The Redshift Evolution of the Relation between Stellar Mass, Star Formation Rate, and Gas Metallicity of Galaxies

We investigate the relation between stellar mass ($M_\star$), star formation rate (SFR), and metallicity ($Z$) of galaxies, so called the fundamental metallicity relation, in the galaxy sample of the Sloan Digital Sky Survey Data Release 7. We separate the galaxies into narrow redshift bins and compare the relation at different redshifts, and find statistically significant ($> 99$%) evolution. We test various observational effects that might cause seeming $Z$ evolution, and find it difficult to explain the evolution of the relation only by the observational effects. In the current sample of low redshift galaxies, galaxies with different $M_\star$ and SFR are sampled from different redshifts, and there is degeneracy between $M_\star$/SFR and redshift. Hence it is not straightforward to distinguish a relation between $Z$ and SFR from a relation between $Z$ and redshift. The separation of the intrinsic relation from the redshift evolution effect is a crucial issue to understand evolution of galaxies.