Measuring Scaling Relationships: Fitting Technique Matters

Scaling relationships, both integrated and spatially resolved, arise due to the physical processes that govern galaxy evolution and are frequently measured in both observed and simulated data. However, the accuracy and comparability of these measurements are hindered by various differences between studies such as spatial resolution, sample selection criteria, and fitting technique. Here, we compare variations of standard least squares techniques to the ridge line method for identifying spatially resolved scaling relations ($\Sigma_*-\Sigma_{\rm SFR}$, $\Sigma_*-\Sigma_{\rm gas}$, and $\Sigma_{\rm gas}-\Sigma_{\rm SFR}$) for TNG100 galaxies. We find that using the ridge line technique to fit these scaling relations with a double linear function results in significantly better fits than fitting with ordinary least squares. We further illustrate the utility of the ridge line technique with an investigation into the dependence of rSFMS measurements on spatial resolution and smoothing scale. Specifically, we find that the slope of the rSFMS at low-$\Sigma_*$ is independent (within $2\sigma$) of spatial resolution and smoothing scale. Finally, we discuss the need for a consistent re-analysis of resolved scaling relations in the literature and physically motivate adoption of the ridge line technique over other fitting methods.