The Thousand Star Magnitudes in the Catalogues of Ptolemy, Al Sufi, and Tycho Are All Corrected for Atmospheric Extinction

1. PRE-TELESCOPIC CATALOGUESThree pre-telescopic star catalogues contain about a thousand star magnitudes each (with magnitudes 1 , 2, 3, 4, 5, and 6), with these reported brightnesses as the original basis for what has become the modern magnitude scale. These catalogues are those of Ptolemy (c. 1 37 A.D., from Alexandria at a latitude of 3 1 .2°), Al Sufi (c. 960, from Isfahan at a latitude of 32.6°), and Tycho Brahe (c. 1590, from the island of Hven at a latitude of 55.9°). Previously, extensive work has been made on the positions of the catalogued stars, but only scant attention has been paid to the magnitudes as reported.1 These magnitudes will be affected by a variety of processes, including the dimming of the light by our Earth's atmosphere (atmospheric extinction), the quantization of the brightnesses into magnitude bins, and copying or influence from prior catalogues. This paper provides a detailed examination of these effects. Indeed, I find all three catalogues to report magnitudes that have near-zero extinction effects, so the old observers in some way extinction corrected their observations.The ancient star catalogue of Ptolemy appears in Books 7 and 8 of the Almagest, with positions and magnitudes for 1028 stars. These magnitudes are in the nowtraditional system of 1, 2, 3, 4, 5, and 6, however with notations for stars that are somewhat brighter or fainter than the integral magnitude. Thus, the notations go, from the nominal brightest to faintest, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, and faint. A handful of stars are duplicates or marked as nebulous instead of being given a magnitude. I adopt the magnitudes and star identifications as given in the translation of G. J. Toomer.2 Ptolemy does tell us how to measure star positions using armillary spheres, but he does not give one word on how the magnitude scale was set nor how to measure magnitudes. There is a substantial long-running debate as to whether the Almagest star catalogue was primarily observed by Ptolemy or rather Hipparchus (c. 128 b.c. from Rhodes with a latitude of 36.4°).3 This debate has a wide variety of arguments running many levels deep, with neither side able to produce decisive evidence to convince the other side. The primary material for this debate is the star positions recorded in the catalogue, with scant use having been made of any of the concurrent magnitude information.4In the Western world, the next star catalogue came from the Persian astronomer 'Abd al-Rahman al-Sufi (903-86) observing from Isfahan (latitude 32.7°). In his Book of fixed stars, published in 964, Al Sufi's star list gives the same stars and star positions (updated for precession) as in the Almagest. However, Al Sufi observed his own magnitudes, and these are substantially different from those in the Almagest. I adopt the magnitudes and star identifications as given for Al Sufi by E. B. Knobel.5 Al Sufi gives magnitudes in the same basic system as the Almagest, with the notation for the brightness bins, nominally from brightest to faintest, being 1, 1-2, 2-1, 2, 2-3, 3-2, 3, 3-4, 4-3, 4, 4-5, 5-4, 5, 5-6, 6-5, 6, and 6-7. These are one-third magnitude bins, with several extra when compared to the Almagest (5-6, 6-5, and 6-7). To say "one-third magnitude bins" is approximately correct, but it is really a schematic description for categories that are variable in size with ill-defined edges and imperfect measurements. Nothing survives which tells us the details of how Al Sufi measured his magnitudes.The next star catalogue is that of Ulugh Begh (1394-1449), the grandson of Tamerlane, who ruled a large region of central Asia from Samarkand. He noted errors in the positions of the stars from the Almagest, collected a group of scholars, and a star catalogue was made from observations in Samarkand (latitude ? = 39.7°) around the year 1437.6 His star catalogue contains the same stars as are in the Almagest. The positions of the stars were newly measured with large sextants, armillary spheres, and meridian circles. …