A Refined Tully-Fisher Relationship and New Scaling Laws 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 TullyFisher and Freeman scaling laws defined on the exterior annular boundary, there are similar scaling laws 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 a unified source both for the Tully-Fisher and Freeman scaling laws and 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 used for the Freeman scaling law. 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.