Annu. Rev. Astron. Astrophys. 1997. 35:
101-136
Copyright © 1997 by Annual Reviews. All rights reserved |

Reprinted with kind permission from Annual Reviews, 4139 El Camino Way, Palo Alto, California, USA

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Tuorla Observatory, Turku University, Piikkiö, FIN-21500 Finland; e-mail: pekkatee@sara.cc.utu.fi

**Abstract.** The
influence of Malmquist bias on the studies of extragalactic distances is
reviewed, with brief glimpses of the history from Kapteyn to Scott. Special
attention is paid to two kinds of biases, for which the names Malmquist
biases of the first and second kind are proposed. The essence of these
biases and the situations where they occur are discussed.

The bias of the first kind is related to the classical Malmquist bias (involving the "volume effect"), while the bias of the second kind appears when standard candles are observed at different (true) distances, whereby magnitude limit cuts away a part of the luminosity function. In particular, study of the latter bias in distance indicators such as Tully Fisher, available for large fundamental samples of galaxies, allows construction of an unbiased absolute distance scale in the local galaxy universe where approximate kinematic relative distances can be derived. Such investigations, using the method of normalized distances or of the Spaenhauer diagram, support the linearity of the Hubble law and make it possible to derive an unbiased value of the Hubble constant.

**Key Words:** galaxies, Tully-Fisher relation, Malmquist bias,
distance scale, cosmology

**Table of Contents**

- INTRODUCTORY REMARKS
- Stars and Galaxies are Gathered from the Sky and not from Space
- Distances and Hubble Law
- Aim of the Present Review

- SOME HISTORY FROM KAPTEYN TO SCOTT
- Kapteyn's Problem I and Problem II
- The Classical Malmquist Bias
- The Scott Effect

- TWO KINDS OF MALMQUIST BIAS
- Biases of the First and Second Kind
- Situations Where the First or General Malmquist Bias Appears
- Situations Where the Second Malmquist Bias Is Important

- ATTEMPTS TO OVERCOME THE SECOND KIND OF BIAS
- The Bias-Free Redshift Range
- The Method of Normalized Distances for Field Galaxies
- Spaenhauer Diagrams and the Triple-Entry Correction by Sandage
- The Cluster Incompleteness Bias
- Normalization: Other Applications

- THE INVERSE TULLY-FISHER RELATION AND THE SECOND
KIND OF BIAS
- The Ideal Case of the Inverse Relation
- Problems in the Use of the Inverse Relation

- THE BIAS OF THE FIRST KIND IN DIRECT AND INVERSE
TF DISTANCE MODULI
- MALMQUIST BIAS AND THE GREAT ATTRACTOR
- SOME RECENT DEVELOPMENTS
- Sosies Galaxies and Partial Incompleteness
- About the Unbiased Plateau in the MND
- Gould's Effect
- Simulation Approach

- CONCLUDING REMARKS
- REFERENCES