Number of Sunspot Groups from the Galileo-Scheiner controversy revisited V.M.S. Carrasco1,2, M.C. Gallego1,2, J.M. Vaquero2,3 1 Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain [e-mail: [email protected]] 2 Instituto Universitario de Investigación del Agua, Cambio Climático y Sostenibilidad (IACYS), Universidad de Extremadura, 06006 Badajoz, Spain 3 Departamento de Física, Universidad de Extremadura, 06800 Mérida, Spain Abstract: We revise the sunspot observations made by Galileo Galilei and Christoph Scheiner in the context of their controversy on the nature of sunspots. Their sunspot records not included in the current sunspot group database, used as a basis to calculate the sunspot group number, are analyzed. 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 filling some gaps in the current group database in the earliest period where the data available is sparse. Moreover, we have detected changes in the quality of the sunspot drawings made by Galileo and Scheiner in their observation series affecting to 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 these differences are mainly because of the observational method used by the observers. Keywords: Sun: activity; Sun: sunspots; astronomical data bases: miscellaneous 1. Introduction The sunspot number index is a measure of solar activity calculated from the number of sunspots observed on the solar photosphere (Clette & Lefèvre 2016; Hoyt & Schatten 1998). This is the most used index to study long-term solar activity and it is employed in studies of different scientific fields such as solar physics or Earth sciences (Kopp et 1 al. 2016; Usoskin 2017). Thus, its reliability is fundamental. Recently, several corrections were applied to the sunspot number to fix scaling problems in the 19th and 20th centuries (Clette et al. 2014) and an ongoing global effort is carried out in order to provide a recalibration of these indices (Muñoz-Jaramillo & Vaquero 2019). Sunspots have been observed before the telescopic era (Yau & Stephenson 1988; Vaquero, Gallego & García 2002). However, the systematic record of sunspot observations did not start until the use of the telescope as an astronomical instrument (Vaquero & Vázquez 2009; Arlt & Vaquero 2020). The first sunspot record available of the telescopic era was made by Thomas Harriot on 18 December 1610 (all dates in this work are referred to the Gregorian calendar). Since this record, several astronomers made sunspot observations in those first years of telescopic observations. According to the current sunspot group database (Vaquero et al. 2016, hereafter V16), the observers with the highest number of sunspot records in the two first decades of telescopic era (1610 – 1629) were Christoph Scheiner (766 observation days), Thomas Harriot (210), Charles Malapert (187), Daniel Mögling (126), and Joachim Jungius (104). It is important to note that the observational coverage in this early period is low. For the period 1610 – 1629, the observational coverage is around 20 % according to V16 and if we only consider the first decade, from December 1610 to 1619, it is even lower (15 %). For this reason, the incorporation of new information on sunspot observations made in those first years of the telescopic era is fundamental to understand how solar activity evolved in that period. We highlight that, recently, Neuhäuser & Neuhäuser (2016), Carrasco (2019), and Carrasco et al. (2019a) found some problems in the sunspot counting from the records of the first years of telescopic observations. Furthermore, Carrasco et al. (2019b) found by revisiting Malapert records, on the one hand, the two first solar cycles of the telescopic era had the shape of the standard 11-year solar cycle and, on the other hand, the solar activity level calculated from Malapert (1633) was one- third greater than that obtained from V16 considering the same documentary source. Recently, Vokhmyanin, Arlt & Zolotova (2020) calculated sunspot areas and positions from Harriot’s drawings. In this context, it is also interesting to revisit the sunspot observations made by astronomers of that time like, for example, Galileo and Scheiner. We also note that these first observations precede the Maunder Minimum (Eddy 1976; Usoskin et al. 2015), the period between 1645 and 1715 characterized by a long and 2 prolonged low solar activity, which makes difficult to connect the first data with modern observation series (Muñoz-Jaramillo & Vaquero 2019). Thus, this gives a significant importance to any new sunspot data series from that early era. There are 51 observation days by Galileo Galilei in V16. Although he did not record many sunspot observations, Galileo was an important sunspot observer. He is the fourth most active sunspot observer if we consider records made during the first decade of telescopic era. Galileo indicated that he observed sunspots in 1610 (Galilei 1895a) and therefore he could be the first astronomer who observed sunspots by telescope but he did not record the exact date. Furthermore, he made very detailed sunspot drawings from May to August 1612 and had a great debate with Scheiner about the nature of sunspots (Sakurai 1980; Galilei & Scheiner 2010). While Scheiner defended the Aristotelian ideas about a perfect Sun, Galileo demonstrated that sunspots are on the solar “surface” (today photosphere). The sunspot observations involved in this famous controversy of the history of the astronomy have allowed us to know the level of solar activity in those first years of the telescopic era. Although these sunspot reports are widely known in the context of this discussion, some of them are not included in V16. Christoph Scheiner was also one of the most important sunspot observers of that time because of his number of sunspot records and the outstanding quality of his drawings published in Rosa Ursina (Scheiner, 1630). The sunspot observations included in this documentary source were made in 1620s, except one of the sunspot drawings made by Malapert (in 1618). We highlight that Casas et al. (2006) estimated the solar differential rotation from the Galileo’s drawings and, more recently, Arlt et al. (2016) and Vokhmyanin & Zolotova (2018) calculated the sunspot positions from the observations published by Scheiner from 1611 to 1631 and Galileo from May to August 1612, respectively. Figure 1 represents the daily number of sunspot groups recorded from 1610 to 1618 according to V16, including the sunspot observations made by Scheiner (red bars) and Galileo (blue bars). We have selected, among the different countings from Galileo’s observations in V16, the observer with the station number 3 because it has the greatest observational coverage for this observer. In this work, we analyze the sunspot observations made by Scheiner from December 1611 to August 1613 and Galileo from February to May 1612. Surprisingly, despite of 3 the fame of these astronomers, these observations are not included in the last revised collection of sunspot group numbers by V16 nor in the previous version (Hoyt & Schatten 1998). We describe the sunspot observations in Section 2. Section 3 includes the sunspot counting carried out from these observations and a comparison to the sunspot observations carried out by other astronomers of that time. Finally, the main conclusions of this work are shown in Section 4. Figure 1. Daily number of sunspot groups recorded by Scheiner (red color) and Galileo (blue color) included in V16, and all the sunspot records available in V16 (grey color) during the period 1610 – 1613 (top panel) and 1614 – 1618 (bottom panel). The sizes of dots are function of the number of identical values recorded by all the observers in the same date such that greater sizes depict greater number of observations per day. 2. Documentary sources and observations 4 Christoph Scheiner recorded sunspot observations from 1611 to 1640 and he is clearly the observer with the highest number of sunspot records before the Maunder Minimum (Arlt et al. 2016; Engvold & Zirker 2016; Vaquero et al. 2016). Scheiner (1630) published a great number of drawings including his own sunspots records and sunspot observations made by other astronomers as, for example, Charles Malapert (Carrasco et al. 2019b). In particular, the sunspot drawings made by Scheiner in 1620s have extraordinary quality due to its high level of detail. Thus, ‘Rosa Ursina’ could be considered the main documentary source of observations and discussion about sunspots regarding the first years of the telescopic era. The first sunspot drawing set recorded by Scheiner includes observations made from 21 October 1611 to 14 December 1611. Another very similar series of observations was published by Scheiner (1612) and includes his sunspot records made from 10 December 1611 to 11 January 1612 and for March–April 1612. They are part of the letters Scheiner sent to Marcus Welser signed under the pseudonym Apelles. These drawings can be consulted, for example, on the website of the Lincean Academy Archive (https://bibdig.museogalileo.it). Furthermore, four sunspot drawings made in 1612 (23 October, 27 and 29 November, and 26 December) and one more in 1613 (6 January 1613) were published by Scheiner (1615). Other sunspot drawing made by Scheiner on 1 August 1613 was sent by Welser to Galileo in a letter written in October 1613 (Galilei 1895b). Figure 2 includes all these observations, except ten common observation days with Galileo and other common observation day with Colonna on 1 August 1613.