Regression of Fluctuating System Properties: Baryonic Tully–Fisher Scaling in Disk Galaxies

In various interesting physical systems, important properties or dynamics display a strongly fluctuating behavior that can best be described using probability distributions. Examples are fluid turbulence, plasma instabilities, textured images, porous media and cosmological structure. In order to quantitatively compare such phenomena, a similarity measure between distributions is needed, such as the Rao geodesic distance on the corresponding probabilistic manifold. This can form the basis for validation of theoretical models against experimental data and classification of regimes, but also for regression between fluctuating properties. This is the primary motivation for geodesic least squares (GLS) as a robust regression technique, with general applicability. In this contribution, we further clarify this motivation and we apply GLS to Tully–Fisher scaling of baryonic mass vs. rotation velocity in disk galaxies. We show that GLS is well suited to estimate the coefficients and tightness of the scaling. This is relevant for constraining galaxy formation models and for testing alternatives to the Lambda cold dark matter cosmological model.