The [OIII]$\lambda5007$ equivalent width distribution at z $\sim2$: The
  redshift evolution of the extreme emission line galaxies
  We determine the [OIII]$\lambda5007$ equivalent width (EW) distribution of
$1.700<\rm{z}<2.274$ rest-frame UV-selected (M$_{\rm{UV}}<-19$) star-forming
galaxies in the GOODS North and South fields. We make use of deep HDUV
broadband photometry catalogues for selection and 3D-HST WFC3/IR grism spectra
for measurement of line properties. The [OIII]$\lambda5007$ EW distribution
allows us to measure the abundance of extreme emission line galaxies (EELGs)
within this population. We model a log-normal distribution to the
[OIII]$\lambda5007$ rest-frame equivalent widths of galaxies in our sample,
with location parameter $\mu=4.24\pm0.07$ and variance parameter $\sigma=
1.33\pm0.06$. This EW distribution has a mean [OIII]$\lambda5007$ EW of
168$\pm1\r{A}$. The fractions of $\rm{z}\sim2$ rest-UV-selected galaxies with
[OIII]$\lambda5007$ EWs greater than $500, 750$ and $1000\r{A}$ are measured to
be $6.8^{+1.0}_{-0.9}\%$, $3.6^{+0.7}_{-0.6}\%$, and $2.2^{+0.5}_{-0.4}\%$
respectively. The EELG fractions do not vary strongly with UV luminosity in the
range ($-21.6<M_{\rm{UV}}<-19.0$) considered in this paper, consistent with
findings at higher redshifts. We compare our results to $\rm{z}\sim5$ and
$\rm{z}\sim7$ studies where candidate EELGs have been discovered through
Spitzer/IRAC colours, and we identify rapid evolution with redshift in the
fraction of star-forming galaxies observed in an extreme emission line phase (a
rise by a factor $\sim10$ between $\rm{z}\sim2$ and $\rm{z}\sim7$). This
evolution is consistent with an increased incidence of strong bursts in the
galaxy population of the reionisation era. While this population makes a
sub-dominant contribution of the ionising emissivity at $\rm{z}\simeq2$, EELGs
are likely to dominate the ionising output in the reionisation era.
