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Astron. Astrophys. 319, 435-449 (1997)

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1. Introduction

The present study prepares the way for our attempt to measure the kinematics of the local galaxy universe (Paturel et al. 1990) using the diameter Tully-Fisher (TF) relation for a sample of 5171 galaxies. This sample was intended to be complete down to the apparent diameter of [FORMULA] arcmin (corresponding to [FORMULA] where [FORMULA] is given in 0.1 arcmin). The completeness of the sample has been discussed by Paturel et al. (1994); see also Bottinelli et al. (1995) for a discussion of the inclination correction based on this sample.

Though generally having larger scatter than the magnitude relation, the diameter TF-relation has some advantages as a distance indicator that may be mentioned here. 1) The sample can be made large, thanks to the establishment of a homogeneous system of diameters [FORMULA], originally coming from different sources (Paturel et al. 1991). 2) The large sample also allows a detailed examination of the properties of the TF-relation. 3) Practically no inclination correction is needed (Bottinelli et al. 1995). However, the scatter in the relation is rather large, and it is important to try to reduce this before attempting to measure distances, e.g. by investigating any possible dependence on galaxy type, which is the central topic of the present paper. We also ask whether the found systematic changes could be interpreted in terms of the mass-to-luminosity ratios of the disc and bulge components, together with a dark halo, making some steps towards a better understanding of the physics of the TF relation.

M. Roberts first noticed in 1978 that for samples of the same absolute magnitude, late type galaxies have systematically smaller intrinsic line widths than early type systems. This type dependence, corresponding to a zero-point difference in the magnitude relation, was also suggested by Rubin et al. (1985) from direct measurements of rotation curves.

The TF-relation based on the diameter measured at the standard B -magnitude isophote of 25 mag (arcsec)-2 is from general considerations expected to depend on type. A simple example explains this best: let us assume that all the galaxies with the same isophotal diameter, have identical discs, on which the diameter is measured. Depending on type, there is in addition a bulge component, providing a fraction of the total mass. Then one expects that going from late (disc-) types towards types with significant bulges, the maximum rotational velocity increases for a fixed isophotal diameter correctly determined on the disc component. One also expects that at a constant absolute magnitude there is a similar, though smaller effect.

This simple model naturally leads one to study the type dependence using in the first place the inverse TF-relation (to see what happens with [FORMULA] at fixed linear diameter). The inverse relation (hereafter iTF) has also the very useful property that it may be constructed in an unbiased manner for a large number of galaxies if a sufficiently good velocity field model is available (kinematic distances) and if certain general conditions are fulfilled. Especially there should be no selection according to [FORMULA] ; this seems to be the case considering the very good detection rates in all HI surveys.

In this study we use the same velocity field model as in the inclination correction study of Bottinelli et al. (1995), in order to derive kinematic distances. In this Virgo centric infall model (Peebles's 1976 model) the velocity of the Virgo cluster is 980 km s-1 and our infall velocity 150 km s-1 (the Virgo distance is taken to be 16.5 Mpc, corresponding to [FORMULA] km s-1 Mpc-1). Because this kinematic model is necessarily simplified and does not take into account larger scale streamings (like the Great Attractor) or random velocities, we make checks on whether the model has a significant influence on the present results. Errors due to the kinematical model tend to make the slope of the inverse TF-relation too shallow. However, experiments with synthetic data and the Tolman-Bondi velocity field have shown that the inverse relation may be derived using the Peebles's model relatively accurately when the random velocity dispersion is not larger than 100 km s-1 (Ekholm, 1995).

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998