A new technique for calibrating Tully-Fisher like relations was proposed. Based on a null-correlation approach, this calibration procedure is efficient when galaxies constituting the calibration sample are homogeneously distributed in space. The NCA technique is thus adequate for calibrating a sample of field galaxies for example.
In a first step was introduced the random variable dependent on a slope parameter a and on the observed apparent magnitude m, log line-width distance indicator p and redshift z. In the case of pure Hubble flow (i.e. radial peculiar velocities are null everywhere), it was shown that variables p and X(a) are not correlated if and only if parameter a equals the slope aD of the Direct TF relation. The NCA estimate of the DTF slope aD was defined as the value of a such that correlation between p and X(a) vanishes. This estimator of aD was found particularly robust since it does not depend on the selection effects on m and p which affect the observed calibration sample and on the specific shape of the luminosity function.
Influences of radial peculiar velocities was investigated in a second step. It was shown that the presence of a peculiar velocity field biases the NCA estimate of aD. A procedure which consists in discarding nearby galaxies of the observed sample was introduced. Such subsampling is achieved by adding an extra selection function in distance estimate . The magnitude of the bias and its variations in function of the cut-off in distance estimate r* have been analysed on a synthetic sample and on the Mathewson spirals field galaxies sample (see Appendix D). The proposed subsampling procedure looks fairly efficient for minimizing bias on the NCA estimate of the DTF slope aD created by the presence of radial peculiar velocities.
In the third step, calibration of the "zero-point" parameter B* entering the definition of the velocity estimator was investigated. It was shown that the variables p and are not correlated if and only if parameter equals the "zero-point" B*. The NCA estimate of the second calibration parameter B* was thus defined as the value of such that correlation between p and vanishes. This B* estimator is robust. It is insensitive to observational selection effects on m and p and to the specific shape of the luminosity function. Moreover, NCA estimate of B* is not biased by the presence of a Maxwellian velocity agitation nor by the existence of bulk flow.
This work is one of the achievements of a long range program focusing on the statistical modelization of TF like relations, launched five years ago by Roland Triay. He is kindly thanked for constructive discussions. The hospitality of the Centre de Physique Théorique of Luminy is recognized. Stéphane Rauzy is cheerfully thanked for a generous financial support.