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

2.3. The Scott Effect

Scott (1957) published an important paper on "The Brightest Galaxy in a Cluster as a Distance Indicator." Looking back to this study, one may find it contained many basic points that were later discussed in connection with the Malmquist bias of the second kind. Her concern was how the availability of a distant cluster of galaxies influences the use of its brightest galaxy as a standard candle. Availability means that (a) at least n cluster members must be brighter than the limiting magnitude m₁ of the plate, and (b) the apparent magnitude of the brightest galaxy must be brighter than another limit m₂, which is needed for measurements of magnitude and redshift. Let us pick up a few conclusions of Scott (1957, p. 249):

• (A)t any given distance, a cluster with many members is more likely to be available to the observer than a cluster containing fewer galaxies, or
• if a very distant cluster is available to the observer, then this cluster must be unusual, and
• the brightest galaxies actually observed in very distant clusters must have a tendency to possess brighter absolute magnitudes than the average brightest galaxies in the nearer clusters, hence,
• for distant clusters, the simple use of the brightest galaxy in the cluster as a distance indicator leads to an underestimate of the distance.

Scott used both numerical simulations and an analytical model to show the size of systematic errors that the condition of availability causes to the derived distance at different true distances, and she concluded that the selection effect is bound to influence seriously the Hubble m-z diagram constructed for brightest cluster galaxies. She (1957, p. 264) also concluded that

• an interpretation of the deviations from linearity in the magnitude redshift relation that occur near the threshold of available instruments cannot be made with confidence without appropriate allowance for selection bias.

She (1957, p. 264) also pondered about how to make a difference between a real and selection-induced deviation from linearity in the Hubble law:

• (T)he question as to whether or not the apparent deviation from linearity is an effect of selection [or a real effect] may perhaps be solved by the accumulation of further data using instruments corresponding to larger values of both m₁ and m₂.

Of the above two extracts, Hubble's application is clearly concerned with the classical Malmquist bias (or Kapteyn's Problem II), whereas the discussion by Scott has a relation to Kapteyn's Problem I, though the effect in galaxy clusters is more complicated. In fact, there is no mention of the classical Malmquist bias in Scott's paper and really no need for it.