How Deep Was the Maunder Minimum?

Solar Phys DOI 10.1007/s11207-016-0908-z SUNSPOT NUMBER RECALIBRATION

N.V. Zolotova1,2 · D.I. Ponyavin1

Received: 30 September 2015 / Accepted: 13 May 2016 © Springer Science+Business Media Dordrecht 2016

Abstract One of the most enigmatic features of the solar history is the Maunder minimum (MM). We analyze reports of solar observers from the group-sunspot-number database. Particular attention is given to short notes that resulted in an underestimation of the sunspot activity. These reports by Derham, Flamsteed, Hevelius, Picard, G.D. Cassini, and Fogel are found to address the absence of sunspots of great signiﬁcance, which could signify a secular minimum with a majority of small short-lived spots. Up to Schwabe’s discovery of the solar cycle, sunspots were considered as an irregular phenomenon; sunspot observations were not dedicated to the task of sunspot monitoring and counting. Here, we argue that the level of the solar activity in the past is signiﬁcantly underestimated.

Keywords Sunspots · Sun: activity

1. Introduction

In view of the poor sunspot statistics in the seventeenth century in comparison to the modern age, it may be wondered whether the Sun is a constant star with a regular behavior or whether there are grand minima without a Schwabe cycle. Parker (1976) wrote: “...the number of sunspots went through two distinct maxima after 1611, and then fell to a minimum at about 1645. . . During the 70 years of inactivity there was occasionally a sunspot or two, but long years with none at all; there was no white-light corona visible during total eclipse by the Moon, whereas the corona is usually so conspicuous then; there were only a few signiﬁcant auroral events. . . The occurrence of the 70-year minimum (sometimes called the Maunder minimum), indicates that there is available to the Sun a convective mode of

Sunspot Number Recalibration Guest Editors: F. Clette, E.W. Cliver, L. Lefèvre, J.M. Vaquero, and L. Svalgaard

B N.V. Zolotova [email protected]

1 St. Petersburg State University, 198504 St. Petersburg, Russia 2 Pulkovo Astronomical Observatory, Russian Academy of Sciences, 196140 St. Petersburg, Russia N.V. Zolotova, D.I. Ponyavin circulation different from its present state. The other mode Ð let us call it the Maunder mode Ð is such as to be less effective in the generation of magnetic field. Evidently the Sun can flip-flop back and forth between the Maunder mode and the present mode.” In the early 1970s, Parker called Maunder’s articles to Eddy’s attention (see Schröder, 2005,the interview with Eddy). Later, Eddy (1976) concluded that the “70-year period was indeed a time when solar activity all but stopped.” In contrast, a year later, Gleissberg (1977) claimed that “the occurrence of the 11-year cycle was not suspended during the Maunder minimum. However, the occurrence of a particularly low minimum of the 80-year cycle produced a sequence of weakly pronounced 11-year cycles.” Eddy commented that his own estimation (Eddy, 1976) of the magnitude of solar activity in the Maunder minimum (MM) might be underestimated by a factor of two or three. Combining this comment by Eddy with the auroral data (Schove, 1979) and the loss of small spots in observations of the past (Kopecky and Kuklin, 1987), Vitinskij, Kopetskij, and Kuklin (1986, Figure 37) concluded that although the level of solar activity was low, the maximum Wolf number was hardly below 40. Eddy (1976) also stated that telescopes were good enough to resolve even small spots; however, Clerke (1894) briefly mentioned that instruments in the seventeenth century were hopelessly defective. With reference to Clerke, Eddy (1976) claimed that during the MM there was also a marked dearth of aurorae. On the other hand, Schröder (1979, 1992) stated that in almost every year Ð before and during the Maunder minimum Ð aurorae have been observed in Middle Europe. He claimed that a regular solar cycle and similar auroral and geomagnetic activity existed during the MM (for further reading see Schröder, 2005). Regarding the length of the MM, Silverman (1993) wrote “. . . Legrand, Le Goff, and Mazaudier (1990) modify the period of the minimum, stating that the frequency of aurora from 1645 to 1670 was only slightly less than for 1582 Ð 1648, but that for the interval 1671 Ð 1710, auroral activity decreased up to 1700, with only eight aurorae reported from 1690 Ð 1700, compared with twenty-eight for 1680 Ð 1689, and seventeen for 1670 Ð 1679. These results are consisted with those presented in my paper. What Legrand et al. have done, essentially, is to place the minimum between 1670 and 1703, rather than between 1645 and 1715...” VaqueroandTrigo(2015), in contrast, recently proposed that the core deep MM spanned from 1645 to 1700, and the wider extended MM for the period 1618 Ð 1723. They used the regional auroral series for Hungary (Réthly and Berkes, 1963) along with a reconstruction of solar activity based on the verified carbon cycle, 14C production, and an archeomagnetic field model (Usoskin et al., 2014). A lively debate on the relation of a lull in solar activity with cold conditions on Earth was launched. For instance, according to some authors (Landsberg, 1980; Legrand, Le Goff, and Mazaudier, 1990), the hypothesis that the MM was notably cold and different from other intervals in recent climatic history cannot be maintained. Other authors (Soon and Yaskell, 2003) described numerous examples of anomalies in the terrestrial climate throughout the world during the MM. On the other hand, Lockwood et al. (2010) stressed that there is only a regional and seasonal effect of solar activity related to European winters and not a global effect. Analyzing the database of the nominal number of sunspot groups [Rg]byHoytand Schatten (1998), Zolotova and Ponyavin (2015) pointed out that some observers, among whom were Marius, Picard, Siverus, Giovanni Domenico Cassini, Dechales, Maraldi, Ric- cioli (G.D. Cassini’s teacher, who never reported even a single spot from 1618 to 1661) made gaps in reports on a blank solar disk when others reported sunspots. They suggested that these gaps appeared as a result of the planetary theory of sunspots. In the same year, How Deep Was the Maunder Minimum?

Usoskin et al. (2015) criticized this suggestion. They found that the Hoyt and Schatten (HS) database for Marius continuously filled in zeros in 1617 Ð 1618 based on his brief note that he saw fewer spots over the last one and a half years. Thus, the database for Marius is continuously filled in with zeros with only gaps when other observers reported sunspots. In other words, continuous zeros with gaps in the Rg-database are an extrapolation of brief notes (like “I did not see any spots several years”) as daily reports on the absence of spots. Most probably, similar periods from 1653 to 1665 for Picard and from 1675 to 1690 for Siverus and others are also extrapolations made by Hoyt and Schatten. Clette et al. (2014) found that solar-meridian observations were included in the Hoyt and Schatten database as nonactive days. However, if no sunspots were mentioned in the meridian passages, it did not necessarily mean that spots were absent. Recently, Gómez and Vaquero (2015) noted that observations by Anton Maria Schyrlaeus Rheita in 1642 were incorrectly interpreted. Instead of eight sunspot groups on 9 Ð 21 February 1642, he reported one group in June. Using the active-day statistics (Kovaltsov, Usoskin, and Mursula, 2004), Vaquero et al. (2015) found cyclic variability throughout the MM. The low fraction of active days has indicated that the magnitude of the sunspot cycles from 1650 to 1700 was very low. In this article, we reflect on the question “What was happening on the Sun during the Maunder minimum?”. Section 2 deals with the views of the scientific world in the seventeenth century. Section 3 describes that the absence of the counting process of sunspots has led to a crucial suppression in the Rg-index over the MM. In the following section, we dis- cuss the underestimation of sunspot groups in textual sources. In Section 5 we compare the MM with the Dalton and Gleissberg minima. Section 7 deals with the ambiguity of the solar activity proxies. Section 8 is devoted to conclusions.

2. History

With confidence, the seventeenth century can be called the era in which physics and mathe- matics were established (known as the scientific revolution). In the time of Johannes Kepler, Robert Hooke, and Isaac Newton, almost all of astronomy was reduced to astrometry. The scientific world view based on Aristotle’s geocentric cosmology and Ptolemy’s epicycles was the generally accepted doctrine for more than ten centuries. Attribution of maculae to the Sun cast doubt on the idea of the immutability of the heavens, which was a strong point in Aristotle’s canons (Mitchell, 1916). The scientific world view gradually transformed during the seventeenth to the second half of the eighteenth century. When Scheiner offered to show sunspots to his colleague Theodore Busaeus, he answered “I have read my Aristotle from end to end many times and I can assure you that I have never found in it anything similar to what you mention.” (Mitchell, 1916; Soon and Yaskell, 2003). Obviously the mention of a scientific authority like Aristotle was an incontrovertible argument at this time. As soon as spots were discovered, the controversy about the origin of maculae arose. The opponents had detected no parallax for the spots (Scheiner, 1612a; Galilei, 1613;Tarde, 1620) and concluded that the spots were not in the atmosphere of the Earth. In 1607, Johannes Kepler (Joannis Keppleri) observed a sunspot (Keppleri, 1609) and mistakenly thought that the spot was a transit of Mercury. Later he realized his mistake (Grego and Man- nion, 2010). Scheiner (1612b) compares “Kepler’s Mercury” with a sunspot (Figure 1a). He reasoned that if spots were present on the Sun, then it would indicate that the Sun rotated (because of the spot motion), and then spots were expected to reappear in 15 days, but if the sunspots were not to return, the Sun would not rotate, and the spots would be small N.V. Zolotova, D.I. Ponyavin

Figure 1 Sunspot drawing from Scheiner (1612b) (a). Rotating Bourbon planet by Tarde (b), diagram from Baumgartner (1987). Figure from Wolf (1861)(c). stars (stellae) that passed near the Sun (Mitchell, 1916), similarly to the moons of Jupiter (Scheiner, 1612a). The two spots in Figure 1a are without their trailing parts, which indicates an interest of astronomers in objects of great significance. Galilei (1613) wrote that the spots might consist of a thousand unknown things, but more similar to terrestrial clouds, vapor, exhalations, or smoke produced by the solar body, or attracted by it from all sides (Mitchell, 1916). In letters to Welser, he adduced several arguments against Scheiner’s. Over the years, Scheiner (1630, 1651) agreed with Galileo that spots are not celestial bodies, but continued to disagree about the rotation of the Sun (Scheiner, 1651). Tarde (1620) fought back against Galileo’s objections. In particular, according to the planetary theory, the spots are numerous. They appear in close configuration as they pass before the Sun. Tarde stated that i) the brightness of the Sun distorts the perfect shape of the spots; ii) therefore they are difficult to observe and the spots seem of irregular shape; iii) spots may appear or disappear because of merging with the sunlight; iv) spots do not emit light and are only seen during a transit across the solar disk; v) the foreshortening near the limb arises because the spots have phases similar to those of the Moon (Figure 1b). The closeness of the spot orbits to the Sun caused them to rotate faster near the center of solar disk. The discussion in the letters by Galileo and Scheiner to Mark Welser led to long-lasting scientific debates, not to the rapid displacement of the Aristotelian doctrine in favor of the new science. The golden age of planetary theory begins in 1633, when Malapert, Kircher, Gassendi, Guerick, and others supported this idea (Baumgartner, 1987). However, Kircher was later of two minds about sunspots (they move either around the Sun, or with the Sun) (Gleissberg, Damboldt, and Schove, 1979). Kircher (1678) drew the solar surface as a rough sea with faculae as bright fires, with volcanoes, vapors, and spots as clouds of dark smoke (Buonanno, 2014). The university was even more resistant to change. For instance, Dobrzycki (1999)mentioned that in Cracow University, Galileo’s followers were a small group; as a rule the published theses strictly adhered to the Aristotle-based philosophy of nature. University teaching remained unchanged until the 1770s. Geocentricism and the planetary theory of spots gradually vanished. However, Wolf (1861) still drew the spots attracted from space to the Sun, with foreshortening toward the limb (Figure 1c). With reference to Scheiner, he argued that spots are not celestial bodies. The discovery of Neptune in the middle of the nineteenth century briefly revived the planetary theory of the sunspot origin. Finally, Maun- der (1922) wrote that the butterfly diagram suggests that the spots are neither planets nor meteors. How Deep Was the Maunder Minimum?

In the era when spots were not counted, when the authority of Aristotle was still great, the historical context, wars, epidemics, and the biography of each observer became important. For example, Jacques Cassini was a fervent Cartesian (Hockey et al., 2007). Cartesianism is the philosophical doctrine, developed by Descartes (1637), according to which theoretical ideas are self-sufficient and cannot be proved by an experiment. In other words, if an experiment contradicts a theory, then preference should be given to the theory. Hence, we may not expect that this philosophical doctrine stimulated regular sunspot observations to dis- close the nature of the spots. The scientific school, profession, location, scientific views and interests, instruments, and other factors should be taken into account. In large cities, telescopic observations could be complicated by anthropogenic factors. For instance, because the price of firewood rose in London in the sixteenth and seventeen centuries, coal became the dominant fuel in London for domestic as well as industrial uses (Thorsheim, 2006;Brim- blecombe, 2012). As a consequence, by the middle of the seventeenth century London and its environs were covered by strong smoke (Evelyn, 1661). This clearly reduced the number of spots seen with a telescope. To gain a pension, some scientists aspired to patronage of the ruling dynasty. For instance, Galilei (1610) named the satellites of Jupiter in honor of the Medici, Malapert (1633) called the spots the Austrian stars and dedicated his work to the king of Spain, Philip IV, and Tarde (1620) to Louis XIII. Tarde argued that spots are bodies orbiting the Sun. These, named Bourbon stars, were the princes, nobles, and archers, close to the Sun, which symbolizes the French monarchy (Baumgartner, 1987). Here we may not say that an investigation of the Sun was unaffected by politics and religion.

3. Why Count Clouds?

The number of sunspots reported by an observer crucially depends on the subject of his interest. Sunspot counting was not a signiﬁcant goal. The president of the Royal Astronomical Society (Johnson, 1858) when presenting to Schwabe the highest award, the Gold Medal, said in his address: “This is, I believe, an instance of devoted persistence (if the word were not equivocal, I should say, pertinacity) unsurpassed in the annals of astronomy. The energy of one man has revealed a phenomenon that had eluded even the suspicion of astronomers for 200 years!” He mentioned such au- thorities as Keill (1739), J. Cassini (1740), Le Monnier (1746), Long (1764), and Lalande (1771), who stated that it was obvious to everyone that there is no regularity in formation, number, shape, magnitude, and time of appearance and disappearance of sunspots. Delam- bre (1814) wrote that spots are more curious than useful. Johnson (1858) also wrote that “...theoldobserversattendedmuchmoretothephysicalcharacteristicsofthespots,and to their time of rotation, than to their number. . . Scheiner’s attention was almost exclusively directed to physical peculiarities, and Derham’s investigations (Phil. Trans. 1711) were obviously very desultory.”

3.1. Short Reports

Derham (1710) tabulated days from 1703 to 1710 when spots and faculae visible at Up- minster (England) were visible to him. This report, like many others during the seventeenth century, is unrelated to sunspot counting, which provides one sunspot group per day. In the text, Derham described the evolution of some maculae and concluded that the spots are a result of erupting volcanos, where the umbra is a crater, the penumbra, a smoke (neb- ula), and the facula, the ﬂame of the volcano. We suggest that Derham must have mainly N.V. Zolotova, D.I. Ponyavin

Figure 2 Comets from Hevelius (1668).

aimed at sufficiently large sunspots, because small spots are short-lived and not variable in their shape and size, hence it would be impossible to prove volcanic eruptions on the Sun. Moreover, while according to La Hire (Ribes and Nesme-Ribes, 1993), 1700 Ð 1710 is the period of strongly asymmetric sunspot appearance, Derham (1710) does not mention such a prominent peculiarity as the hemispheric skewness. Derham (1710) also wrote that there are sometimes frequent spots on the Sun and sometimes none in many years, as between the years 1660 and 1671, 1676 and 1684. He explains that the long disappearance of spots probably arises “from the want of extraordinary Erup- tions in that fiery Globe.” On 2 May 1684, Flamsteed (Cambridge) wrote to Molyneux “Aprill in the morneing as ' 1 I was taking the distance of from the Sun I discovered a large spot. . . tis neare 7 2 yeares since I saw one before they have of late beene so scarce how ever frequent in the days of Galileo and Scheiner.” On 8 July 1684, he wrote to Bernard that this month he observed large spots (translated by Forbes, Murdin, and Wilmoth, 1997): “The magnitude and consistency of the spot emerging from the Sun seems to me to be such that I believe it may still last for another solar rotation. . . I think that this one spot will not last for three solar rotations, but that two or more have arisen. . . in the vicinity of the first; . . . that Etna-like mountains have been raised up from the thick subcutaneous matter of the Sun.” Weiss and Weiss (1979) translated Hevelius (1668), who noted that “sometimes there is a long interval of time when hardly any spots are observed upon the Sun. Indeed, for a good many years recently, ten and more, I am certain that absolutely nothing of great significance (apart from some rather unimportant and small spots) has been observed either by us or by others. On the other hand, in former times (as Rosa Ursina and Solenographia confirms) a great many spots, remarkable for their size and density of distribution, appeared within a single year.” We note that Hevelius related the spots to comets (Figure 2). In 1671, Picard, G.D. Cassini, and Fogel reported a large sunspot (Weiss and Weiss, 1979). Picard wrote that it was ten years since he had seen a large spot (Picolet, 1978; Vaquero and Vázquez, 2009), and with reference to G.D. Cassini, Oldenburg (1671) noted How Deep Was the Maunder Minimum? that it was about twenty years since astronomers have seen any considerable spots. For Fogel (Hamburg) the HS database consists of zeros from 15 October 1661 to 31 July 1671, which gives 365 observational days per year. However, this is impossible if only due to weather conditions. Finally, these short text reports do not indicate that activity was all but stopped. As- tronomers wrote that it was a long time when significant spots (similar to those observed by Scheiner in 1625) had not appeared. Here, we can speculate that the period of Galileo and Scheiner was a secular maximum, while the MM was a secular minimum. It is noteworthy that the weak Cycle 24 exhibits a deficit of large spots; most of the spots are small and short-lived (Nagovitsyn, Pevtsov, and Livingston, 2012).

3.2. Excess of Zeros

Continuous zeros in the database lead to the illusion of a well-observed Sun (365 observational days per year) and an underestimation of the activity level. While short reports about the absence of spots over years were included in the database, short notes about non-stop sunspot activity can hardly be involved. For example, in the bibliography of the database, Hoyt and Schatten wrote that according to a letter by Crabtree to Flamsteed in 1640 the average number of spot groups seen in 1638 and 1639 was four to five per day.1 The database has Greenwich fill values to give four to five groups per day. This substitution was discussed by Vaquero et al. (2011). As another example, Gleissberg, Damboldt, and Schove (1979) quoted a report by von Guericke and Schott (1672): “At times, although infrequently, one can count 30, at times 20 etc., well distinguishable spots at the same time, occasionally but one or two and sometimes none”; and a remark by Ettmüller (1693), who observed in 1689 and 1690: “...thedimensionsofthespotscomparedwith each other are different is proved by daily experience”. On the one hand, this means that there were spots in the core of the MM, on the other hand, it is impossible to include this sort of information in the database. Gleissberg, Damboldt, and Schove (1979) also pointed out that observers were often interested in the reappearance of spots in the next solar rotation (to prove or disprove the external nature of spots), hence the long-lived spectacular spots with prominent changes in their shape and size mainly attract attention, not small ones.

3.3. Transit of Sunspots

Hevelius, Derham, and G.D. Cassini mentioned that Cristoph Scheiner often reported large spots. Here, we suggest that the 1620s probably belong to a secular maximum. Scheiner argued that the Sun rotates around the Earth; he drew sunspot transits (Scheiner, 1630, 1651) to check their reappearance in the next solar rotation. Figure 3 shows sunspot drawings of 12 Ð 26 July 1629 (red frame), 9 Ð 22 August (blue), and 5 Ð 24 September (green).2 Com- parison of the drawings within each month demonstrates that the observer is not interested in the transit of small spots, which are drawn with gaps. Finally, Scheiner gave his attention

1Concerning the Crabtree letters, we did not find his letter to Flamsteed, but in the letter to Gascoigne (Der- ham, 1710), he wrote that Gassendi affirms that sometimes 40 spots at once are seen on the Sun. Because observers of the seventeenth century did not count sunspots as groups, four to five objects per day in 1638 Ð 1639 can mean umbras or spots, not groups. 2We note that each drawing in a frame covers the entire time interval, 12 Ð 26 July, 9 Ð 22 August, or 2 Ð 24 September. N.V. Zolotova, D.I. Ponyavin

Figure 3 Sunspot drawings in 1629 from Scheiner (1651): August (a Ð c), July (e Ð g), September (h Ð j). Daily number of sunspot group (k). Black denotes number of sunspot groups (NSG) from the HS database; red, blue, and green, the same from drawings. only to the large spots (Figures 3d, 3g, 3i, and 3j), usually without penumbra and trailing spots. We counted (Table 1 and Figure 3k) the daily number of sunspot groups (NSG) from Scheiner (1651). In 1629, the HS database for Scheiner provides one sunspot group per day (black in Figure 3k). Since sunspot groups tend to appear at almost the same latitudes, the pattern of transits is complicated. In Figure 3h, the transit of the sunspot on 19 September (designated by a How Deep Was the Maunder Minimum?

Table 1 Daily number of sunspot groups in 1629 from July August September Scheiner (1651). Day NSG Day NSG Day NSG

1219151 131 10262 142 11272 152 12282 162 13292 17 2 14 3 10 3 18 2 15 3 11 4 19 2 16 3 12 6 20 2 17 3 13 6 21 2 18 3 14 5 22 2 19 2 15 4 23 2 20 2 16 4 24 1 21 1 17 4 25 1 22 1 18 4 26 1 19 5 20 2 21 2 22 2 23 1 24 1

Figure 4 Sunspot sketch of 14 August 1947 from the Greenwich photoheliographic catalog (Gyori,˝ Baranyi, and Ludmány, 2011) (a), the photoheliogram of 23 March 2014 from the Kislovodsk Solar Station (Tlatov et al., 2014)(b). small green circle) is skipped because it overlaps with that of the nearest sunspot on 14 Ð 15 September. During 5 Ð 24 September, Scheiner drew transits of seven new sunspot groups. Figures 4aand4b demonstrate that the solar disk was covered by sunspots on 14 August 1947 (secular maximum) and 23 March 2014 (secular minimum). According to the Green- N.V. Zolotova, D.I. Ponyavin

Figure 5 Butterﬂy diagram of sunspot groups: with an area larger than 500 msh (a), with an area smaller than 500 msh (b), and with an area smaller than 50 msh (c). wich catalog, during 5 Ð 24 August 1947 there were 43 new sunspot groups (we recall that there were only seven groups from 5 to 24 September, according to Scheiner). The area of the largest complex sunspot group number 15106 is 2464 msd (1322 msh). On 23 March 2014, there were nine groups; the area of the largest, number 2014, is 355 msd (190 msh). In both cases, the transit drawing would lead to the overlap of sunspots, hence most of the groups will certainly be lost.

3.4. Signiﬁcance of Small Sunspots

Figure 5 shows the four recent Cycles 21 Ð 24 from the GreenwichÐUSAF/NOAA database. Figure 5a illustrates the timeÐlatitude distribution of sunspot groups with an area larger than 500 msh, Figure 5b an area smaller than 500 msh, and Figure 5canareasmallerthan 50 msh. The number of small spots is many times greater than that of larger spots. Moreover, Svalgaard and Schatten (2016) found that Wolfer with the larger telescope saw 65 % more groups than Wolf did with the small, handheld telescopes. Absence of a sunspot-counting routine and loss of small spots can dramatically distort the solar-cycle profile, especially during a period of suppressed activity such as a secular minimum. For example, disinter- est in counting of naked-eye sunspots leads to absence of the 11-year periodicity in their statistics. We also suggest that sunspot counting was not an objective of La Hire’s observations, hence, some sunspot groups could be neglected, which would lead to numerous zeros in the database. Philippe de La Hire was found to have reported fewer sunspot groups than the number reported by other observers (Zolotova and Ponyavin, 2015, Figure 7). La Hire’s biographer (Hockey et al., 2007) states that he was a mathematician and painter. In 1678, he was brought in as an astronomer although he lacked astronomical experience. His first task was to assist Jean Picard with surveys for the new atlas of France. La Hire studied geome- try, optometry, mechanics, meteorology, map-making, drawing, and other subjects. He also extended the meridian line that Picard had begun, and worked on the scheme to provide a water supply for Versailles. In the HS database, sunspot reports by La Hire started in 1682. La Hire acquired a mastery of the instruments Ð a new quadrant in the plane of the meridian How Deep Was the Maunder Minimum? was installed in 1683. However, astronomy never monopolized La Hire’s attention (Hockey et al., 2007). He obtained a good grounding in astronomical theory, but concluded that it rested on uncertain foundations. We also note that unlike observations of objects that are not formed regularly in number and magnitude (spots), measurement of the solar diameter (Ribes and Nesme-Ribes, 1993) was an important astrometric task. Picard and La Hire also regularly made observations of the meridian-circle instrument during the Sun’s upper culmi- nation (Wolf, 1856 Ð 1959, page 72). In 1669, G.D. Cassini carried out sunspot observations to improve estimates of solar rotation (Kopecky and Kuklin, 1987, with reference to King, 1955 and Wolf, 1902). This suggests to us that attention was mainly given to long-lived sunspot groups. Recently, Usoskin et al. (2015) analyzed the latitudinal extent of the butterfly-diagram wings for Cycles 0 Ð 4 from Staudacher’s drawings that were digitized by Arlt (2008), Cy- cles 7 Ð 10 from Schwabe’s drawings (Arlt et al., 2013), Cycle 8 from drawings by Spörer (Diercke, Arlt, and Denker, 2015), and since Cycle 12, from the Royal Greenwich catalog. Considering sunspots with the projected area greater than 100 msd (50 msh), they found that the latitudinal extent of the butterfly wings was always greater than 28◦, while according to Picard and La Hire (Ribes and Nesme-Ribes, 1993), it was smaller than 15◦ during the core of MM, and smaller than 20◦ from 1700 to 1710 (Vaquero, Nogales, and Sánchez-Bajo, 2015). Here, we would like to note that Cycles 0 Ð 4 and 8 Ð 11 belong to secular maxima. The latitudinal extent for large cycles is significantly (nearly a factor of two) wider than that for small cycles (Hathaway, 2010, Figure 8). Hence, we should compare the MM only with low cycles like Cycles 7, 12, 14, and 24. According to a suggestion by Zolotova and Ponyavin (2015), the amplitude of Cycle −4 (1700 Ð 1710) is comparable to or slightly higher than that of the just mentioned cycles. For Cycle 24, Figure 5a demonstrates that only a small proportion of sunspot groups with an area larger than 500 msh were located higher than 20◦ from 2010 to 2015. We also note that the GreenwichÐUSAF/NOAA database provides areas of sunspot groups that are usually bipolar and consist of several spots (see Figure 4b). Hence, an individual spot in a sunspot group with an area of 500 msh (≈ 1000 msd) is small. We also note that the larger sunspot groups tend to arise at lower latitudes than the smaller ones (Vitinskij, Kopetskij, and Kuklin, 1986). The schematic cycles in the core of MM (Zolotova and Ponyavin, 2015,Figure9)weredrawnas≈ 30 Ð 50 % weaker than Cycle −4. Hence, the latitudinal span of the butterfly wings in the core of MM should be narrower than in Cycle −4. To summarize, it is natural that large spots during weak cycles arise at low latitudes. We also note that before the MM all spots that were reported by Hevelius (1647) from 1642 to 1644 lie lower than 20◦ as well. Svalgaard and Schatten (2016) quoted the letter by Woeckel (1846, page 21), who wrote that from 1700 to 1710 (Cycle −4), the spots were again very numerous, with reference to the time of sunspot discovery and Scheiner. If this is the case, then Cycle −5 (1690 Ð 1700) consisted of only one sunspot group, followed by Cycle −4 with very numerous sunspots. This is a challenge for dynamo theory. Another challenge is the sudden onset of the MM in 1645, because according to Hevelius, as early as 1643 Ð 1644 (when he drew spots) there were 100 to 200 spots visible in a hemisphere during one year, as Hevelius himself stated (Weiss and Weiss, 1979). We note that Vaquero et al. (2011) proposed a gradual onset of the MM with reduced activity starting two cycles before 1645. The problems mentioned can be resolved by the suggestion of the low secular minimum when sunspot monitoring and counting were not the principal objective of sunspot observation. A prominent northÐsouth asymmetry is valid for large sunspots (Zolotova and Ponyavin, 2015, Figure 11). N.V. Zolotova, D.I. Ponyavin

Figure 6 Number of sunspot groups. Color deﬁnes the observer. Gray bars mark periods when the observers made drawings.

4. Drawings and Text Reports

Zolotova and Ponyavin (2015) discussed the difference between the NSGs extracted from drawings and text reports. They pointed out that drawings provide more sunspot groups than can be extracted from text. Figure 6 demonstrates the NSGs from 1611 to 1684 provided by Scheiner (pink), Gassendi (purple), and Hevelius (red), from the HS database. Black denotes the NSGs extracted by us (Table 1) from Scheiner (1651), yellow and green the corrected NSGs from Hevelius reports extracted by Vaquero and Trigo (2014) and Carrasco, Villalba Álvarez, and Vaquero (2015), correspondingly. Carrasco, Villalba Álvarez, and Vaquero (2015) published the translation of short notes on sunspots by Hevelius (1679). In green we show in Figure 6 the NSGs estimated by us from these short notes. In Machina Coelestis Hevelius (1679) measured the solar meridional altitude. The azimuth-quadrant is mentioned in the column “Instrumente”. Hence, without a telescope, only sufﬁciently large spots were rarely reported by Hevelius. Moreover, observers of the seventeenth century did not distinguish between sunspots and sunspot groups. Summarizing these ﬁndings, we interpret “Three obvious spots observed near the eastern limb” on 18 September 1654 and “Four spots discovered near the center of the Sun” on 19 September 1654 (see Carrasco, Villalba Álvarez, and Vaquero, 2015) as one group con- sisting of several umbrae on 18 September 1654 and two groups on 19 September 1654. Of course, this interpretation is subjective because the notes by Hevelius are poor. For instance, Hoyt and Schatten tabulated these notes as three and four sunspot groups, correspondingly. Usoskin et al. (2015) objected that drawings provide more sunspot groups than text reports. They processed the book by Smogulecki, Schönberger, and Meyer (1627) and found that the number of sunspots mentioned in the text exceeds that from drawings. Indeed, Smogulecki, Schönberger, and Meyer (1627) schematically drew transits of sunspots. In the text, the observers wrote about the number of stellae (stars), which means the number of spots, not the number of sunspot groups. This causes the difference between the number of stellae in the text and the number of transits in the drawings. In Figure 6 we do not compare the number of spots in the text of a report and drawings of the same report. We are interested in how many NSGs are provided by books with drawings in comparison to other sources of the same author, but without drawings. Certainly, drawings are not a panacea for reconstructing the NSGs. For instance, consider drawings from Kircher (1660, 1678). Figures 7aand7b correspond to observations in 1646, and Figure 7c, 1635. The Sun is full of spots, but these drawings are not suitable to extract NSGs. We can only suggest that 1645 is not the year when sunspot activity was all but stopped. How Deep Was the Maunder Minimum?

Figure 7 Drawings of the solar disk from Kircher (1660) (a and b) and Kircher (1678)(c).

Figure 8 Comparison of the NSG by Svalgaard and Schatten (2016) for different time periods. The red-solid line shows the NSG from 1610 to 1810, the blue-dashed line deﬁnes the NSG from 1815 to 2015, and the blue-dashÐdotted line that from 1745 to 1945. Numbers deﬁne the cycle number, according to the Zürich numbering.

5. Comparison of the Secular Minima

Based on the backbone method, Svalgaard and Schatten (2016) reconstructed the sunspot- group count (identical to the NSG). Using these data, we compared solar grand and secular minima. We only skipped the period of the 1650s because the Machina Coelestis by Hevelius (1679) does not provide up to four sunspot groups per day (see Section 4). This book in particular is devoted to the meridional observations by means of the azimuth-quadrant without a telescope. Figure 8a shows the overlapping of the MM (red line) with the Gleisberg minimum (dashed line), Figure 8b, with the Dalton minimum (dashÐdotted line). The solar cycles are variable, but precisely eighteen cycles fit in 200 years. Especially good agreement in duration and amplitude exists between Cycles −2 to 5 (cycles just after the MM) and Cycles 15 to 24 (Figure 8a). Moreover, Figure 8b shows that Cycles 1 to 7 fit the poor sunspot data from 1610 to 1700 reasonably well. This in turn suggests a persistence of solar cyclicity through the centuries. All of the findings of this work and especially the fact that observers were not counting sunspots in the seventeenth century cast doubt on the singularity of the MM. Poor statistics along with a lack of homogeneity, due to a different style of historical records, hides the N.V. Zolotova, D.I. Ponyavin characteristics of the cycles in the past. Unfortunately, instead of reconstruction we are left with speculations. The 90 Ð 100-year amplitude variation has been established over 1500 years of solar proxies (Feynman and Ruzmaikin, 2011). Secular minima took place in about 1710, 1810, 1910, and 2010. We note that each previous secular minimum is lower than the subsequent one: the Maunder minimum is lower than the Dalton minimum, which is lower than the Gleiss- berg minimum, and finally Cycle 12 is lower than Cycle 24. We also note that each secular minimum is preceded by a notably prolonged 11-year cycle (Frick et al., 1997; Zolotova and Ponyavin, 2014). Since the protracted minimum of Cycles 23/24, numerous publications reported peculiarities of the solar activity. The onset of Cycle 24 is characterized by a decrease of the magnetic-field strength in spots (Livingston and Penn, 2009), reduced solar irradiance (Fröhlich, 2013), 40 % suppression of the polar field (Svalgaard, Cliver, and Kamide, 2005), slow polar-field reversal (Sun et al., 2015), atypical form of the solar corona (de Toma et al., 2010), decreases in the speed (to 250 km s−1), density, and other parameters of the solar wind even at the maximum of Cycle 24 (McComas et al., 2013), and as a consequence, a weak interplanetary magnetic field (Lee et al., 2009) and low geomagnetic activity (Feyn- man and Ruzmaikin, 2011). These changes in solar parameters are probably not unique in the history of the Sun, but they are the first observed since instrumental recording began. In the seventeenth century, observers also reported solar peculiarities in comparison to secular maximum (observations by Galilei and Scheiner). Here, we suggest that the MM was an ordinary secular minimum.

6. Scenario of Secular Minimum

Our study shows that the observational data during the seventeenth century are poor, inho- mogeneous, and are not dedicated to sunspot counting. These data permit various scenarios of sunspot activity. The simplest was proposed by Gleissberg, Damboldt, and Schove (1979), Kopecky and Kuklin (1987), and Zolotova and Ponyavin (2015) who claimed that the level of the solar activity during the seventeenth century is underestimated, and it could be not dramatically different from that over the past 300 years. Here, we give some more attention to this hypothesis. In Figure 9, the red points are the nominal daily number of sunspot groups for all individual observers, excluding Johann Leonhard Rost, who probably reported on the number of spots, not sunspot groups. In other words, these are the daily group numbers, which are the basis for the GN index by Clette et al. (2015) and Svalgaard and Schatten (2016). Owing to poor statistics, and taking into account that skipped small sunspot groups and pores increase the activity level by more than a factor of two, we schematically drew cycles with amplitudes equal to the maximal daily NSG. The averaging technique was not used because any statistics applied to a dataset with excess zeros results in near-zero values. In Figure 9, the light-red cycles demonstrate a possible scenario, our artistic imagination driven by the simplest suggestion Ð continued 11-year cycle with secular modulation. For convenience we divided cycles into three groups: low cycles with NSG up to 4, middle cycles with NSG from 4 to 7, and high cycles with NSG more than 7. We successively consider each decade. 1610 Ð 1620: observations by Galileo. We evaluate his observations as among the best during the seventeenth century because he drew sunspot groups extended in longitude (which means that the trailing spots were not lost) and made instantaneous images of the solar disk, not transits when several days overlap in one picture. Sunspot drawings by Galileo How Deep Was the Maunder Minimum?

Figure 9 Red points are the daily nominal number of sunspot groups for each observer, according to the database by Hoyt and Schatten (1998). Light red defines the assumed amplitudes of solar cycles. Light-gray bars mark the assumed solar minima. Numbers from −13 to −3 define the cycle number, according to the Zürich numbering. also demonstrate that his 32-power telescope with two lenses and 7 arc-minute field of view (Hockey, 1998) resolved sufficiently small spots. We note that only from his drawings sunspots are far from the Equator (Soon and Yaskell, 2003; Casas, Vaquero, and Vazquez, 2006). We propose that activity was high ≈ 10. 1620 Ð 1630: observations by Scheiner. He was interested in long-lived sunspots, to check their reappearance in the next solar rotation. He drew transits of sunspots across the solar disk, which was prone to the loss of some sunspot groups. We propose that activity was ≈ 10 or higher. 1630 Ð 1640: observations by Gassendi. According to the HS database, he reported one to four groups per day. Gassendi schematically drew some very large (only large) groups, hence the actual activity level is underestimated and unknown. We hypothesize that in the 1630s sunspot activity could be medium or high (two cycles in Figure 9) because large spots in Gassendi’s drawings hint at powerful sunspot formation. The amplitude is higher than 6, andupto10. 1640 Ð 1650: In comparison with Zolotova and Ponyavin (2015), we improved NSG from observations by Rheita in 1642, in accordance with Gómez and Vaquero (2015). The 1640s are mainly covered by Hevelius’s observations. He drew transits of the spots. The style of his drawings is similar to Scheiner’s. The size of sunspots in the drawings is mainly medium, but when a sunspot group consisted of numerous umbrae, Hevelius did not draw the penumbra. In these cases the sizes of sunspot groups are unknown. Hevelius also thought that spots were related to comets. His Selenographia, which is the basis of our knowledge about solar activity in the 1640s, is not in itself dedicated to sunspot observations. The sunspot observations are only listed in the Appendix of the book. This approach casts doubt on the idea that Hevelius was interested in monitoring sunspots and gave appropriate attention to small spots. We propose that activity was medium ≈ 5 or higher up to ≈ 8. 1650 Ð 1670: Two decades when observations were either episodic or were not dedicated to sunspot observations. According to the text translation, which was made by Carrasco, Villalba Álvarez, and Vaquero (2015)ofMachina Coelestis by Hevelius (1679), the observer N.V. Zolotova, D.I. Ponyavin listed in the table measurements at solar meridian, and in column “Notanda” he made short notes about the presence or absence of sunspots, which mainly says nothing about process of counting. This sort of information is too poor to evaluate the cycle amplitude. In Figure 9, we draw three cycles (low, medium, and high), which means strong uncertainty. 1670 Ð 1700: We suggest that this is the period of low sunspot activity ≈ 3Ð4.According to Callebaut, Makarov, and Tlatov (2007), the yearly mean sunspot number has to exceed 40 to reverse the polar fields. 1700 Ð 1710: It is unclear whether the northern hemisphere was free of sunspots at all or if it was significantly asymmetric only in large sunspot groups. The cycle was medium: ≈ 6. 1710 Ð 1720: The cycle is high, but lower than 10. Finally, in accordance with the suggestion of continuing 11-year cyclicity and its secular suppression, the MM can consist of five cycles (1650 Ð 1700) or three cycles (1670 Ð 1700). Here we would like to stress that we draw a hypothetical scenario of the MM, not a reconstruction of solar activity, which can be found in Clette et al. (2015) and Svalgaard and Schatten (2016).

7. Proxies of Solar Activity

To reconstruct the sunspot activity over the MM, indirect records are used. Usoskin et al. (2015) presented an analysis of the multiple proxy datasets that indicated near-zero solar activity level during 70 years. Unfortunately, proxies are influenced also by climatic and other factors. Reconstructing the solar signal from indirect data is a complex inverse problem, which does not have an exact solution because of multiple uncertainties (Kuleshova et al., 2015; McCracken and Beer, 2015). Reconstructions are therefore numerous and may differ significantly from each other. Concerning time series of solar activity reconstructed from 10Be concentrations in ice cores from Antarctica and Greenland, the Antarctic data have a broad maximum near 1650 Ð 1700, while the Greenland records have a sharp peak only after 1700. We also note that the actual reconstruction results (without correcting for the group sunspot number, which according to Hoyt and Schatten (1998) from 1645 to 1715 is close to zero) does not show a dramatic increase near the MM (see Usoskin et al., 2003, Figure 2). Moreover, according to Usoskin et al. (2003), the 10Be isotope shows a dramatic decreasing trend toward the middle of the last century, which in turn signifies the unusually active Sun since the 1940s. On the other hand, Bard et al. (2000), Muscheler et al. (2007), Berggren et al. (2009) claimed that 10Be and 14C radionuclide records from ice cores and tree rings do not indicate unusually high recent solar activity compared to the past. The recent recalibration of the sunspot group count also does not reveal abnormal solar activity (Svalgaard and Schatten, 2016). Here we would like to reason that if the grand minimum (the MM) exists, the grand maximum should also be seen. Conversely, if there is no grand maximum, then the grand minimum becomes questionable. Analyzing data on radiocarbon in tree rings, Kocharov et al. (1995) found that the 22-year modulation during the MM is more pronounced than the 11-year modulation. Combining sunspot, auroral, and 14C radiocarbon data, Nagovitsyn (2007) concluded that the 11-year cycle did not cease. Moreover, Beer, Tobias, and Weiss (1998), Berggren et al. (2009), Poluianov, Usoskin, and Kovaltsov (2014) found large 11-year solar cycles in cosmogenic 10Be and 14C data during the MM. McCracken et al. (2001) claimed that the international sunspot numbers, aurorae, and solar proton event data indicate that the MM ended about 1700, not 1715. How Deep Was the Maunder Minimum?

Figure 10 Number of aurorae from Loysha, Krakovetsky, and Popov (1989).

Analyzing the 14C data records from 1617 to 1745, Miyahara et al. (2005) found the remarkable 22-year cycle, which they attributed to a cyclic magnetic reversal of the Sun. We note that Callebaut, Makarov, and Tlatov (2007) estimated that the yearly mean Wolf number has to exceed 40 (20 per hemisphere) to have polar reversals. Comparison of the 14C data from several sources shows their differences. Some records strongly vary near the 1650 Ð 1660s, while others demonstrate only a monotonic increase since 1610 with a maximum near 1700 (Miyahara et al., 2005, Figure 1b). Recently, using the 10Be data from Greenland, McCracken and Beer (2014) also argued that the cosmic-ray intensity increased steadily during the Maunder minimum. For a long time, aurorae were not counted and were attributed to weather phenomena. Systematic studies started only in the nineteenth century. That is why different databases argued for different behavior of aurorae in the past (Schröder, 2005). For instance, according to Loysha, Krakovetsky, and Popov (1989), the seventeenth century does not demonstrate a dearth of aurorae (Figure 10). The Mazurinsky chronicler Peter Zolotarev (Buganov and Rybakov, 1968) described the observations of meteors by the Astrakhan guard of archers on 13 July 7178 (the year since the creation of the world, which means 1670) and auroral observations (“three pillars of different colors, like the heavenly arc in the cloud, and crowns of many colors on top” as translated by us) of the same guard (July Ð August 1670, according to Loysha, Krakovetsky, and Popov, 1989). Astrakhan is a Russian city located at latitude 46◦, which means a strong geomagnetic storm and appearance of a large activity complex on the Sun. However, the HS database for Picard, Mangoli, and Fogel does not contain a sunspot throughout 1670. These discrepancies arise from the absence of a count procedure. In summary, interpretation of indirect proxies of the solar activity (such as aurorae and cosmogenic isotopes) is varied. We can hypothesize in favor of either a longer period of near-zero sunspot activity or a shorter period of an ordinary secular minimum. Neither the amplitude nor the duration of the MM is unambiguously restored.

8. Conclusions

We here continued to develop the hypothesis that the Maunder minimum was not so grand as it seemed to be (Zolotova and Ponyavin, 2015). The reports of observers from the Hoyt and Schatten (1998) database, among them Hevelius (1642 Ð 1684), Derham (1703 Ð 1715), Picard ( 1660Ð 1682), La Hire (1682 Ð 1719) father and son, G.D. Cassini (1656 Ð 1695), and others, were analyzed. We demonstrated that scientific reports of the seventeenth century N.V. Zolotova, D.I. Ponyavin should not be considered in isolation from the historical context. The authority of Aristotle, scientific school, profession, location, scientific views and interests, instruments, relations with the Church and ruling dynasty all affect the style of scientific reports. Until the beginning of the nineteenth century, solar reports are not dedicated to the problem of sunspot monitoring and counting. Astronomers were focused on the nature of sunspots. This led to interest in sufficiently large objects from whose evolution the answer to the question was expected of whether the spots were planets, stars, clouds, volcanos, smoke, or foam. Interest in the location of the spots (on the Sun or in space) gave birth to the tra- dition of drawing the transit of spots and interest in the reappearance of spots in the next solar rotation. The transit drawings lost spots because of their emergence at the same latitudes, and checking for reappearance forced observers to pay attention mainly to long-lived objects. Short text notes about appearance of large sunspots, which were absent over a long period of time but numerous in the time of Galileo and Scheiner (secular maximum), suggest that observers dealt with the prominent objects, not the small ones. We note that the portion of small sunspot groups is more than half of their total number. Short reports were found to play a significant role in the formation of the Rg-index. The style of notes similar to “Today, it is ten years since I had seen a large spot” resulted in continuous zero in the HS database. On the other hand, short notes on non-zero sunspot activity are quite common. They provide neither the number of groups nor an exact date of observation. Finally, the short notes on non-zero sunspot activity are not valid for a qualitative estimation of Rg. We also compared the MM with the Dalton and Gleissberg minima and with Cycle 24. The last of these is characterized by small short-lived sunspots, suppressions and peculiarities of other solar parameters. We demonstrated that Schwabe cycles before Cycles 5 and 24 fit cycles before the MM reasonably well. To conclude, we state that sunspot observations not dedicated to the task of sunspot counting underestimate the activity level. We suggest that the phenomena of extraordinary grand minima or maxima are instead a result of unavoidable uncertainties that are involved in the reconstruction process of the solar indexes and are not a real phenomenon.

Acknowledgments We use data from the Royal Greenwich Observatory, United States Air Force, Na- tional Aeronautics and Space Administration (RGO/USAF/NOAA: solarscience.msfc.nasa.gov/greenwch. shtml), the revised version of Greenwich Photoheliographic Results (GPR) sunspot catalogue provided by the Debrecen Heliophysical Observatory (DHO: fenyi.solarobs.unideb.hu/deb_obs_en.html), regular solar observations at the Kislovodsk Mountain Astronomical Station GAS GAO (en.solarstation.ru), the database by Hoyt and Schatten (1998) provided by the National Geophysical Data Center (NOAA/NGDS: ngdc.noaa.gov/stp/SOLAR), and the average group number provided by Svalgaard and Schatten (2016). The reported study was funded by RFBR according to the research projects No. 15-02-06959-a and No. 16-02-00300-a.

Disclosure of Potential Conﬂicts of Interest The authors declare that they have no conﬂicts of interests.

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