3 Selection of sosie galaxies

The sosie galaxies of a given calibrator are defined with a given range around relevant parameters for the application of the Tully-Fisher relationship (morphological type code T, log of axis ratio $\log R_{25}$and log of maximum rotation velocity $\log V_{\rm M}$). The range of a given parameter is related to the typical error attached to this parameter. In order to choose the best range for each parameter we plot histograms of actual uncertainties (Fig. 4) as they are extracted from LEDA, for galaxies having known T, $\log R_{25}$ and $\log V_{\rm M}$.

Figure 4: Histogram of actual uncertainties on morphological type code T, log of axis ratio $\log R_{25}$ and log of maximum rotation velocity $\log V_M$. For each parameter, we show the limit (vertical doted lines) beyond which the parameter is considered as different from the one of the calibrator.

Thus, we define a sosie of a calibrator with the following conditions (the parameters of the calibrator are noted with the upperscript "calib''):

$$T = T^{\rm calib} \pm 1.5$$ (2)

$$\log R_{25} =\log R_{25}^{\rm calib} \pm 0.06$$ (3)

$$\log V_M =\log V_M^{\rm calib} \pm 0.03.$$ (4)

A galaxy obeying these criteria does not have parameters significantly different from those of the considered calibrator, and thus, following the TF precepts, it has the same absolute magnitude. The distance modulus is then simply deduced from the relation:

$$\mu = \mu^{\rm calib} + m_{\rm o} -m_{\rm o}^{\rm calib}$$ (5)

where $m_{\rm o}$ are corrected apparent magnitudes (in B or I).

The application of the previous criteria to galaxies of the LEDA2002 gives a sample of 2732 galaxies which are sosie of one of the 21 calibrators of Table 1. 495 galaxies are sosie of two or three calibrators. For these galaxies we compared the distance moduli obtained from different calibrators. The mean standard deviation of their distance moduli is 0.29.