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Variation Of The Tully-Fisher Relation As A Function Of The Magnitude Interval Of A Sample Of Galaxies

In this paper we carry out a preliminary study of the dependence of the Tully-Fisher Relation (TFR) with the width and intensity level of the absolute magnitude interval of a limited sample of 2411 galaxies taken from Mathewson \& Ford (1996). The galaxies in this sample do not differ significantly in morphological type, and are distributed over an $\sim11$-magnitude interval ($-24.4 < I < -13.0$). We take as directives the papers by Nigoche-Netro et al. (2008, 2009, 2010) in which they study the dependence of the Kormendy (KR), the Fundamental Plane (FPR) and the Faber-Jackson Relations (FJR) with the magnitude interval within which the observed galaxies used to derive these relations are contained. We were able to characterise the behaviour of the TFR coefficients $(α, β)$ with respect to the width of the magnitude interval as well as with the brightness of the galaxies within this magnitude interval. We concluded that the TFR for this specific sample of galaxies depends on observational biases caused by arbitrary magnitude cuts, which in turn depend on the width and intensity of the chosen brightness levels.