A critical look at the mass-metallicity-star formation rate relation in the local universe. I. An improved analysis framework and confounding systematics

It has been proposed that the (stellar) mass-(gas) metallicity relation of galaxies exhibits a secondary dependence on star formation rate (SFR), and that the resulting M_∗-Z-SFR relation may be redshift-invariant, i.e., "fundamental." However, conflicting results on the character of the SFR dependence, and whether it exists, have been reported. To gain insight into the origins of the conflicting results, we (1) devise a non-parametric, astrophysically motivated analysis framework based on the offset from the star-forming ("main") sequence at a given M_∗ (relative specific SFR); (2) apply this methodology and perform a comprehensive re-analysis of the local M_∗-Z-SFR relation, based on SDSS, GALEX, and WISE data; and (3) study the impact of sample selection and of using different metallicity and SFR indicators. We show that metallicity is anti-correlated with specific SFR regardless of the indicators used. We do not find that the relation is spurious due to correlations arising from biased metallicity measurements or fiber aperture effects. We emphasize that the dependence is weak/absent for massive galaxies (logM_∗ > 10.5), and that the overall scatter in the M_∗-Z-SFR relation does not greatly decrease from the M_∗-Z relation. We find that the dependence is stronger for the highest SSFR galaxies above the star-forming sequence. This two-mode behavior can be described with a broken linear fit in 12+log(O/H) versus log (SFR/M_∗), at a given M_∗. Previous parameterizations used for comparative analysis with higher redshift samples that do not account for the more detailed behavior of the local M_∗-Z-SFR relation may incorrectly lead to the conclusion that those samples follow a different relationship.