2002A&A...385..431R

In Roscoe (1999A&A...343..697R), it was described how the modelling of a small sample of optical rotation curves (ORCs) given by Rubin et al. (1980ApJ...238..471R) with the power-law V_rot=AR^α, where where the parameters (A,α) vary between galaxies, raised the hypothesis that the parameter A (considered in the form ln A) had a preference for certain discrete values. This specific hypothesis was tested in that paper against a sample of 900 spiral galaxy rotation curves measured by Mathewson et al. (1992ApJS...81..413M), but folded by Persic & Salucci (1995ApJS...99..501P), and was confirmed on this large sample with a conservatively estimated upper bound probability of 10^–7 against it being a chance effect. In this paper, we begin by reviewing the earlier work, and then describe the analyses of three additional samples; the first of these, of 1200+ Southern sky ORCs, was published by Mathewson & Ford (1996), the second, of 497 Northern sky ORCs, is a composite sample provided by kind permission of Giovanelli & Haynes published in the sequence of papers Dale et al. (1997AJ....114..455D, 1998AJ....115..418D, 1999AJ....118.1468D) and Dale & Uson (2000AJ....120..552D), whilst the third, of 305 Northern sky ORCs, was published by Courteau (1997AJ....114.2402C). These analyses provide overwhelmingly compelling confirmation of what was already a powerful result. Apart from other considerations, the results lead directly to what can be described as a ``second generation of Tully-Fisher methods''. We give a brief discussion of the further implications of the result.