The MOSDEF Survey: The Mass-Metallicity relationship and the existence
  of the FMR at z~1.5
  We analyze the rest-optical emission-line ratios of z~1.5 galaxies drawn from
the MOSFIRE Deep Evolution Field (MOSDEF) survey. Using composite spectra we
investigate the mass-metallicity relation (MZR) at z~1.5 and measure its
evolution to z=0. When using gas-phase metallicities based on the N2 line
ratio, we find that the MZR evolution from z~1.5 to z=0 depends on stellar
mass, evolving by $\Delta\rm log(\rm O/H)\sim0.25$ dex at
$M_*<10^{9.75}M_{\odot}$ down to $\Delta\rm log(\rm O/H)\sim0.05$ at
$M_*>10^{10.5}M_{\odot}$. In contrast, the O3N2-based MZR shows a constant
offset of $\Delta\rm log(\rm O/H)\sim0.30$ across all masses, consistent with
previous MOSDEF results based on independent metallicity indicators, and
suggesting that O3N2 provides a more robust metallicity calibration for our
z~1.5 sample. We investigated the secondary dependence of the MZR on SFR by
measuring correlated scatter about the mean $M_*$-specific SFR and
$M_*-\log(\rm O3N2)$ relations. We find an anti-correlation between $\log(\rm
O/H)$ and sSFR offsets, indicating the presence of a $M_*$-SFR-Z relation,
though with limited significance. Additionally, we find that our z~1.5 stacks
lie along the z=0 metallicity sequence at fixed
$\mu=\log(M_*/M_{\odot})-0.6\times\log(\rm SFR / M_{\odot} yr^{-1})$ suggesting
that the z~1.5 stacks can be described by the z=0 fundamental metallicity
relation (FMR). However, using different calibrations can shift the calculated
metallicities off of the local FMR, indicating that appropriate calibrations
are essential for understanding metallicity evolution with redshift. Finally,
understanding how [NII]/H$\alpha$ scales with galaxy properties is crucial to
accurately describe the effects of blended [NII] and H$\alpha$ on redshift and
H$\alpha$ flux measurements in future large surveys utilizing low-resolution
spectra such as with Euclid and the Roman Space Telescope.
