Eddington-Malmquist bias in a cosmological context

Tuorla ObservatoryDepartment of Physics and Astronomy, University of Turku, 21500 Piikkiö, Finland
e-mail: pekkatee@utu.fi

Received: 9 December 2014
Accepted: 27 February 2015

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 = −σ_M²$\frac{\mathrm{d}\ln \mathit{a}\mathrm{\left(}\mathit{m}\mathrm{\right)}}{\mathrm{d}\mathit{m}}$ 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.