The EDGE-CALIFA survey: The local and global relations between ∑_∗, ∑_SFR, and ∑_mol that regulate star formation

We present a new characterization of the relations between star-formation rate, stellar mass, and molecular gas mass surface densities at different spatial scales across galaxies (from galaxy-wide to kpc scales). To do so, we make use of the largest sample combining spatially resolved spectroscopic information with CO observations, provided by the Extragalactic Database for Galaxy Evolution (EDGE)-Calar Alto Legacy Integral Field Area (CALIFA) survey, together with new single-dish CO observations obtained by the Atacama Pathfinder Experiment (APEX). We show that these relations are the same at the different scales explored, sharing the same distributions for the explored data, with similar slope, intercept, and scatter (when characterized by a simple power law). From this analysis, we propose that these relations are the projection of a single relation between the three properties that follows a distribution described well by a line in three-dimensional parameter space. Finally, we show that observed secondary relations between the residuals and the parameters considered are explained fully by the correlation between the uncertainties, and therefore have no physical origin. We discuss these results in the context of the hypothesis of self-regulation of the star-formation process.