HOMOGENEOUS VELOCITY-DISTANCE DATA FOR PECULIAR VELOCITY ANALYSIS .1.CALIBRATION OF CLUSTER SAMPLES

We have combined five Tully-Fisher (TF) redshift-distance samples for peculiar velocity analysis: the cluster data of Han, Mould, and cowork ers (HM) and Willick (W91CL), and the held data of Aaronson et al., Wi llick, Courteau & Faber, and Mathewson et al., totaling over 3000 spir al galaxies. We treat the cluster data in this paper, which is the fir st of a series; in Paper II we treat the field TF samples. These data are to be combined with elliptical data (e.g., Faber et al. 1989) to f orm the Mark III Catalog of Galaxy Peculiar Velocities, which we will present in Paper III. The catalog will be used as input for POTENT rec onstruction of velocity and density fields, described in later papers, as well as for alternative velocity analyses. Our main goal in Papers I and II is to place the TF data onto a self-consistent system by (1) applying a uniform set of corrections to the raw observables, (2) det ermining the TF slopes and scatters separately for each sample, (3) ad justing the TF zero points to ensure mutually consistent distances. Th e global zero point is set by the HM sample, chosen because of its dep th and uniformity on the sky and its substantial overlap with each of the other samples. In this paper, we calibrate the ''forward'' and ''i nverse'' TF relations for HM and W91CL. We study the selection criteri a for these samples and correct for the resultant statistical biases. The bias corrections are validated by comparing forward and inverse cl uster distances. We find that many sample clusters are better modeled as ''expanding'' than relaxed, which significantly affects the TF cali brations. Proper corrections for internal extinction are derived self- consistently from the data.