The Relation Between [OIII]/H$\beta$ and Specific Star Formation Rate in
  Galaxies at $z \sim 2$
  Recent surveys have identified a seemingly ubiquitous population of galaxies
with elevated [OIII]/H$\beta$ emission line ratios at $z > 1$, though the
nature of this phenomenon continues to be debated. The [OIII]/H$\beta$ line
ratio is of interest because it is a main component of the standard diagnostic
tools used to differentiate between active galactic nuclei (AGN) and
star-forming galaxies, as well as the gas-phase metallicity indicators $O_{23}$
and $R_{23}$. Here, we investigate the primary driver of increased
[OIII]/H$\beta$ ratios by median-stacking rest-frame optical spectra for a
sample of star-forming galaxies in the 3D-HST survey in the redshift range
$z\sim1.4-2.2$. Using $N = 4220$ star-forming galaxies, we stack the data in
bins of mass and specific star formation rates (sSFR) respectively. After
accounting for stellar Balmer absorption, we measure
[OIII]$\lambda5007$\AA/H$\beta$ down to $\mathrm{M} \sim 10^{9.2} \
\mathrm{M_\odot}$ and sSFR $\sim 10^{-9.6} \ \mathrm{yr}^{-1}$, more than an
order of magnitude lower than previous work at similar redshifts. We find an
offset of $0.59\pm0.05$ dex between the median ratios at $z\sim2$ and $z\sim0$
at fixed stellar mass, in agreement with existing studies. However, with
respect to sSFR, the $z \sim 2$ stacks all lie within 1$\sigma$ of the median
SDSS ratios, with an average offset of only $-0.06\pm 0.05$. We find that the
excitation properties of galaxies are tightly correlated with their sSFR at
both $z\sim2$ and $z\sim0$, with a relation that appears to be roughly constant
over the last 10 Gyr of cosmic time.
