Malmquist bias in the determination of the distance to the Hercules supercluster.

To estimate the bias in the determination of the distance to a cluster due to the Malmquist effect, the author defines a reference sample and calculates the bias as a function of the kinematic distance of this cluster, the magnitude limit at which it is observed, and the accuracy of the distance indicator. This template is used to investigate the bias in the determination of the distance to the Hercules supercluster calculated by Buta and Corwin (1986) in the short distance scale. It is found that the distance moduli obtained from the luminosity index of spirals and the Tully-Fisher relation should be increased by 0.25 to 0.70 mag, a value that depends on the accuracy of the distance indicators and on the method of determination of the bias. The absence of Tully-Fisher relation found for a set of data can be predicted by the Malmquist effect. It is found that the theoretical bias fit is roughly consistent with the observations, but this effect may be enhanced if the B-band Tully-Fisher relation is not single-valued.