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.

web@ed-phys.fr