An analysis of 900 optical rotation curves: the universal rotation curve as a power-law and the development of a theory-independent dark-matter modeller

One of the largest H-alpha rotation curve data bases of; i. introduction sp iral galaxies currently available is that Provided by Persic & Salucci, her eafter PS 1995, which has been derived by them from unreduced rotation curv e data-of 965 southern Shy Spirals obtained by Mathewson, Ford & Buchhorn, hereafter MFB 1992. Of the original sample of 965 galaxies, the observation s on 900 were considered by PS 1995 to be good enough for rotation curve st udies, and the present analysis concerns itself with these 900 rotation cur ves. The analysis is performed within the context of-the basic hypothesis that t he phenomenology of rotation curves in the optical disc(that is, away from the dynamical effects of the bulge) can be systematically described in term s of a general power-law V = R-alpha, valid for R > R-min, where R-min is a n estimate of the transition radius between bulge-dominated and disc-domina ted dynamics. The analysis begins by showing how this model:provides an ext remely good description of the generic behaviour of rotation curves in the optical:disc and, furthermore, how it imposes very detailed correlations be tween the free parameters, A and alpha, of the model; These correlations are investigated, and shown to imply, via first and seco nd-order models, a third-order model according to which the rotation veloci ty, V, at any radial displacement in the optical disc of any given spiral g alaxy is given by V/V-0 = (R/R-0)(alpha), where R-0 > R-min, and V-0 are gi ven as approximate functions of the galaxy's absolute magnitude and surface brightness whilst alpha is an unidentified function of other galaxy parame ters - of which the most significant ones will be the relative proportions of the disc, bulge and halo mass-components. It is this;latter function whi ch provides the opportunity for a dark-matter modelling process which is in dependent of any particular dynamical theory. Furthermore,:it is shown that the conclusion of PS 1986, that optical-disc dynamics contain no signature of the transition from disc-dominated dynamic s to halo-dominated dynamics, is extremely strongly supported by this analy sis.