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Atmospheric Extinction Effects on Stellar Alignments

The extinction angle is the lowest angle on the horizon at which a star is visible. In other words, if the star were any lower on the horizon than the extinction angle, then the increased amount of atmospheric scattering and haze would render the star invisible. It should be noted that the value of the extinction angle can vary from place to place and from night to night. In this paper, the extinction angle will be measured from the zenith and will be denoted by z. The determination of extinction angles is an important problem for archaeoastronomy, because z is usually needed for calculations regarding the azimuth of proposed stellar alignments: errors in the value of z will translate into errors in azimuth of the first or last sighting of a star. In many practical cases, the error in azimuth is greatly magnified from the error in z by the low angle at which stars may rise relative to the horizon. Hence, a thorough understanding of extinction angles is required to discover and assess any stellar alignment. There have been many studies of models of extinction as a function of zenith distance, which is an important quantity in modern astrophysical photometry. There is a survey of much of this earlier work in Schoenberg (1929), including a reference to an interesting study by Muller (1891) of extinction at all zenith distances up to 89 from both low and high altitude observing sites. Unfortunately, to the best of my knowledge, no accurate model of extinction angles as defined in this paper has ever been proposed; and worse, no actual observations of such extinction angles have ever appeared in the literature. In this paper, I seek to fill these gaps with a three-part approach. In Section 2, I will present numerous observations of extinction angles for objects ranging between -2.7 and 5.4 magnitudes (m). In Section 3, I advance a quantitative and modern astronomical model for predicting z. In Section 4, I analyse the statistical errors associated with the azimuth of a star's first appearance. The results from these sections are then applied to a wide variety of claimed stellar alignments.