## 8. The calibrator sample bias when one uses relevant field slopeIn the above discussion it is noteworthy that one does not have to know the intrinsic slope for the calibrators. However, the calibrator sample must fulfill a special condition. It must be equivalent to a volume-limited sample, or reflect the cosmic Gaussian distribution, as was already noted in Teerikorpi (1990). From Eq. (23), it is clear that two calibrator samples with different yield different zero-points for the same of the field galaxies, while there can exist only one such correct , the one corresponding to or . If of the calibrator sample deviates from the cosmic , there is a systematical error in , resulting in an average error in the derived : or in terms of the average This source of error is very significant if the calibrator sample
has not been constructed with the intention of reaching the cosmic
distribution of That this could be a genuine problem, consider the calibrator
sample of KLUN with Cepheid distances. An indication of the calibrator
sample bias is seen by comparing the distribution of calibrator
Application of Eqs. (25-26) requires a knowledge of the average or of the cosmic distribution functions to be compared with those of the calibrator sample. It is clear that any calculation of from the field sample requires, besides a suitable method, the value of itself, hence an iterative approach. Below we show that there is another much more convenient route which does not require an explicit knowledge of the difference (or the value of ). However, it assumes a radial space distribution law of galaxy number density. © European Southern Observatory (ESO) 1999 Online publication: March 1, 1999 |