level from the active day fraction for that solar minimum, as follows: where N is the number of days in a year (365), s is the total number of active days within the year which is to be estimated, n the number of observations of the sample, and r the number of active days of the sample (see more details in Kovaltsov et al. 2004). Thus, we obtained that the most probable value, and the upper and lower limits of the active day fraction with a 99% significance level are 14.8%, 23.9%, and 5.7%, respectively. Regarding SILSO's data, only years 2019 (24.9%), 2008 (27.6%), and 2009 (28.2%), which are the solar minima of Solar Cycle 24 and 25, are comparable to the upper limit of the active day fraction obtained for 1632. Figure 6 depicts the active day fraction computed from SILSO data, and the most probable value and limits of the active day fraction obtained in this work for 1632.
We must take into account that SILSO data are obtained from observations with a modern telescope. Therefore, we should apply some constraint to modern data to level with the earliest observations. For example, we can apply area thresholds to modern sunspot records. Thus   Mandal et al. 2020) for the last two solar cycles corresponding to the period 1996-2020, which is published at: http://158.250.29.123:8000/web/Soln_Dann/. We have calculated the annual active day fraction range from raw Kislovodsk data, as well as discarding groups whose observed areas are between 10 and 100 millionths of solar disk ( Figure 6). We highlight that the threshold of 10 millionths of solar disk would be an optimistic threshold to be applied to the earliest observations, while 100 millionths of solar disk would be conservative (Usoskin et al. 2016). One small difference can be seen between results obtained from SILSO and raw Kislovodsk data. The solar minimum in 2008 is deeper than that in 2019 from Kislovodsk data (2008: 24.3%, 2019: 26.8%), while 2019 is slightly more active than 2008 from SILSO data (2008: 27.6%, 2019: 24.9%). By applying the area thresholds to Kislovodsk data, the minima of Solar Cycle 24 in 2008 (5.3%-23.7%) and Solar Cycle 25 in 2019 (11.3%-22.3%) have a similar solar activity level as 1632. In addition, the solar activity level obtained for 2009 (10.4%-24.8%) and 2018 (8.3%-30.4%) is also comparable to that in 1632. We highlight that the solar activity level in 2008 and 2018, according to the most conservative constraint applied in this work, is comparable to the lower limit of the solar activity level estimated for 1632.

Conclusions
Christoph Scheiner made sunspot observations in the earliest period of the telescopic era. These observations were analyzed previously by Wolf (1859) and Hoyt & Schatten (1998). Then, V16 incorporated the number of groups indicated in these works into the updated sunspot group number database. We have detected several significant errors in the number of groups assigned to Scheiner in V16. Consequently, a revision of sunspot observations recorded by Scheiner was necessary. We have reanalyzed the observations published by Scheiner in his documentary sources Rosa Ursina and Prodomus from 1611 to 1632. The sunspot records included in these historical works are very important because they form the vast majority of the observations available in the databases, particularly, for the 1620s.
The number of observations studied in this work were 1083, which were included in more than 100 sunspot drawings made by several observers (Scheiner, Schönberger, Malapert, Cysat, Grünberger, and an anonymous astronomer) on 928 different observation days. We found 108 observation days that were not included in V16. Moreover, no observation was recorded by Scheiner on 44 observation days assigned to him in V16. Other errors in V16 from Scheiner's data are related to the number of groups recorded by the observers. The most striking case is the highest daily number of groups in the 1620s (second solar cycle known from telescopic observations). According to V16, Scheiner observed 10 groups on 1625 July 4, but in reality he recorded six groups. The new highest daily number of groups for that solar cycle obtained in this work was eight groups recorded by Scheiner on 1625 October 12 (i.e., the raw maximum amplitude was 20% lower). In addition, we obtained that the average of the number of groups from Scheiner's observations recorded in 1611 was 5.0, while it is 3.8 using the same data set from V16, which is around one third greater. Our comparison of observations of different astronomers also shows that Scheiner generally recorded more groups that the other astronomers who recorded observations on the same dates.
We also compared our group counts with the number of groups defined by A16 using the same documentary sources. The group counting is similar in both works but: (i) A16 did not provide information on the observers responsible of the sunspot records, (ii) no spotless day was included in A16, (iii) we provide 177 additional observation days not included in A16 (332 sunspot records if we also consider observers different to Scheiner), and (iv) the way in which some groups was defined is the reason for the differences found in both works according to the highest number of sunspot groups counted from Scheiner's drawings in the first and second solar cycle of the telescopic era.
We know that Scheiner made a large number of observations around the maximum of second solar cycles (511 observation days for 1625-1626), while he would have carried out his observations just before the maximum of the first solar cycle according to all observations recorded in V16. However, the maximum daily number recorded by Scheiner in each solar cycle was eight groups: on 1611 November 1 and 2 and 1625 October 12. It was even larger in the first solar cycles according to the group counting by A16 (12 groups in the first cycle versus nine groups in the second cycle). Moreover, Scheiner made his observations in the first cycle through the telescope with colored lens. Meanwhile, he used the projection method and improved telescopes during the second cycle, which could allowed him to observe more sunspot groups (Arlt et al. 2016;Carrasco et al. 2020). This fact may suggest a gradual decrease of solar activity before the Maunder Minimum instead of a sudden drop, which further supports the achievements in Vaquero et al. (2011). Note that Miyahara et al. (2021) estimated that the second solar cycle was only slightly smaller than the first cycle using cosmogenic radionuclides in contrast with our raw group counting from Scheiner (1630Scheiner ( , 1651. Our results provide valuable hints on the operation of the solar dynamo because the transition between a normal activity regime and the onset of the Maunder Minimum seems more gradual after these corrections, unlike the previous knowledge (see Figures 2  and 7). This gradual transition is also observed during the recovery of solar activity at the end of the Maunder Minimum.
Another important result of our group number recount is that the solar cycle that took place in the 1620s now has the standard 11 yr solar cycle shape with a fast (but not sudden) rise and a slow decay. This is visible in Figure 7 (bottom panel), where we show the annual averages of the raw number of groups. Previously, this solar cycle seemed to be a rather short 8 yr cycle (1624-1632), which would rise to maximum in one year according to V16. This solar minimum has been variously located somewhere between 1620 June-December in Neuhäuser & Neuhäuser (2016) and around 1621 in Carrasco et al. (2019a). After our recount, it seems to start ∼1620 and finish in ∼1632 (with the maximum in ∼1625). A similar result is obtained if we replace the observations made by Galileo, Cigoli, Cologna, Colonna, Mögling and Gassendi in V16 by the new group counts obtained by Vokhmyanin & Zolotova (2018a), Carrasco et al. (2020Carrasco et al. ( , 2021a, Vokhmyanin et al. (2021), Hayakawa et al. (2021) from observations made by those observers (Figure 7, top panel). The years of minima obtained in this work agree with those by Usoskin et al. (2021) from annual 14 C data but are slightly different to those found by Miyahara et al. (2021) also from 14 C data because the latter values set those minima in 1622 and 1633.
Finally, we calculated the active day fraction for the solar minimum in 1632 (the solar cycle before the Maunder Minimum) and compared it with modern minima. According to the raw data, the upper limit obtained for the solar minimum of 1632 is comparable to the solar minimum of Solar Cycle 24 and 25. The solar activity level computed for 2008-2009 (minimum of Solar Cycle 24) and 2018-2019 (minimum of Solar Cycle 25) once we discard those groups whose observed areas are between 10 and 100 millionths of solar disk from Kislovodsk data is comparable to that in 1632. In addition, the solar activity level calculated for 2008 and 2018 after applying the most conservative constraint is comparable to the lower limit value estimated for 1632. Note that the active day fraction value obtained in this work for the solar minimum in 1632 is slightly lower than that found by Carrasco et al. (2021c) for 1709 (which is one of the most active years in the Maunder Minimum).
This work demonstrates, as other previous studies have done, how sensitive historical observations are to mistakes in translation and interpretation. It also shows the critical need to improve the databases on which the sunspot number index is based. Only in this way will we be able to reach a more complete understanding of the past, present, and future of solar activity.