Sunspots from the past

  Johann Heinrich Müller (1671-1731) is a German astronomer and mathematician. We examine his sunspot observations stored in the Collection 998 of the Manuscript department of the National Library of Russia, St. Petersburg.

   9–14 October 1705

  This drawing by Müller stored in volume 35, folio 57 was made with both pencil and ink. It depicts sunspots labeled as a, b, c, and a chain of sunspots labeled as d-d-d (in Latin: maculae tres d,d,d, vinculo quasi cunctae observatae...) along with the corresponding time of observation (Figure 8 Left). Here, we exploit only Method I due to limited observations.

  At first sight, the location of the east and west limbs suggests that the image should be flipped horizontally from right to left, as shown in Figure 1 Top. Sunspot latitudes vary in the range of 15 – 20^o, while longitudes differ significantly. This indicates that either the sunspots belong to four different groups, or the initial assumption of flipping the image horizontally is incorrect. We lean towards the latter assumption. Therefore, we also examined the original orientation of the image and a version rotated by 180^o. However, in both cases, sunspot latitudes and longitudes exhibited significant changes, indicating that these orientations are also incorrect.

  Another possibility is that the drawing was flipped vertically, as shown in Figure 1 Bottom. The longitudes and latitudes of the sunspots a, b, and c on 9 and 10 October (highlighted in red) remain consistent, indicating that they belong to the same sunspot group. The sunspot chain labeled as d-d-d on 14 October (in blue) appears to belong to another group. Although the results following from this interpretation are the most consistent, the image designations of East and West would then be incorrect.

  Spoerer (1889) did not include the exact sunspot latitude. However, he wrote that on 4 October 1705, there were eastern sunspots (östlich Flecke) that had already moved to the western part of the disk by 12 October. This description matches the transit of sunspot groups a, b, and c. Further, Spoerer noted that on that day (12 October) new sunspots came from the East, which he considered a "rare case" (quotation marks by Spörer). This simultaneous appearance of sunspots in distant regions of the Sun had only been observed once before, in January 1704, following Scheiner's observations.

  Neuhäuser et al. (2018) translated a letter by Kirch: "This afternoon [1705 Oct 16] around 2:30 h, we got to see two fine spots in the Sun, about 3 inches from the egress edge." and a letter by Wurzelbaur "...in the last October [1705], when two [sunspots] did not have fully crossed the solar disc, when two other spots with an accompaniment entered the disc." They determined the latitude of the spots ranged from −13.9^o to 23.3^o. This is consistent with the position of the sunspot chain d-d-d (Figure 1 Bottom), which should be located about 3 inches from the western limb toward 16 October.

  Based on the analysis presented above, we suggest sunspot groups a, b, c, and d-d-d were simultaneously present on the visible disk of the Sun for several days between 10 and 14 October. Müller's original drawing depicts the upside-down image of the Sun with an east-west orientation that is consistent with that of the Sun, but with an incorrect E–W annotation. A similar conclusion was obtained by Hayakawa et al. (2021) who evaluated the sunspot groups' latitudes to be about −5^o and −8^o, while our analysis suggests a latitude of approximately −7^o.

   14 December 1706

  Another drawing by Müller is stored in volume 36, folio 19. The text description (Figure 2 Left) says that sunspots were observed in Nürnberg on 14 December 1706 at Noon and the smallest sunspot was barely visible near the circumference (In Latin: Macula minima ad modum...). The cardinal directions are also indicated, West and East are opposite to the solar ones. In the corner of the original drawing, Müller wrote: "D. 2[?] Dec. mac. dispar." This might be interpreted as sunspot(s) disappearing on 2[?] December. The inscription is faint, and it looks like something is written behind the 2, possibly indicating 21 or 22 December. This interpretation would make sense with the small spot on the left side of the drawing. The term "disparare" can mean to separate or divide, but it may also carry the sense of dissolve. Given that the spot should still have been visible on the disk, it is possible that it had split or dissolved.

  Here, we also considered four image orientations and chose the most probable one that yields consistent sunspot positions. As displayed in Figure 2 Right, the drawing is flipped upside down (red spots), and the heliographic grid corresponds to UT time of the local Noon. Here, we assign two sunspot groups.

  Neuhäuser et al. (2018) analyzed letters by Kirch and his wife. Maria Kirch reported the distance of the largest sunspot to the limbs on 13 December 1706 before Noon, at around 11:30 local time. We suggest that the sunspot location measurements were made on a line parallel to the celestial Equator. Thus, the possible position of the largest sunspot on 13 December is shown in pink (Figure 2 Left). On the other hand, Gottfried Kirch reported that on 16 December 1706, before noon, the large spot was 1/2 inch from the western limb. A possible location of the sunspot is shown in dark red. The resulting sunspot track is consistent with the solar-rotation rate, and the derived sunspot latitudes are in agreement with those obtained by Hayakawa et al. (2021).

   26 February – 7 March 1707

  A collection of drawings produced by Müller between 26 February and 7 March 1707 is stored in volume 36, folios 107 – 116 (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). They were drawn with both ink and pencil and accompanied by a day and a time. On nine separate drawings, the spots of an individual day are shown. An additional drawing exhibits the passage of sunspots on the solar disk throughout the entire observation period.

  Images were reversed vertically. Figure 3 Left shows sunspot positions derived by Method I. On 28 February 1707, sunspots were drawn with a pencil and overlaid with ink. Hence, there are two sunspot contours on this day. On the back of the folios, Müller also sketched sunspots in more detail (Figure 3 Right). Therefore, sunspot areas derived from Müller's drawings of the whole solar disk and presented in Data, may not accurately reflect the actual size.

  Neuhäuser et al. (2018) calculated the most probable latitude for the sunspot to be −3.5 ± 27^o, which is in agreement with the value provided by Hayakawa et al. (2021). Spoerer (1889) also provided a similar estimate of −6^o for the sunspot latitude. From nine separate drawings, our analysis using Method I yielded an average sunspot latitude of −2.5 ± 1.5^o, while Method II yielded an average of −3.6 ± 0.4^o. Moreover, from the drawing showing the passage of sunspots on the disk for all days, the estimated latitude is −3.2 ± 0.7^o using Method I and −5.8 ± 0.5^o using Method II.

   12 August – 18 November 1708

  Three similar sunspot drawings of 12 August – 5 September 1708 with different orientations provided by Müller are stored in volume 36, folios 136 – 137 (1, 2, 3). One of the drawings is shown in Figure 4a, where sunspots from 12 to 17 August are marked with letters. Also, two sunspots on 4 and 5 September 1708 appeared on the same line. Similar to the previous observations, cardinal directions are opposite to the solar ones. On the back of one of the drawings, three sunspot groups are shown in detail on 15 August and 5 September (Figure 4b). It follows that Müller sketched only the largest sunspot of a group passing on the solar disk.

  The handwritten text is hard to make out, but the meaning of the note is probably the following. Toward 15 August, the sunspot labeled as a became weak; on 16 and 17 August, only the sunspot labeled as b could be seen in the helioscope. The same sunspot returned on 4 and 5 September and was seen until 14 September 1708, the day of the solar eclipse.

  Figure 4c shows a colored replica of three original drawings. As can be seen, the sunspot locations do not always match. The largest discrepancies are shown by small arrows. Data provide sunspot parameters for all three drawings. Since Müller did not report the time of observation, only Method II was applied, giving a sunspot latitude of 6 – 7^o in the southern hemisphere. Referring to Wideburg, Spoerer (1889) gave a latitude of −7^o for 11 – 18 August and −5^o for 2 – 14 September 1708. Reconstructing sunspot positions from letters by Kirch, Neuhäuser, Arlt, and Richter (2018) yielded 8.9 ± 10.5^o for 10 – 18 August and −2^o for 14 September 1708.

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