The mass-metallicity and fundamental metallicity relations at z>2 using
  VLT and Subaru near-infrared spectroscopy of zCOSMOS galaxies
  In the local universe, there is good evidence that, at a given stellar mass
M, the gas-phase metallicity Z is anti-correlated with the star formation rate
(SFR) of the galaxies. It has also been claimed that the resulting Z(M,SFR)
relation is invariant with redshift - the so-called Fundamental Metallicity
Relation (FMR). Given a number of difficulties in determining metallicities,
especially at higher redshifts, the form of the Z(M,SFR) relation and whether
it is really independent of redshift is still very controversial. To explore
this issue at z>2, we used VLT-SINFONI and Subaru-MOIRCS near-infrared
spectroscopy of 20 zCOSMOS-deep galaxies at 2.1<z<2.5 to measure the strengths
of up to five emission lines: [OII], Hbeta, [OIII], Halpha, and [NII]. This
near-infrared spectroscopy enables us to derive O/H metallicities, and also
SFRs from extinction corrected Halpha measurements. We find that the
mass-metallicity relation (MZR) of these star-forming galaxies at z~2.3 is
lower than the local SDSS MZR by a factor of three to five, a larger change
than found by Erb et al. (2006) using [NII]/Halpha-based metallicities from
stacked spectra. We discuss how the different selections of the samples and
metallicity calibrations used may be responsible for this discrepancy. The
galaxies show direct evidence that the SFR is still a second parameter in the
mass-metallicity relation at these redshifts. However, determining whether the
Z(M,SFR) relation is invariant with epoch depends on the choice of
extrapolation used from local samples, because z>2 galaxies of a given mass
have much higher SFRs than the local SDSS galaxies. We find that the zCOSMOS
galaxies are consistent with a non-evolving FMR if we use the
physically-motivated formulation of the Z(M,SFR) relation from Lilly et al.
(2003), but not if we use the empirical formulation of Mannucci et al. (2010).
