Annu. Rev. Astron. Astrophys. 1997. 35: 101-136 Copyright © 1997 by Annual Reviews. All rights reserved

8.2. About the Unbiased Plateau in the MND

In the method of normalized distances (MND), the basic concept is the unbiased plateau, which corresponds to the separate unbiased parts of the Spaenhauer diagram in TEC. After its first utilization by Bottinelli et al (1986), several new developments have matured the understanding of the unbiased plateau. Bottinelli et al (1995) recognized that in the Equation 12 of MND, one should add terms describing how the effective magnitude limit changes due to internal extinction (inclination effect) and galactic extinction; it is also possible that the limiting magnitude depends on the TF parameter p (Bottinelli et al 1988a). One must also include the type dependence in the method (Theureau et al 1997).

Numerical simulations by Ekholm (1996) supported the reliability of MND. An interesting result was that in certain kinds of studies (e.g. for determination of the slope of the TF relation), it is admissible to use galaxies somewhat beyond the unbiased plateau, which increases the sample. In fact, it is a handicap in MND, as well as in TEC, that the number of "useful" galaxies remains small in the unbiased regions, e.g. when one determines the value of H_o. One remedy is to use increasingly large samples. For instance, Bottinelli et al (1986) used the total number of galaxies of 395, and the size of the adopted plateau was 41. Theureau et al (1997) used a KLUN sample (with diameters) that was, after necessary restrictions, 4164, and the adopted plateau contained 478 galaxies. It seems that generally the visible empirical plateau contains about 10% of the total sample. Theureau et al (1997) confirmed this by an analytical calculation, where the cumulative error of <log H> was seen to reach about 1% when the fraction of the sample is 0.1.

Because of the small number of plateau galaxies, one would be willing to use for the determination of H_o the inverse relation, where, in principle, one could use the whole sample. However, the various problems with the inverse relation (Section 5) must be solved before it can be safely used as an independent distance indicator.