17th Century Photometric Data in the Form of Johannes Heveliuss Telescopic Measurements of the Apparent Diameters of Stars

In 1662 Johannes Hevelius published in his Mercurius in Sole Visus Gedani a table of observations of stars that included, among other things, their magnitudes and apparent telescopic diameters (Figure 1). Hevelius's data are consistent with a simple mathematical model published in this journal that explains, via circular aperture diffraction and a detection threshold, the apparent stellar diameters reported by early telescopic astronomers such as Galileo Galilei (Graney 2007;Graney and Sipes 2009). Hevelius's data provide support for the model and context for understanding early telescopic observations. But Hevelius's data also suggest that telescopic astronomers in the 17 th century could obtain, in their measurements of apparent diameters of stars, what is essentially photometric data of some precision. Besides being an interesting point of astronomical history, Hevelius's work suggests that useful historical photometric data may be available to researchers who are willing to look for it --a task that is becoming easier with the passage of time, thanks to the growing collection of historical material available electronically.

Historians of astronomy generally report that early telescopic astronomers did not take much interest in the stars –that for almost two centuries after the advent of the telescope the stars remained primarily reference points in the sky against FIGURE 1 –Johannes Hevelius’s 1662 Mercurius in Sole Visus Gedani. which to measure the positions of solar system objects; with the exception of William Herschel, few astronomers studied stars carefully; what interest existed concerning stars was focused on variable stars (Pannekoek 1961, pp. 311-312;Mason 1962, pp. 298-300;Hoskin 1997, pp. 198-201). According to the noted historian of astronomy Michael Hoskin (1997), even the efforts to study variable stars “seemed to be leading In other words, until Herschel created a method of comparative photometry, no reliable method of photometry existed. On the subject of photometry Hoskin (1997) Hoskin, as seen in the first quote from him above, sets the dawn of practical photometry in the 19 th century. This view prevails in a variety of history of astronomy sources published over a long span of time (Grant 1852, p. 541;King 1955, pp. 295-297;Miczaika and Sinton 1961, pp. 154-157;Pannekoek 1961, pp. 385-387;Hearnshaw 1996, p. 105;Hoskin 1997, pp. 201, 297;Miles 2007, pp. 174-175).

Recent work by this author and others has shown that, from the very beginning of telescopic astronomy, telescopic astronomers took interest in and made detailed observations of the stars.

In particular, astronomers such as Simon Marius and Galileo Galilei report that stars seen through a telescope have noticeable disks –disks which are larger for brighter stars and smaller for fainter stars (Ondra 2004, Siebert 2005, Graney 2007). This author has proposed that these disks, which are of course spurious in nature, are simply the visible central maxima of Airy patterns formed via diffraction. All stars seen with a given telescope at a given wavelength have the same Airy Disk Radius. However, the eye cannot see indefinitely low levels of intensity. Thus while the diffraction pattern for a circular aperture consists of a central maximum and an infinite number of rings of declining intensity, usually only a few diffraction rings are visible to the eye (Born and Wolf 1999, p. 442). The rest fall below the eye’s threshold of detection. If the peak intensity of the pattern is low enough, no rings will be visible (for none cross the detection threshold) and the radius of the visible central maximum will be significantly smaller than the Airy Disk Radius. For progressively lower peak intensities, the radius of the visible central maximum will decrease (Figure 2). The result is that, for a telescope whose aperture is sufficiently small versus the magnification used, stars will appear as disks, with brighter stars having larger disks than fainter stars.

The relationship between a star’s magnitude and the diameter of its image seen through a telescope will appear roughly linear to an observer who is measuring these quantities visually. Thus when Galileo states in his Dialogue Concerning the Two Chief World Systems that stars of magnitude 1 measure 5” in diameter while stars of magnitude 6 measure 5/6" in diameter (Galileo 1967, p. 359) Graney -Hevelius pg. 9 decrease linearly with magnitude, Hevelius explicitly shows them to decrease linearly with magnitude (Table 1; Figure 3). However, the more interesting results are found from comparing Hevelius’s star image diameters against modern magnitude measurements from the SIMBAD database. Hevelius’s data conform remarkably well to the results of the Airy pattern with threshold (APT) model (Table 2; Figure 4). The model’s output is in turn consistent with the sort of instrument Hevelius might use (Figure 5). Besides providing support for the APT model, this suggests that Hevelius’s m

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