Galaxy pairs in the Sloan Digital Sky Survey -- XIV. Galaxy mergers do
  not lie on the Fundamental Metallicity Relation
  In recent observational studies, star-forming galaxies have been shown to
follow a relation often dubbed the fundamental metallicity relation (FMR). This
relation links the stellar mass of a galaxy with its star formation rate (SFR)
and its gas-phase metallicity. Specifically, the FMR predicts that galaxies, at
a given stellar mass, exhibit lower metallicities for higher SFRs. This trend
is qualitatively consistent with observations of galaxy pairs, which have been
robustly shown to experience increasing gas-phase metallicity dilution and
enhanced star formation activity with decreasing projected separation. In this
work, we show that, despite the qualitative consistency with FMR expectations,
the observed O/H dilution in galaxy pairs of the Sloan Digital Sky Survey is
stronger than what is predicted by the FMR. We conclude that the evolutionary
phase of galaxies interacting with companions is not encoded in the FMR, and
thus, mergers constitute a clearly defined population of outliers. We find that
galaxies in pairs are consistent with the FMR only when their separation is
larger than 110 kpc. Finally, we also quantify the local environment of the
pairs using the number of galaxy neighbours within $2\, \mathrm{Mpc}$, $N_2$,
and the projected separation to the second closest galaxy, $r_2$. We find that
pairs are more sensitive to a second companion than to the local galaxy
density, displaying less elevated SFRs with smaller values of $r_2$.
