The EDGE-CALIFA survey: The local and global relations between
  $\Sigma_\ast$ , $\Sigma_{SFR}$ and $\Sigma_{mol}$ 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 EDGE-CALIFA survey, together
with new single dish CO observations obtained by APEX. We show that those
relations are the same at the different explored scales, 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 well described by a line in the
three-dimension parameter space. Finally, we show that observed secondary
relations between the residuals and the considered parameters are fully
explained 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.
