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 <sup>2,3

1</sup> 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

• 1. Introduction
• 2. Influence of cutoffs in : schematic treatment
• 3. "Unbiased plateau" for the inverse relation
• 4. Analytic calculation of vs.
• 5. Calculation of the average bias
• 6. Application of the average bias formula
• 7. Problems of slope and calibration
• 8. The calibrator sample bias when one uses relevant field slope
• 9. Another route: using calibrator slope and making and Malmquist corrections
• 10. Concluding remarks
• Acknowledgements
• References

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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