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

1.3. Aim of the Present Review

In the recent literature, comprehensive and technical discussions of various aspects of the Malmquist bias exist (Willick 1994, Strauss & Willick 1995, Hendry & Simmons 1995). The reviews by Sandage (1988a, 1995) put the subject in the general context of observational cosmology. I have in mind a wide audience, from the general astronomer to the quantum cosmologist, who may need an introduction to the Malmquist biases. This problem is so characteristic of the special nature of astronomy that it should be included in introductory astronomy text books. In the otherwise versatile work on the cosmological distance ladder by Rowan-Robinson (1985), the problem of Malmquist bias receives only a passing note, and the extensive review article on distance indicators by Jacoby et al (1992) is also relatively silent in this respect.

The concepts of the different kinds of Malmquist biases are rather simple, though it is possible to dress the discussions in mathematics "complicated enough to be but dimly understood except, perhaps, by their authors" as Sandage (1988a) noted. On the other hand, one sometimes sees references to "the well-known Malmquist bias," which is usually a sign of an insufficient treatment of this problem. The present review is written in the spirit of a useful middle path.

I do not discuss in detail different distance indicators but concentrate on the central issues of the biases. Also, this is not a discussion of the Hubble constant, though it occasionally appears. I also leave aside the question of local calibration. Of course, the biases discussed here are not the only problems of the distance scale. For instance, the supposed distance indicators may not at all fulfill Lundmark's definition, an example of which is Hubble's brightest stars in distant galaxies that were actually HII regions (Sandage 1958).

I take examples mostly from the Tully-Fisher (TF) indicator, which is the most widely applied method in the local universe, with samples of several thousands of galaxies and the calibration of which can now be based on an increasing number of Cepheid distances. Understanding the biases in such large and fundamental samples will always be the test bench on which to build the distance scale and where differing alternative scales must be ultimately compared.

The theory of how to deal with the selection effects affecting distances has gradually evolved to such a level that one may already speak about an emerging general theory of distance indicators. Relevant results are often scattered in articles concerned with a variety of topics, and though I have tried to find a representative reference list, I apologize if some interesting aspects go unnoticed. Finally, I should admit that my several years of pleasant collaboration with the Meudon and Lyon groups must somewhat "bias" this review.