Magnitude systems in old star catalogues.pdf

a r X i v : a s t r o - p h / 0 3 0 9 3 2 2 v 4 2 6 J a n 2 0 0 4 Magnitude systems in old star catalogues Tomoko Fujiwara ? Hitoshi Yamaoka? ? Department of Physics, Graduate School of Science, Kyoto Sangyo University, Kyoto 603-8555, Japan E-mail: tomochan@cc.kyoto-su.ac.jp ?Department of Physics, Faculty of Science, Kyushu University, 4-2-1, Ropponmatsu, Chuo-ku, Fukuoka 810-8560, Japan E-mail: yamaoka@rc.kyushu-u.ac.jp Abstract The current system of stellar magnitudes first introduced by Hipparchus was strictly defined by Norman Robert Pogson in 1856. He based his system on Ptolemy’s star catalogue ‘Almagest’, recorded in about 137 A.D., and defined the magnitude-intensity relationship on a logarithmic scale. Stellar magnitudes observed with the naked eye recorded in seven old star catalogues were analyzed in order to examine the visual magnitude systems. Despite that psychophysists have proposed that human’s sensitivities are on a power-law scale, it is shown that the degree of agreement is far better for a logarithmic magnitude than a power-law magnitude. It is also found that light ratios in each star catalogue nearly equal to 2.512, excluding the brightest (1st) and the dimmest (6th and dimmer) stars being unsuitable for the examination. It means that the visual magnitudes in old star catalogues fully agree with Pogson’s logarithmic scale. keywords stars: general – historical star catalogues – stellar magnitude system – visual magni- tude estimates – astronomical photometry 1 Introduction The concept of magnitudes was introduced by Hipparchus in c.2 B.C. (cf. Hearnshaw 1996). Hipparchus compiled his catalogue of 850 stars with ecliptical coordinates and visual mag- nitudes. This work was triggered by the discovery and the observation of a nova (not yet explained) in the constellation Scorpius in 134 B.C. He started to record the coordinates and magnitudes of fixed stars in order to aid discoveries of such objects, and to record the bright- ness. He def