*Astron. Astrophys. 343, 713-719 (1999)*
## Theoretical aspects of the inverse Tully-Fisher relation as a distance indicator:
incompleteness in log *V*_{Max}, the relevant slope, and the calibrator sample bias
**
P. Teerikorpi**^{ 1},
T. Ekholm^{ 1},
M.O. Hanski^{ 1} and
G. Theureau^{ 2,3}
^{1} Tuorla Observatory, FIN-21500 Piikkiö, Finland
^{2} Osservatorio di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
^{3} Observatoire de Paris-Meudon, CNRS URA1757, F-92195 Meudon Principal Cedex, France
*Received 24 August 1998 / Accepted 24 November 1998*
**Abstract**
We study the influence of the assumption behind the use of the
inverse Tully-Fisher relation: that there should be no observational
cutoffs in the TF parameter . It is
noted how lower and upper cutoffs would be seen in a
vs. "normalized distance" diagram.
Analytical expressions, under the simplifying assumption of a normal
distribution and the use of the correct TF slope, are derived for the
resulting biases, especially the average bias which
cutoffs produce in the derived value
of . This bias is shown to be
relatively weak, and as such cannot explain the large differences in
the reported values of derived from
direct and inverse TF relations.
Some problems of slope and calibration are shown to be more
serious. In particular, one consequence of fitting through the
calibrators either the slope relevant for field galaxies or the
steeper slope followed by calibrators is that the derived value of the
Hubble constant comes to depend on the nature of the calibrator
sample. If the calibrator sample is not representative of the cosmic
distribution of , large errors in the
derived value of are possible.
Analytical expressions are given for this error that we term the
calibrator sample bias.
**Key words:** galaxies: distances and
redshifts
galaxies:
spiral
cosmology: distance scale
*Send offprint requests to:* P. Teerikorpi (pekkatee@astro.utu.fi)
This article contains no SIMBAD objects.
### Contents
© European Southern Observatory (ESO) 1999
Online publication: March 1, 1999
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