During this last decade, increasing efforts have been made attempting to extract information concerning the distribution of mass in the universe from the radial peculiar velocity field of distant galaxies (see for example Aaronson et al. 1986; Lynden-Bell et al. 1988; Bertschinger et al. 1990; Rauzy et al. 1992; Newsam et al. 1995; Rauzy et al. 1995). Quantitative results based on peculiar velocity studies, such as constraints on the value of the density parameter , can nowadays be found in the literature (see Dekel 1994 for a review). Reliability of such results is however closely related to the various working hypotheses assumed throughout the successive steps of the analysis. The first of these steps is to obtain redshift-independent estimates of galaxies distance. It is performed by using Tully-Fisher (TF) like relations (Tully-Fisher 1977 for spirals and Faber-Jackson 1976 for ellipticals). These observed statistical relations linearly correlate the absolute magnitude M (or similar quantity) of a galaxy with an observable parameter p ( for spirals and for ellipticals). Assuming that the TF relation has been correctly calibrated, an estimate of the absolute magnitude M is obtained by measuring the observable p. Measurement of the apparent magnitude m (or similar quantity) provides then with an estimate of the distance of the galaxy, and comparing it with the redshift z finally furnishes the deviation from the mean Hubble flow (i.e. the radial peculiar velocity).
The preliminar calibration step of the TF relation is of crucial importance for kinematical analyses since errors on the calibration parameters interpret indeed as fictitious large-scale and coherent peculiar velocity fields. Unfortunatly, selection effects in observation, such as upper bound in apparent magnitude, bias the estimates of the TF calibration parameters. Many studies devoted to correct on these biases have been already proposed (see for example Schechter 1980; Bottinelli et al. 1986; Lynden-Bell et al. 1988; Fouqué et al. 1990; Hendry & Simmons 1990; Teerikorpi 1990; Bicknell 1992; Triay et al. 1994; Willick 1994; Hendry & Simmons 1994; Sandage 1994; Willick et al. 1995; Willick et al. 1996; Rauzy & Triay 1996; Ekholm 1996; Triay et al. 1996).
Motivations leading to introduce a new calibration technique are twofold. First, bias correction requires generally a full description of the calibration sample (i.e. the specific shapes of the observational selection function on m and p and of the luminosity function have to be assumed). Since available samples are often constituted of data inherited from various observational programs, modelization of such characteristics still remains a difficult problem. The philosophy is herein to reduce as far as possible the number of dubious assumptions made on these composite samples when deriving calibration parameters. Second, it is not clear how existing calibration procedures are affected by the presence of radial peculiar velocities. The aim is herein to quantify, and if possible to minimize, influences of peculiar velocity fields on the estimates of the calibration parameters.
In Sect. 2 (click here) is summarized the basic statistical model describing Tully-Fisher like relations. The new calibration technique is presented Sect. 3 (click here). Cumbersome calculations and proofs can be found Appendices A, B and C. Potentialities of the method are illustrated in Appendix D where NCA calibration of the Mathewson spirals field galaxies sample is performed.