Metallicity calibrations of low star-forming galaxies: the influence of
  a stochastic IMF
  We present a study of the consequences of an initial mass function that is
stochastically sampled on the main emission lines used for gas-phase
metallicity estimates in extra-galactic sources. We use the stochastic stellar
population code SLUG and the photoionisation code Cloudy to show that the
stochastic sampling of the massive end of the mass function can lead to clear
variations in the relative production of energetic emission lines such as
[OIII] relative to that of Balmer lines. We use this to study the impact on the
Te, N2O2, R23 and O3N2 metallicity calibrators. We find that stochastic
sampling of the IMF leads to a systematic over-estimate of O/H in galaxies with
low star formation rates (< $10^{-3}$ M$_\odot$/yr) when using the N2O2, R23
and O3N2 strong-line methods, and an under-estimate when using the Te method on
galaxies of sub-solar metallicity. We point out that while the
SFR(Ha)-to-SFR(UV) ratio can be used to identify systems where the initial mass
function might be insufficiently sampled, it does not provide sufficient
information to fully correct the metallicity calibrations at low star formation
rates. Care must therefore be given in the choice of metallicity indicators in
such systems, with the N2O2 indicator proving most robust of those tested by
us, with a bias of 0.08 dex for models with SFR = $10^{-4}$ M$_\odot$/yr and
solar metallicity.
