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 the identification of an annular region of the optical disc which is such that, corresponding to the 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.