Abstract
Aims: In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars “in space” or gathered “from the sky”. In 1920, Malmquist derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. Methods: We derived the Malmquist relation within a general cosmological framework, including Friedmann’s model, analogously to the way Malmquist showed in 1936 that his formula is also valid in the presence of extinction in Euclidean space. We also discuss some conceptual aspects that explain the wide scope of the bias relation. Results: The Malmquist formula for the intrinsic difference ⟨ M ⟩ m – M0 = -σM2{d ln{ a(m)}/{dm}} is also valid for observations made in an expanding Friedmann universe. This holds true for bolometric and finite-band magnitudes when a(m) refers to the distribution of observed (uncorrected for K-effect or z-dependent extinction) apparent magnitudes.
Author
Teerikorpi, P.
Journal
Astronomy & Astrophysics
Paper Publication Date
April 2015
Paper Type
Astrostatistics