The I-Band Tully-Fisher Relation for Cluster Galaxies: a Template Relation, its Scatter and Bias Corrections

Infrared I band photometry and velocity widths for galaxies in 24 clusters, with radial velocities between 1,000 and 10,000 \kms, are used to construct a template Tully--Fisher (TF) relation. The sources of scatter in the TF diagram are analyzed in detail; it is shown that the common practice of referring to a single figure of TF scatter is incorrect and can lead to erroneous bias corrections. Biases resulting from sample incompleteness, catalog inaccuracies, cluster size and other sources, as well as dependences of TF parameters on morphological type and local environment, are discussed and appropriate corrections are obtained. A template TF relation is constructed by combining the data from the 24 clusters, and kinematic cluster offsets from a putative reference frame which well approximates null velocity with respect to the cosmic microwave background, are obtained