Sunspots from the past

  Johann Christoph Müller (1673-1721), the brother of Johann Heinrich Müller, is the most significant Austrian cartographer and military engineer. We examine his sunspot observations stored in the Collection 998 of the Manuscript department of the National Library of Russia, St. Petersburg.

   20 April 1719 – 27 May 1720

  An album containing solar-disk drawings by Johanne Christophoro Müller (in Latin transcription) is stored in volume 56. As listed in the catalog, the drawings were made in ink, watercolors, brush, and pen and are accompanied by dates and times. Recently, Hayakawa et al. (2021a) analyzed this archive, extracting the number of sunspots, sunspot groups, and their positions. They also provided a review of Müller's observational equipment.

  In comparison with Hayakawa et al. (2021a), we assigned the same number of sunspot groups. However, we have made two slight differences in our analysis on 4 May and 2 June 1719. Specifically, we have ignored two small objects on these dates, which differ in color from the other sunspots and rather appear to be paper defects. Figure 1 shows sunspot-group numbers assigned by Hoyt and Schatten (1998) and our analysis of Müller's album. Apart from very few discrepancies, the number of groups is generally consistent with our results. In addition, we have also included the group numbers from the observations by La Hire in yellow. In the references, Hoyt and Schatten noted that the primary source of the La Hire observations was the re-examination of original notebooks made by Elizabeth Nesme-Ribes. As an example of the fine structure of a sunspot, the La Hire drawings were examined by Ribes and Nesme-Ribes (1993, Figure 1 therein) who suggested that sunspots as large as one arcsecond could not have been missed by Parisian telescopes.

  We suggest that La Hire's reports may not have been sunspot observations but rather were made for different purposes. This is similar to the case of Georg Christoph Eimmart's solar-altitude measurements, which should not be confused with reports on a spotless solar disk (Hayakawa et al. 2021b). Out of the 13 observations made by La Hire, 8 overlap with those by Müller, and on 12 of those days, Müller reported sunspot groups with areas ranging from 33 msh to 871 msh based on our measurements.

  Figure 2 compares the spatio-temporal distribution of sunspot groups defined by Hayakawa et al. (2021a) in Methods I and II and one Parisian observation. As the notebooks by Elizabeth Nesme-Ribes are lost, Vaquero, Nogales, and Sánchez-Bajo (2015) provided a machine-readable version of the Ribes and Nesme-Ribes (1993, Fig. 6 therein) butterfly diagram. The only point overlapping in time with the Müller's observations is about 22 April (or 1719.30771, as expressed in a fraction of year), −16.2^o of latitude. Compared to the Hoyt and Schatten (1998) findings, this observation was apparently made by La Hire on 25 April 1719 (green diamond in Fig. 2). In April, Müller reported one sunspot group in the southern hemisphere above −10^o with a maximal area of 71 msh. Hence, both La Hire and Müller had equipment capable of resolving the fine structure of sunspots, but did not report all objects present on the solar disk. There may be other reasons for this discrepancy.

  The mean latitude discrepancy between latitudes defined by Hayakawa et al. (2021a) and the two methods is about 3^o, i.e. within the uncertainty range. However, on several days the difference significantly increases (marked in blue in Fig. 2).

  Figure 3 compares latitudes of sunspot groups G1 – G6 in our numbering (G4 is a one-day-lifetime sunspot at 31^o, not shown). The dashed blue curve represents the latitudes derived by Method I in accordance with the time noted by Müller. On 20 – 24 April 1719, Hayakawa et al. (2021a) apparently minimized the latitude scatter of sunspots also around the time noted by Müller (yellow and blue curves are close). On 25 and 27 April, latitudes of groups G1 – G3 significantly rise (in blue). One may suggest that either Müller indicated the wrong time or incorrectly drew the position of the sunspots. In Hayakawa et al. (2021a), the heliographic grid was rotated inconsistently with the time noted by Müller. Consequently, in the next few days, the scatter of groups G5 and G6 has risen (Fig. 3).

  Figure 4 reproduces three consecutive drawings originally signed by Müller as observations on 9, 15, and 16 May 1719. The longitude distance between the red and blue sunspots (which we have numbered as S14 and S15, respectively, as shown in Data) equals 46^o on each of the three days. Therefore, we hypothesize that these are the same sunspots. However, the rotational matching analysis states that on 15 – 16 May, the sunspots should have been much closer to the western limb. If we assume that there was a typographical error in the date of the first observation (9 May), it would break the coherence of sunspot latitudes and longitudes in the days prior to 9 May. Eventually, we suggest that the observations originally labeled as 15 and 16 May are actually the observations of 12 and 13 May 1719. The improved heliographic grids defined by means of Method I and sunspot coordinates are shown in Figure 4. On the contrary, it could also be argued that the sunspots observed on 9 May decayed, and new objects emerged on 15 May. Both Hoyt and Schatten (1998) and Hayakawa et al. (2021a) provide the observation dates as originally noted by Müller, which affects the reconstructed longitudes.

  On 29 May – 1 June 1719 (Fig. 2) the latitudes defined by Hayakawa et al. (2021a) significantly deviate from results by Method I. Such a difference suggests that the sunspot positions defined by Hayakawa et al. (2021a) are less consistent with what should have been seen in the telescope. We also ignore the sunspot on 2 June 1719 at −31.5^o. It has a different color compared to other sunspots, and we believe this is rather a paper defect.

  The reproduced images of five consecutive drawings of 1 – 4 June 1719 are shown in Figure 5. For similar reason as in Figure 4, we believe that Müller observed the transit of the same sunspots marked in blue and red (S34 and S36 in Data) during these four days. We imposed four grids of 1 – 3 June reconstructed by Method I on a reproduction of the original images, while a grid of 4 June was imposed on the vertically flipped image. Utilizing the original image, the latitudes of sunspots on 4 June deviate from their means on 1 – 3 June as much as 25 – 30^o. However, if we flip the image, the difference reduces to only 3^o. It is possible that Müller rectified the original images viewed on a projection screen but forgot to do so on 4 June. Hayakawa et al. (2021a) used the original orientation of the drawing of 4 June 1719 with a grid orientation different from the one indicated by Müller’s time note.

  Another difference in the spatio-temporal distributions is seen in the observations made on 6 May 1720. According to the original note, the drawing was reversed, or "situ inverso" (Fig. 6a). To find a suitable orientation of the image, we followed the approach used by Hayakawa et al. (2021a) and referred to the drawings by Alischer, published by Kanold (1721). Figures 6b and c compare a reproduction of Müller's horizontally reversed drawing and Alischer's drawing, showing sunspot groups in different colors. We selected the proposed reversal of the Müller's drawing because the orientations of a large sunspot group reported by Müller and Alischer were similar, with four sunspots directed toward high latitudes and a smaller number toward the Equator (as seen in the sunspot skeletons in the small rectangles). However, groups in the Müller's drawings are located further West than in Alischer's version. Notice that the following day, Alischer shifted sunspots about 30^o to the western limb. Figure 6d shows the apparent orientation of the image chosen by Hayakawa et al. (2021a), where the original image is rotated 145^o counterclockwise.