A demonstration is made of the existence of the Teerikorpi Cluster Population Incompleteness Bias (CPIB) in the Tully-Fisher (TF) method of distance determination. A bias exists if the cluster is sampled incompletely into its luminosity function, despite the fact that all the cluster galaxies are at nearly the same distance. Neglect of the bias will give too small a cluster distance and, therefore, too high a Hubble constant. The bias is modeled using graphical methods based on properties of Spaenhauer diagrams following the method of Papers II and III. It is shown that the bias is the same as the individual Msun M(m, z) corrections derived in Paper I, generalized to the M₀- M(m, Vrot,Z) corrections in Papers II and III for the TF method. Four predictions of the model are that (1) the slope of the apparent TF regression depends on how far we sample into the cluster luminosity function, (2) the highest rotators will lie closest to the unbiased fiducial TF ridge line, (3) the error in the distance modulus decreases as the magnitude grasp into the cluster luminosity function (LF) increases, reaching zero only at ∼6 mag into the cluster LF if the intrinsic dispersion is as high as we obtain here, and (4) the observed, not the true, dispersion is a strong function of the sampling depth into the luminosity function. The small TF dispersions in clusters derived in a number of current discussions are artifacts of the bias caused by using incomplete samples. The predictions are verified using two independent data samples of real galaxies. Values of the Hubble constant near H₀ = 90 km s⁻¹ Mpc⁻¹ found using incomplete cluster data reduce to unbiased values between 45 and 55 when corrections for the cluster incompleteness bias are applied.
No takes yet. Share an insight, caveat, or question.
Sandage et al. (1995) studied this question.