## 5. Type dependence in the direct relationThe direct TF-relation is naturally expected also to show a type
dependence. However, special care is needed in the analysis, because
especially the zero-point shifts may be here deformed by the Malmquist
bias. Our tool, as in our several previous studies, is the method of
normalized distances. Details may be found in Bottinelli et al.
(1995). Because we now know that there are zero-point differences,
these must be incorporated in the formula for normalized distances as
an additional factor . A few iterations are
needed when one calculates from the unbiased "plateau" the regression
lines for each type. The procedure is facilitated by our assumption
that the slopes of the lines are identical. Note that this is not
necessarily true, because intrinsic variations of
at a constant In order to derive the slope, we made several experiments with
different normalized distance limits defining the plateau. It was
found that the slope does not change when different reasonable
plateau-limits are used. This is as expected from the simulations
performed by Ekholm (1996). For the diameter relation, we finally
adopted the slope
Bottom panels of Fig. 7 show the zero-points from the regressions giving the slopes in the top panel, and after fixing the slope to 1.04. The zero-points for the constant slope are given in Table 1. It should be noted that the zero-points in Table 1 are not calibrated in the usual sense, but correspond to the adopted kinematical distance scale. © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |