Volume 576, April 2015
|Number of page(s)||5|
|Section||Cosmology (including clusters of galaxies)|
|Published online||01 April 2015|
Eddington-Malmquist bias in a cosmological context
Tuorla ObservatoryDepartment of Physics and Astronomy, University of
Received: 9 December 2014
Accepted: 27 February 2015
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 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.
Key words: methods: statistical / galaxies: distances and redshifts / distance scale
© ESO, 2015
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