An Overview of Sunspot Observations in the Early Maunder Minimum: 1645–1659 Open Access

Abstract

Within four centuries of sunspot observations, the Maunder Minimum (MM) in 1645–1715 has been considered a unique grand minimum with weak solar cycles in group numbers of sunspots and hemispheric asymmetry in sunspot positions. However, the early part of the MM (1645–1659) is poorly understood in terms of its source records and has accommodated diverse reconstructions of the contemporaneous group number. This study identified their source records, classidied them in three different categories (datable observations, general descriptions, and misinterpreted records), and revised their data. On this basis, we estimated the yearly mean group number using the brightest star method, derived the active day fraction (ADF), reconstructed the sunspot number based on ADF, and compared them with proxy reconstructions from the tree-ring data sets. Our results revised the solar activity in the early MM downward in yearly mean group numbers using the brightest star method and upward in the active day fraction and sunspot number estimates. Our results are consistent with the proxy reconstruction for 1645–1654 and show more realistic values for 1657–1659 (against the unphysical negative sunspot number). These records have paid little attention to sunspot positions, except for Hevelius' report on a sunspot group in the northern solar hemisphere in 1652 April. Therefore, slight caveats are required to discuss if the sunspot positions are located purely in the southern solar hemisphere throughout the MM.

1 INTRODUCTION

Since 1610, telescopic sunspot observations have formed one of the longest and most well-studied observation-based indices of solar activity (Clette et al. 2014, 2023; Arlt & Vaquero 2020; Usoskin 2023). Apart from regular solar cycles of each ≈11 yr, these multicentury observations have detected an unusual period, a ‘grand minimum’ in 1645–1715 (Spörer 1889; Maunder 1922; Eddy 1976), which is currently known as the Maunder Minimum (MM). This period has been characterized by extremely weak sunspot cycles, significant hemispheric asymmetry of the reported sunspots, and an apparent loss of solar coronal streamers (Ribes & Nesme-Ribes 1993; Soon & Yaksell 2003; Riley et al. 2015; Usoskin et al. 2015, 2021; Vaquero et al. 2015; Owens et al. 2017; Hayakawa et al. 2021a,b,c; Carrasco et al. 2022). These characteristics contrast solar cycles in the MM with other solar cycles, including those in the Dalton Minimum (Hathaway 2015; Muñoz-Jaramillo & Vaquero 2019; Hayakawa et al. 2020a,b ,d, 2021c; Carrasco 2022; Illarionov & Arlt 2023). Their cycle lengths appear different from those of regular solar cycles, whereas it remains debated whether they are extended (Miyahara et al. 2004, 2021) or shortened (Owens et al. 2012; Vaquero et al. 2015; Usoskin et al. 2021).

These unique and outstanding features of the MM have posed a challenge to modellers of physical mechanisms of the Sun. Using solar-dynamo models, researchers were able to reproduce many of the features observed in the solar magnetism in the second half of the 20th century (see e.g. Choudhuri 2015). However, it is still an ongoing challenge to reproduce the features of the solar activity observed during the MM by solar dynamo models (Riley et al. 2015; Owens et al. 2017; Charbonneau 2020; Petrovay 2020; Karak 2023; Usoskin 2023). Today, the most widespread opinion associates the MM -- and the grand minima of solar activity in general -- with a particular state of the solar dynamo, while the periods of regular solar cycles would be linked to a typical state of the solar dynamo (see, for example, Charbonneau, 2020; Usoskin 2023). As the only grand minimum within the coverage of direct sunspot observations, the MM has formed a benchmark reference for other grand minima detected in proxy reconstructions with cosmogenic isotopes during the last 10 millennia (Usoskin et al. 2007, 2021; Inceoglu et al. 2015; Usoskin 2023).

However, previous studies have shown significantly different reconstructions for the solar cycles in the MM (Hoyt & Schatten 1998a,b; Usoskin et al. 2015; Vaquero et al. 2015; Svalgaard and Schatten 2016; Muñoz-Jaramillo & Vaquero 2019), partially because of different calibration methods and different uses of historical data sets (Muñoz-Jaramillo & Vaquero 2019). Some authors have even claimed that the MM is not a grand minimum and just a cluster of moderate solar cycles (e.g. Zolotova & Ponyavin 2015), whereas analyses on contemporaneous data sets did not support such ideas (Usoskin et al. 2015; Vaquero et al. 2015; Carrasco et al. 2021; Hayakawa et al. 2021c).

Initially, it was considered that the Sun during the MM was diligently observed and that the daily group counts had been acquired for ≥ 90 per cent of this interval with a significant dominance of spotless days (Hoyt & Schatten 1996, 1998a,b; hereafter, HS98). Some of the latest studies have also shared HS98’s base idea for the MM and regard this period as almost completely spotless despite dense contemporaneous observations (Velasco Herrera et al. 2022).

However, some of the recent efforts have revealed that the existing data sets around the MM are frequently derived from problematic sources, such as general statements on the absence of sunspots and observations with different purposes, such as those for solar altitudes and solar diameters (Vaquero 2007; Clette et al. 2014, 2023; Arlt & Vaquero 2020; Hayakawa et al. 2021b). These issues have prompted recent studies to revise the data sets of each observer with daily cadence (e.g. Vaquero et al. 2011; Carrasco et al. 2015; Usoskin et al. 2015; Carrasco & Vaquero 2016; Hayakawa et al. 2021b). Vaquero et al. (2016, hereafter V + 16) have compiled their initial revisions and have formed the basis for further analyses and applications (e.g. Svagaard & Schatten 2016; Cliver & Herbst 2018; Usoskin et al. 2021), whereas further revisions and re-analyses remain ongoing with regard to the MM (e.g. Vokhmyanin et al. 2018; Carrasco et al. 2019; Hayakawa et al. 2021b).

To date, our knowledge of the MM has primarily been derived from data sets collected from 1671 onward (Ribes & Nesme-Ribes 1993; V + 16; Hayakawa et al. 2021a,b). However, reconstructions of the early MM (1645–1659) have remained predominantly unclear owing to data scarcity (Vaquero et al. 2015; Muñoz-Jaramillo & Vaquero 2019). Consequently, the early MM has occasionally been considered to be out of the core of the MM (e.g. Vaquero & Trigo 2015; Svalgaard & Schatten 2016). This is because actual observations are inadequately understood, except for those of Hevelius (Vaquero & Trigo 2014; Carrasco et al. 2015). Therefore, this study aims to review the original records of known sunspot observations during the early MM (1645–1659) in the existing data bases (HS98 & V + 16), comprehensively re-analyse these source documents, and revise the group number in this period. We consulted their original texts (mainly in Latin) and revised the sunspot data sets in this interval (Tables 1 and 2), according to the following three categories: datable observations (Section 3), general descriptions (Section 4), and misinterpreted records (Section 5). On their basis, we revised the group counts and active day fractions (ADFs). We have revised the yearly mean group number of the brightest star method following the method of Svalgaard and Schatten (2016) in Section 6. Following Carrasco et al. (2022), we estimated the sunspot number from the ADF and compared our estimate with a proxy-based reconstruction of the sunspot number based on tree-ring data sets (Usoskin et al. 2021) in Section 7.

2 SOURCE REPORTS

To re-analyse sunspot records in the early MM, we first identified source reports of the known sunspot data sets (1645–1659) in existing data bases, as summarized in Table 1. The majority were listed in HS98. We identified the source reports following HS98’s supplementary bibliography and Wolf’s Mittheilungen (Wolf 1850, 1874). In addition, recent studies have revised and added data for Hevelius (Vaquero & Trigo 2014; Carrasco et al. 2015, 2019) based on Hevelius (1647, 1652, 1679). We have re-analysed all their source records.

3 DATABLE OBSERVATIONS

For 1645, two data series were available in the V + 16 data base: Gassendi and Hevelius. Gassendi's observation was located on 1645 August 21 in the existing data bases (HS98; V + 16). In this case, Pierre Gassendi reported his eclipse observations with his new assistant, Jean Picard (Vaquero & Vázquez 2009). While his observation was known as an active day (G = 1) in the existing data bases (HS98 & V + 16), Gassendi attached only an empty solar disc and did not provide any information on presence or absence of sunspots at that time (Gassendi 1658, pp. 454–455; see also Carrasco et al. 2021). Therefore, Gassendi's record does not allow us to derive group counts for 1645 August 21, neither as quiet nor active days (ADs). Accordingly, Gassendi's data on 1645 August 21 should be removed from quantitative discussions on solar activity in 1645.

Furthermore, Hevelius reported as follows: ‘until November 5, because the atmosphere was ‘turbulent’, nothing could be noted. On 1644 November 14, 25, 28, 29, and 30 and 1644 December 2, 3, 4, 5, 6, 11, 16, and 21, and 1645 January 5, 6, 13, and 24, the Sun was clearly clean of sunspots [Original Text: Ad diem usque 5 Novembris, ob aerem nimis turbulentum, nihil annotatum neque animadversum; sic et die 14, 25, 28, 29, 30, 2 Decembris 3, 4, 5, 6, 11, 16, 21, ut et 5 Ianuarii Anno 1645, 6, 13 et 24, Sol plane ab omnibus Maculis defaecatus extitit.]’ (Hevelius, 1647, p. 525; Carrasco et al. 2019, p. 9). This record enabled us to derive four spotless days in 1645 (see also Carrasco et al. 2019) that were missed in V + 16.

In 1652, Hevelius reported sunspots in 1652 April (Hevelius, 1652). Vaquero & Trigo (2014) analysed these records and identified two groups with five spots on April 1, one group on April 3, and spotless days on April 6 and 7. This group count was then incorporated from V + 16. However, we located Hevelius’ full text (Hevelius, 1652, p. 8), found that Vaquero and Trigo (2014) overlooked the beginning of the original text, and revised the translation and nuances.

Our revised translation reads as follows: ‘So, there is nothing more to add, except one thing to be noted: during this eclipse, as well as during that whole day, no spot appeared on the sun, although on April 1 at 11:45 a.m. five spots could be seen on the solar disc: two very faint ones not far from the eastern limb, surrounded by fainter faculae and shadows, and three quite dense ones near the centre, in the northern latitude. Among the latter, only two were visible on April 3, and by April 6 they had completely degenerated into faculae. As for the other two, they were fainter. They had completely disappeared on April 7. [Original Text: Atque ita restat amplius nihil, nisi quod admonendum insuper censeo: durante hac Eclipsi, ut et tota ea die nihil prorsus in sole macularum apparuisse, quanquam die 1 Aprilis hora 11.45 in disco solis quinque visae fuerint maculae, duae quidem debilissimae non procul a limbo orientali, dilutioribus concomitantibus faculis umbrisque; tres autem satis densae, circa centrum, in latitudine Boreali. Ex quibus posterioribus die 3 Aprilis tantum duae conspectae, quae die sexta in faculas penitus degeneravere. Reliquae vero duae debiliores, die 7 omnino etiam sunt extinctae]’ (Hevelius, 1652, p. 8).

Thus, we translated Hevelius’ Latin records and added a spotless observation on 1652 April 8 in contrast with V + 16. Moreover, three of the sunspots recorded on April 1 were observed near the central meridian of the Northern Hemisphere in Hevelius’ statement.

In 1659, Hevelius also witnessed a partial solar eclipse on 1659 November 14 (Hevelius 1679, II, p. 182). Hevelius reported the following: ‘There appeared no sunspot on November 14 [Original Text: Nulla macula hac die 14 Novembris in Sole apparuit]’ (Hevelius 1679, II, p. 182). On this basis, we confirmed a spotless day on 1659 November 14.

Hevelius listed his datable sunspot observations from 1652–1675 in the third section of Machina Coelestis (Hevelius 1679), as translated in the appendix of Carrasco et al. (2015). We revisited the original text and corrected one date from 1659 May 19 to 1659 May 18, added one date (1657 December 21), revised three dates from active to quiet days (1653 March 27, 1654 August 27, and 1657 December 26), and revised one date from a quiet to an active day (1653 June 27). Here, Hevelius’ original text used macula(e) to describe individual spot counts (F). So far, V + 16 interpreted number of Hevelius’ macula(e) for each date as group counts (G). However, this is not necessarily correct. For example, on 1653 August 6 and 8, Hevelius reported: ‘three very tiny spots on the Sun, next to the ortho [Original Text: Tres Maculae minutissimae in sole circa Ortum]’; and ‘Seven spots sighted in a single mass. The seventh had increased significantly on the Sun [Original Text: Septem Maculae in una congerie conspectae. Septima vero multum in Sole erat promotior]’ (Hevelius 1679, III, p. 3). V + 16 interpreted their group counts as 3 and 0 on 1653 August 6 and 8, respectively. Hevelius’ original text requires us to immediately correct 1653 August 8 from a spotless day to an active day with one sunspot group (in a single mass) with seven individual sunspots. Hevelius’ original text also indicates these spots (maculae) on 1653 August 6 locate somewhat in a similar location. This record most probably indicates one sunspot group with three individual sunspots as his subsequent report on 1653 August 8 that indicates one sunspot group with seven individual sunspots. In other cases, Hevelius reported multiple individual sunspots (maculae) without their relative positions. In such cases, their sequence tends to have us prefer conservative group counts, whereas we need to accommodate margins for the exact group counts on the date. Therefore, we revised the group counts (G) for three cases (1653 March 25, 1653 August 6, and 1653 August 8) and accommodated uncertainty ranges for three cases (1654 August 25 and 1654 September 18–19).

In 1652 and 1659, Peter Petitus also reported sunspots upon solar eclipses on 1652 April 8 and 1659 November 14. He stated as follows: ‘We did not see any spots in the solar disc [Original Text: Nullae maculae in disco Solis a nobis conspectae fuerunt]’ on 1652 April 8 (Du Hamel 1660, p. 11); and ‘So, I have nothing more to say here about solar spots; indeed, no sunspots were observed, but the disc of the Sun was seen free from any spots, except for the clouds [Original Text: De maculis porro solaribus nil hic dicendum habeo; nullae enim tum observatae sunt, sed ab omni labe detersus si nubes excipias visus est Solis discus.]’ on 1659 November 14 (Du Hamel 1660, pp. 6–7)’. In addition, Petitus was associated with several sunspot observations during 1671–1672 and 1676–1677 in HS98 and V + 16. However, this was not confirmed in the original references cited in HS98’s bibliography: Du Hamel (1660) and Reference 87 of Wolf's Mittheilungen (Wolf 1850, p. 155). Wolf (1850, p. 155) cited Du Hamel (1660) for two observations on 1652 April 8 and 1659 November 14. In fact, it is unrealistic for Du Hamel (1660) to involve records (1671–1672 and 1676–1677) after publication (1660). Therefore, Petitus’ observations were confirmed only for 1652 and 1659. Petitus' records from 1671–1672 and 1676–1677 should be removed.

Another series of early sunspot observations in 1656 has been associated with Bose (1655) in the existing data sets (HS98; V + 16). However, this seems chronologically unrealistic. Bose’s original report is translated as: ‘… and what Antonio Maria de Rheita reported in 1642, that the month of June was cold because of the high number of spots. And in this same month of February, in which the atmosphere was so cloudy and rainy at all times with entire days when the Sun could not be seen for a single minute, even through the clouds, a whole row of spots could be seen from the 9th to the 21st. Of these spots, sometimes I was able to count eight quite large and black spots clearly. So, this changing situation in the atmosphere, though largely due to our vapours, is also much due to the rays of the Sun. These rays, when they strike the Earth in great numbers, make the atmosphere and the surface of the Earth in contact with it more calm, warm, and dry under normal conditions; when they strike in smaller numbers, then it is colder, wetter, and cloudier. [Original Text: … quodque Antonius Maria de Rheita animadvertit anno MDCXLII, mense Iunio fuisse frigus ob multitudinem macularum. Et hoc ipso mense Februario, quo tam nubilus et pluviosus ubique fuit aer, ut interdum per aliquot dies integros ne uno horae minuto solem, ne quidem per nubes, licuerit intueri, totus macularum tractus apparuit a die IX usque ad XXI. Quarum aliquando octo satis magnas et nigras distincte potui numerare. Nempe varia aeris temperies etsi magnam partem a vaporibus nostris provenit, tamen et solis radiis multum debet. Qui quo plures pertingunt ad terram, eo caeteris paribus, sereniorem, calidiorem et sicciorem; quo pauciores, eo magis frigidum, humidum et nubilosum reddunt aerem, eique subiectam terrae superficiem.]’ (Bose 1655, p. 18).

The publication in 1655 did not enable us to date this report on 1656 February 9–21 (as in HS98 and V + 16). Instead, the date of those records should be corrected from 1656 to 1655. This is likely identical with another unknown observer's report of a single sunspot on the same date in Maunder (1922, p. 141), whereas they were dated as 1655 March 9–21 in the existing data bases (HS98; V + 16). The revised dates are identical to an anonymous account for ‘a single group, which ran its course from 1655 February 9 to February 21’ in Maunder (1922, p. 141). Accordingly, this anonymous account most likely matches that of Bose (1655). Thus, that unknown observer (Unknown/Maunder) should be merged to Bose and their redundancy should be removed.

Here, Bose contrasted his observations with De Rheita's observations in 1642. This sentence cites Antonius Maria Schyrleus de Rheita for his observations in 1642. De Rheita recorded his sunspot observations on 1642 June 9–22 (De Rheita 1645, pp. 242–243; Vaquero et al. 2011). It is most probably Bose, who observed the sunspot in ‘[t]his very month in February’. De Rheita received an accusation from the Inquisition in 1653 and was later imprisoned in Northern Italy (Dupré 2014, p. 1822). Therefore, De Rheita is unlikely to have observed sunspots in 1655 February. As such, it is more appropriate to identify this observer as Bose, the author of Bose (1655). Moreover, Bose was an astronomer in Leipzig, where the Julian calendar was used by 1700 (Von Aufgebauer 1969). Therefore, we revised the observational year to 1655, as in Wolf (1874), corrected their dates to the Gregorian calendar as 1655 February 19–March 3, and merged the anonymous account in 1655 (Maunder 1922, p. 151) with Bose's data set. As this series accounted for 13 out of the 15 d of the known observations in 1656, transferring them to 1655 led to significant changes in the yearly means of group numbers for 1655 and 1656 against the previous studies. Our revision leaves no records in 1656, as the remaining 2 d with records (Hevelius) were not actual sunspot observations (Section 5). Nevertheless, without whole-disc drawings or measurements, his sunspot descriptions did not enable us to derive the sunspot positions at that time.

4 GENERAL DESCRIPTIONS

Apart from these datable observations, we have a series of sequential ‘spotless days’ in the existing data bases (HS98; V + 16), which are not categorized as datable observations but as general descriptions.

In 1648, the only known observations were dated during 1648 May 1–August 21 as a sequence of spotless days associated with an unknown observer in ‘Kraft’ (HS98; V + 16). HS98 associated this observer with Gassendi in their online supplementary material. Based on Wolf (1874, p. 263), we identified the original reference as a dissertation of Georg Wolfgang Krafft, citing the correspondence of Hevelius with Gassendi on 1648 August 21 (Krafft 1746, p. 25). His original statement was translated as follows: ‘From the beginning of May until now, no sunspots were observed, which is surprising. [Original Text: solares maculae ab initio Maii hucusque nullae prorsus, id quod admirabile, extitere]’ (Krafft 1746, p. 25). Subsequently, we confirmed that the observer was not Gassendi but Hevelius. Hevelius’ general statement did not allow us to identify datable observations except for 1648 August 21, although this statement qualitatively indicates the sunspot activity in this interval to have been extremely quiet. Therefore, we confirmed only a single spotless day on 1648 August 21 and associated it not with Krafft (or Gassendi) but with Hevelius.

In Maunder (1922), an unknown observer was cited for continuous spotless days between 1652 and 1654. Maunder (1922) describes the following: ‘indeed, from November 14, 1652, to August 12, 1654, no spots were reported at all’ (Maunder 1922, p. 141). While his source is unclear, Maunder (1922) emphasized his intention to summarize the achievement of Spörer, ‘It appears to me that this discovery of Spoerer's [sic] has not received as much attention as it deserves, and I would ask permission of the Association to summarize the main facts’ (Maunder 1922, p. 140). Consulting Spörer (1889, p. 315), we found the following statement: ‘In contrast, it is striking that there were no spots from 1648 May to August (W. 309), and that nothing was mentioned for sunspots when observing the solar eclipse in 1649 November (W. 155). However, if it were assumed that the minimum would have been prolonged after 1645, it would not be true that Hevel [NB Hevelius] saw spots of short duration in 1652 April and the Sun was spotless on three of them (W. 75), and that too of 1652 November 14 (W. 87), and also of 1654 August 12 (W. 74) the Sun is reportedly free from spots’ (Spörer 1889, p. 315).

Our discussions clarified their origin based on the absence of sunspots in 1648 May–August and ADs in 1652 April in the correspondence of Hevelius (1654b), Hevelius (1652), and Hevelius cited by Krafft (1746). Maunder (1922) likely misinterpreted the absence of sunspots on 1652 November 14 and 1654 August 12 as a chain of spotless days in this interval. Consulting Wolf's source references 75 and 87 in his Mittheilungen (Wolf 1850, pp. 151 and 155), we also found these dates to be a mixture of the existing observations. Wolf's Reference 87 (Wolf 1850, p. 155) showed its onset on 1652 November 14, likely confusing the dates of the two eclipses that Petitus observed on 1652 April 8 and 1659 November 14. These dates were mixed and caused an incorrect onset of spotless days on 1652 November 14. In contrast, Wolf's Reference 75 (Wolf 1850, p. 151) shows that its end on 1652 November 14 was associated with Hevelius’ eclipse observations on 1654 August 12 in Epistolae (Hevelius 1654a; see Fig. 1). This discussion confirms that the existing spotless days between 1652 November 14 and 1654 August 12 were not based on scientific evidence but derived from multiple misinterpretations. Therefore, these data should be removed. Moreover, Hevelius (1679, II, pp. 35–40) mentioned neither presence nor absence of sunspots on on 1654 August 12 upon his eclipse observation. Hevelius reported at least 11 active days in this interval.

Another sequence of general spotless days was derived from the observations of Jean Picard in 1653–1659, cited in John Keill (HS98). V + 16 speculatively suggested the removal of his data from 1655–1659 on the basis of continuations of the spotless days (see also Zolotova and Ponyavin (2015, pp. 5–6)). HS98’s supplementary bibliography described this sequence as the following: ‘Keill says Picard saw one or two sunspots from 1653 May to 1670 June (pp. 51–53 of Institutiones). From other sources we can identify the spots seen in 1660 and conclude none were seen for 1653–1659. Keill in 1745 [sic] was the last person to see these early notebooks by Picard’. The original statement in Keill's Institutions was translated as the following: ‘… but (mais) from 1653 until (jusqu'en) 1670 at best one or two were discovered; since then they have reappeared quite often in abundance. It seems that they do not follow any rule in their appearance [Original Text: … maisdepuis 1653jusqu'en1670 à peine en a-t-on découvert une ou deux; depuis elles ont reparu assez souvent en abondance. Il semble qu'elles ne suivent aucune loi dans leur apparition]’ (Keill 1748, p. 52; emphases added). Keill's statement does not support continuous spotless days in this interval. Moreover, while a parallel description is also found in his Latin monograph (Keill 1746, pp. 44–49), the monthly descriptions (1653 May and 1670 June) are not described here either. This was the same with Wolf (1850, p. 75), where Keill (1748) was directly cited. HS98 might have misinterpreted the French words mais and jusqu'en as mai (May) and juin (June). Therefore, it is not realistic to derive continuous spotless days from Keill (1746, 1748) as done in HS98 (or – to less extent – in V + 16).

Overall, Keill's statement indicates that the sunspot activity was rather quiet in 1653–1670, even though this general description does not warrant entire spotless days in this interval. At least, such an assumption contradicts other datable sunspot observations, such as those of Bose and Hevelius (see our Section 2 and appendix of Carrasco et al. 2015). Therefore, this general description should be entirely removed from the group count data bases but should be used as a qualitative indication for a quiet solar activity in 1653–1670.

5 MISINTERPRETED RECORDS

In addition, two other cases were derived from misinterpretations of other observations in the early MM. The first is Hevelius. In addition to his April observations in 1652, the existing data bases include Hevelius’ observations of spotless days in 1652 October–December. However, Hevelius (1679) described these observations as those of the ‘solar meridian altitudes (altitudo meridiana solis)’, as shown in Fig. 2. We have found similar cases in Hevelius' solar altitude records without explicit annotations for presence/absence of sunspots (see Hevelius 1679, III, pp. 1-8). The actual sunspot observations of Hevelius from 1653–1659 are only those discussed in Section 3 (c.f., Carrasco et al. 2015) and his eclipse observation on 1659 November 14 (Hevelius 1679, II, p. 182). Otherwise, Hevelius' ghost spotless days in 1653–1659 should be removed.

Mouton's observations in 1659–1661 were also the case, as stated in HS98’s supplementary bibliography as the following: ‘Dates of transits, plus absence of sunspots, establishes days when no spots were on the sun’. HS98 describe their source as ‘Manuscript. Paris Observatory’. We identified Mouton's ‘manuscript’ in the Paris Observatory with MS A2/11 and found its contents to be virtually identical to those of Mouton (1670). Comparisons with Mouton (1670) indicate that the observational dates of Mouton are identical to his solar diameter observations (Mouton 1670, pp. 299–315). No explicit mentions of sunspots were found in Mouton's solar diameter observations. Such observations cannot be used to reconstruct group counts without explicit sunspot descriptions (e.g. Vaquero 2007; Clette et al. 2014; Vaquero and Gallego 2014; Hayakawa et al. 2021a). Therefore, these data should be removed from the group count data bases.

6 GROUP COUNTS

In Sections 3–5, we reviewed and revised the group counts from 1645–1659 (Appendix). Our revision is summarized in Fig. 3, in contrast with V + 16 in the upper panel. Our revision has eliminated contamination and reduced data availability for the early MM. From 1645–1659, our revision accommodates 107 observations performed over 105 d by three observers: Hevelius, Bose, and Petitus. The majority originated from Hevelius (92 observations), offering homogeneous data sets over the early MM. Bose and Petitus reported their sunspots observations for 13 and 2 d, respectively.

Our revision also reduced the number of maximal sunspot groups in the early MM. V + 16 recorded the maximum group counts in the early MM as four on 1654 September 19. However, this is likely no longer the case, as this was not the number of sunspot groups (group counts) but the number of individual sunspots (spot counts). Conservatively, these modifications reduced the credibility of the greatest group counts of four on 1654 September 19 and located a conservative maximum as G = 2 on 1652 April 1. Consequently, these modifications indicate that the early MM was less active than what Svalgaard and Schatten (2016) suggested.

Fig. 4 compares the yearly mean group numbers in the early MM in Svalgaard and Schatten (2016) with our conservative brightest star estimates following the methods of Svalgaard and Schatten (2016). This figure illustrates that our conservative reconstruction indicates that the early MM was less eventful than that considered by Svalgaard and Schatten (2016). Caveats must be noted for the brightest-star estimates, as these estimates, as little is known for the scale factors of individual observers before the mid-18th century and any variability can immediately affect the resulting estimates (e.g., Chatzistergos et al., 2017).

7 ACTIVE DAY FRACTIONS AND SUNSPOT NUMBER ESTIMATES

We compared V + 16’s data set and our revised data set in terms of the ADF (Kovaltsov et al. 2004; Carrasco et al. 2021) and sunspot number estimates obtained from the ADF (Kovaltsov et al. 2004; Vaquero et al. 2012, 2014; Carrasco et al. 2022). In periods of low solar activity, such as the MM, solar activity is accurately tracked by the ADF because it is simpler and more robust than the sunspot number.

The yearly ADF (in percentage) was defined as 100 multiplied by the number of ADs in a particular year divided by the number of observation days (ODs) in the same year, where an active day was defined as a day on which at least one sunspot was detected in the Sun. In this study, the OD, AD, and ADF values were calculated for both the data set of V + 16 and our revised data set over 1645–1959. The results are presented in Table 2 and Fig. 5 (upper panel). The upper and lower limits for the ADF were computed as 90 per cent two-sided uncertainties of a hypergeometric probability distribution given by the following expression:

where N is the number of days in a year (365 or 366), s is the total number of ADs within the year to be estimated, n is the number of observations in the sample, and r is the number of ADs in the sample (Kovaltsov et al. 2004). The probability distribution assumes that a sample is composed of random elements. In practice, contemporaneous astronomers did not observe the Sun in a random manner for our target period. They performed more observations on ADs because they made observations on consecutive days when sunspots were detected. Thus, the probability of reporting an active day was higher than that of reporting an inactive day; therefore, the elements in our sample were not perfectly randomly distributed. Therefore, the values in Table 2 and Fig. 5 must be considered as upper limits.

From the ADF values, estimates of the yearly mean sunspot number (S_N) were computed in this work. For this purpose, the optimal fit calculated by Carrasco et al. (2022) was used, which is as follows:

where a = −9.442 × 10⁻², b = 0.110, c = –1.617 × 10⁻³, and d = 9.820 × 10⁻⁶. Carrasco et al. (2022) obtained the equation after comparing S_N data (version 2) provided by the Sunspot Index and Long-term Solar Observations (SILSO) with ADF values computed from SILSO data for the period 1818–2020. According to Carrasco et al. (2022), this equation cannot be employed to estimate S_N values associated with ADF equal to 100 per cent. However, we employed this equation because it represents the best ADF–S_N relationship when compared with other studies, and the relationships of Kovaltsov et al. (2004) and Vaquero et al. (2012, 2014) are more restricted because they consider ADF values lower than 60 per cent, 95 per cent, and 85 per cent, respectively, for their S_N estimates. Fig. 5 (lower panel) depicts the S_N estimates calculated in this study for the data set of V + 16 and those obtained after our revision.

Table 2 and Fig. 5 show the change in values caused by our revision of the data set of V + 16 for 1645–1659. As mentioned in the previous section, our revision removed contaminations extensively. This is verified in Table 2. For most years, the number of ODs decreased. In contrast, Table 2 and Fig. 5 show that the values of ADF and S_N increased for most years. Notably, our revision resulted in the loss of available data for 1656. Therefore, there are no values of ADF or S_N in Fig. 5 associated with our revision for 1656, whereas there are values associated with the V + 16 data base. In addition, since the equation used to estimate S_N cannot be used for ADF = 100 per cent (Carrasco et al. 2022), Fig. 5 does not show a S_N estimate in 1645 (or upper limits in 1645 and 1656) for the V + 16 data set or a S_N estimate in 1655 (or upper limits in 1654 and 1655) for our data set.

8 SUMMARY AND OUTLOOKS

In this study, we collected and re-analysed all known sunspot records in the early MM (1645–1659) based on their source reports. We first identified their source reports (see Table 1), consulted their original records, and classified them into three categories: datable observations, general descriptions, and misinterpreted records. We analysed their individual records to revise the datable records and remove general descriptions and misinterpreted records. Accordingly, we revised the data for Hevelius, Petitus, and Bose. In contrast, we removed general descriptions in Krafft (actually Hevelius and merged to Hevelius), Unknown/Maunder, and Picard/Keill and misinterpreted records in Hevelius (actually solar meridian observations), and Mouton (actually solar diameter observations). The results are summarized in Appendix (Table A1).

Our results confirmed a temporal coverage of the sunspot records for 2 per cent of the total dates in this interval, in contrast to 18 per cent and 92 per cent in V + 16 and HS98, respectively (Fig. 6). We highlight this significant decrease in the temporal coverage in our work as an improvement of the sunspot record data bases, because we have removed numerous contaminations included in the existing data bases (HS98; V + 16). Our results found that source reports (three and four groups in 1654 September) for the greatest group counts in V + 16 actually gave the spot counts (F) rather than group counts (G). Thereby, the group counts remained ≤2 throughout the early MM. Following the brightest star method, we must revise the group counts from 1653–1654 significantly downward, in contrast to Svalgaard and Schatten (2016). This result contradicts the alleged regular solar cycles in the MM in several studies (Zolotova and Ponyavin 2015; Miyahara et al. 2021).

We also computed the ADF and reconstructed the sunspot number in the early MM in terms of the upper limits. Our results led us to revise the ADF and sunspot numbers significantly upward in contrast to Carrasco et al. (2022), as we removed numerous ghost spotless days from the previous studies. We also compared our results with proxy-based sunspot numbers reconstructed from ¹⁴C in tree rings (Usoskin et al. 2021). For 1645–1654, our results were consistent with those of Usoskin et al. (2021). For 1657–1659, our results show a more realistic sunspot number than Usoskin et al. (2021), who showed negative sunspot numbers. Thus, our results lead to a better agreement with the proxy-based reconstructions.

These source records originate from textual reports and provide little information about sunspot positions. However, Hevelius reported sunspots in the ‘northern latitude’ in 1652 April (Hevelius, 1652, p. 8; Vaquero and Trigo 2014). This is in contrast to the southward hemispheric asymmetry of the sunspot groups reported in the late MM (1671–1715), as shown in previous studies (Ribes and Nesme-Ribes 1993; Hayakawa et al. 2021b). It is unclear whether this description can be generalized to early MM, as this is a unique report on sunspot positions in the early MM. It is possible that (1) sunspots appeared in the northern solar hemisphere more frequently (general trend), (2) sunspots appeared in both solar hemispheres (a random mention), or (3) sunspots in the northern solar hemisphere were unique in contrast to the majority of the sunspots in the southern solar hemisphere (an exception). However, further studies are required to resolve this issue. Currently, our results require the scientific community not to overgeneralize hemispheric asymmetry in the late MM to the entire MM.

ACKNOWLEDGEMENTS

This research was conducted under the financial supports of JSPS Grant-in-Aids JP15H05812, JP20K20918, JP20H05643, JP21K13957, JP20KK0072, JP21H01124, JP21H04492, and JP22K02956. HH has been part funded by JSPS Overseas Challenge Program for Young Researchers, the ISEE director's leadership fund for FYs 2021, 2022, and 2023, Young Leader Cultivation (YLC) programme of Nagoya University, Tokai Pathways to Global Excellence (Nagoya University) of the Strategic Professional Development Program for Young Researchers (MEXT), and the young researcher units for the advancement of new and undeveloped fields, Institute for Advanced Research, Nagoya University of the Program for Promoting the Enhancement of Research Universities. HH acknowledges the International Space Science Institute and the supported International Teams #417 (Recalibration of the Sunspot Number Series), #510 (SEESUP Solar Extreme Events: Setting Up a Paradigm), and #475 (Modeling Space Weather And Total Solar Irradiance Over The Past Century). AJP Aparicio thanks Universidad de Extremadura and Ministerio de Universidades of the Spanish Government for the award of a postdoctoral fellowship Margarita Salas para la formación de jóvenes doctores (MS-11).

Data Availability

Our revised spot and group counts, based on the source records in Table 1, are fully listed in Table A1 in the Appendix below and https://doi.org/10.18999/2009259.

References

APPENDIX: OUR REVISED SUNSPOT DATA SET IN THE EARLY MM.