Fig. 1. Example of drawing by Colonna (1613).
Sorting sunspots into groups
At first, sunspots in the drawing are collected into groups. We use the classification of sunspot groups by McIntosh (1990) and suggest that the linear size of a sunspot group is on average limited to 7o of latitude and 15o of longitude. In complicated cases, groups were assigned arbitrarily. The separation of sunspots into groups is a non-trivial task, and therefore we detail our sorting graphically in Calendar. Figure 1 shows an example of the complex activity chain, for which various researchers can assign different number of groups.
Figure 2 demonstrates the example of the uncertainty introduced by sorting spots into groups. On the Top, drawings of 12–15 September 1613 made by Fabio Colonna with the underlaid heliographic grid are shown. The arrow defines the direction of rotation, i.e. Colonna drew an inverted image of the Sun from right to left. On 12th September, both Hoyt and Schatten (1998, hereafter, H&S) and we assigned 3 groups (grey ovals). On the next day, activity complex A apparently was counted by H&S as one group (dashed oval), while we assigned two groups (solid ovals). Here, we say “apparently”, since we only know from the H&S database how many groups they assigned per day. Note that such a discrepancy in sorting spots into groups also occurs in databases of modern observatories. On 14th September, on contrary, two activity complexes near the eastern limb were sorted into four groups by H&S and into two groups by us. Finally, on the next day, both H&S and we assigned 7 groups, while the sorting seems to have been done differently.
Figure 2 (Bottom) compares the number of groups defined by H&S (grey dots) and by us (open circles). On average, H&S and we assigned nearly the same number of groups. However, in the second half of September, either H&S assigned 1–2 more groups, or we assigned 1–2 more groups. If the average activity level in the second half of September is about 7 groups per day, then such a discrepancy introduces an error of about 15–25%. Hence, reconstructed parameters of solar activity in the past not only depend on accuracy, aim, and method of historical observations (Ogurtsov 2013; Karachik et al. 2019), but are also affected by the processing of these historical reports by modern researchers.
Fig. 3. (a) Original drawings by Saxonius (Eimmart Archive Coll. 998, v. 11, f. 99; National Library of Russia); (b) our sorting sunspots into groups and reconstructed heliographic grid; (c) number of groups defined by Hoyt and Schatten (1998) and Vokhmyanin and Zolotova (2023).
Another example of the uncertainty is shown in Figure 3. Figure 3a gives a reproduction of the drawings by Petrus Saxonius (1616, Petri Saxonis in Latin transcription). The diameter of the solar disks is about 5 cm. Original dates are in the Julian calendar. Sunspots marked with letters.
Figure 3b shows sunspot groups assigned by us. Figure 5c compares groups defined by Hoyt and Schatten (1998) and Vokhmyanin et al. (in press). The blue square of 14 March 1616 on Gregorian calendar is apparently a misprint, it should be the next day. Significant divergence occurred on 15–19 March 1616. We assume that Hoyt and Schatten appointed groups in accordance with Saxonius's lettering.
One more factor affecting the number of recovered spots and groups is paper defects and objects that are not sunspots, e.g. faculae. Figure 4 shows the original drawings by Cigoli (1612). Two objects we mark as paper defects, due to they differ in color from sunspots drawn with ink. One more object we recognize as facula, because it is close to the limb. If it was a spot group, then it should have been observed the next day. In general, there is no certainty here: the table illustrates the discrepancy in number of groups defined by Hoyt and Schatten (1998) and Vokhmyanin et al. (2021).
So, the sorting of spots into groups can be done in different ways. More examples can be found in Vokhmyanin et al. (2021, Fig. 4 therein) and Vokhmyanin and Zolotova (2023, Fig. 14 therein). Discrepancy in the number of groups assigned by researchers can reach dozens of percents.