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Title:
Selection, covariance, and Malmquist bias
Authors:
Gould, Andrew
Affiliation:
AA(Inst. for Advanced Study, Princeton, NJ)
Publication:
Astrophysical Journal, Part 2 - Letters (ISSN 0004-637X), vol. 412, no. 2, p. L55-L58. (ApJL Homepage)
Publication Date:
08/1993
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
Bias, Galaxies, Spatial Distribution, Astronomical Catalogs, Computational Astrophysics, Correlation Coefficients, Error Analysis, Hubble Constant
DOI:
10.1086/186939
Bibliographic Code:
1993ApJ...412L..55G

Abstract

The correction for Malmquist bias is generally thought to have the form alpha Delta-squared, where Delta is the rms fractional error for a given distance indicator and alpha is a numerical coefficient which depends on the galaxy distribution and other aspects of the problem. In fact, this form of the correction is valid only when the objects are selected on the same observable that is used to make the distance measurement. In many applications of the Tully-Fisher relation, the galaxies are selected from B catalogs, but the distances are measured using H, I, or R magnitudes. In these cases, the proper form for the mean Malmquist bias is alpha c12, where c12 is the covariance between the fractional distance error in the band in which the measurements are made with the fractional error in the band on which the galaxies are selected. The Malmquist bias for the Dn-sigma relation is also proportional to a covariance. Failure to use the proper Malmquist correction may lead to significant errors in estimates of the Hubble parameter and to the introduction of spurious motions in peculiar-velocity studies.

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