Magnitude systems in old star catalogues

TL;DR

This paper analyzes old star catalogues to verify if their visual magnitudes align with Pogson's logarithmic scale, finding strong agreement and supporting the historical use of a logarithmic magnitude system.

Contribution

It provides empirical evidence that ancient star magnitudes conform to a logarithmic scale, confirming Pogson's system over alternative power-law models.

Findings

Old star catalogues' magnitudes match Pogson's logarithmic scale.

Light ratios in catalogues are close to 2.512, supporting the logarithmic model.

Power-law sensitivity models are less consistent with historical data.

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.