Eddington-Malmquist bias in a cosmological context

TL;DR

This paper extends the Malmquist bias formula to a cosmological context, demonstrating its validity in expanding Friedmann universes and clarifying its conceptual scope in observational cosmology.

Contribution

The authors derive the Malmquist relation within a general cosmological framework, including Friedmann models, and discuss its conceptual implications for observational biases.

Findings

Malmquist bias formula applies in Friedmann universes.

The bias relation holds for bolometric and finite-band magnitudes.

Conceptual analysis explains the broad applicability of the bias relation.

Abstract

In 1914, Eddington derived a formula for the difference between the mean absolute magnitudes of stars "in space" or gathered "from the sky". Malmquist (1920) derived a general relation for this difference in Euclidean space. Here we study this statistical bias in cosmology, clarifying and expanding previous work. 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. The Malmquist formula for the intrinsic difference <M>_m - M_0 = - sigma_M^2 dlna(m)/dm is also valid for observations made in an expanding Friedmann universe. This is 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.