A refined Tully-Fisher relationship and a new scaling law for galaxy
  discs
  We show how the hypothesis that galaxy discs conform to self-similar dynamics
leads to an objective identification, in the data, of an annular region of the
optical disc which is such that, corresponding to the classical Tully-Fisher
scaling law defined on the exterior annular boundary, there is a similar
scaling law defined on the interior annular boundary. This result is confirmed
at the level of statistical certainty over several large ORC samples.
Furthermore, the same analysis provides insight into the uncertainties
associated with the best way of defining Vmax, the rotation velocity used for
the Tully-Fisher scaling law and Rmax, the galaxy radius at which Vmax is
measured. Finally, as a direct consequence, we are led to a refined
Tully-Fisher law which is largely insensitive to the means by which a galaxy's
rotation velocity is defined.
