Bias Properties of Extragalactic Distance Indicators. X. The Teerikorpi Cluster Population Incompleteness Bias for a Modified Lema?tre-Robertson-Hubble-Humason Distance Method That Uses Luminosity Functions

摘要

The Teerikorpi cluster incompleteness bias for galaxy clusters is demonstrated using a simplified model of an artificial cluster. The distance indicator for this demonstration is the combination of the Hubble morphological type (T) and the van den Bergh luminosity class (L) introduced in Paper V. The model shows that the luminosity function must be sampled to ~3.5 mag fainter than the brightest cluster galaxy if a distance modulus that is accurate to ~0.1 mag is to be achieved using the T-L method. The bias properties of the artificial model are demonstrated using actual data from the complete catalogs of the Virgo and the Ursa Major Cluster galaxies. The derived bias-free distance moduli derived from the data are (m - M)0 = 31.95 ± 0.15 mag for the Virgo complex and (m - M)0 = 31.61 ± 0.13 for the Ursa Major Cluster. These are larger than the values of (m - M)0 = 30.80 mag for Virgo and 30.95 mag for Ursa Major derived by Pierce & Tully in 1988 from the Tully-Fisher method. The Virgo modulus here is also larger than the (m - M) = 30.81 mag adopted by the "Key Project" consortium in their work for the Hubble constant, but it is consistent with 31.7 derived earlier by many methods. This modulus, combined with other data, led to H0 = 58 ± 6 km s-1 Mpc-1 in earlier papers and derived most securely from the Cepheid calibration of the mean absolute magnitude of Type Ia supernovae (e.g., Saha et al.; Parodi et al.).