On the 3D structure of the mass, metallicity, and SFR space for SF   galaxies
  We demonstrate that the space formed by the star-formation rate (SFR), gas-phase metallicity (Z), and stellar mass (M), can be reduced to a plane, as first proposed by Lara-Lopez et al. We study three different approaches to find the best representation of this 3D space, using a principal component analysis, a regression fit, and binning of the data. The PCA shows that this 3D space can be adequately represented in only 2 dimensions, i.e., a plane. We find that the plane that minimises the chi^2 for all variables, and hence provides the best representation of the data, corresponds to a regression fit to the stellar mass as a function of SFR and $Z$, M=f(Z,SFR). We find that the distribution resulting from the median values in bins for our data gives the highest chi^2. We also show that the empirical calibrations to the oxygen abundance used to derive the Fundamental Metallicity Relation (Nagao et al.) have important limitations, which contribute to the apparent inconsistencies. The main problem is that these empirical calibrations do not consider the ionization degree of the gas. Furthermore, the use of the N2 index to estimate oxygen abundances cannot be applied for ~8.8 because of the saturation of the [NII]6584 line in the high-metallicity regime. Finally we provide an update of the Fundamental Plane derived by Lara-Lopez et al. 
Maritza A. Lara-Lopez, Angel R. Lopez-Sanchez, Andrew M. Hopkins
astro-ph.CO