HST Grism-derived Forecasts for Future Galaxy Redshift Surveys
  The mutually complementary Euclid and Roman galaxy redshift surveys will use
Halpha- and [OIII]-selected emission line galaxies as tracers of the large
scale structure at $0.9 \lesssim z \lesssim 1.9$ (Halpha) and $1.5 \lesssim z
\lesssim 2.7$ ([OIII]). It is essential to have a reliable and sufficiently
precise knowledge of the expected numbers of Halpha-emitting galaxies in the
survey volume in order to optimize these redshift surveys for the study of dark
energy. Additionally, these future samples of emission-line galaxies will, like
all slitless spectroscopy surveys, be affected by a complex selection function
that depends on galaxy size and luminosity, line equivalent width, and redshift
errors arising from the misidentification of single emission-line galaxies.
Focusing on the specifics of the Euclid survey, we combine two slitless
spectroscopic WFC3-IR datasets -- 3D-HST+AGHAST and the WISP survey -- to
construct a Euclid-like sample that covers an area of 0.56 deg$^2$ and includes
1277 emission line galaxies. We detect 1091 ($\sim$3270 deg$^{-2}$)
Halpha+[NII]-emitting galaxies in the range $0.9\leq z \leq 1.6$ and 162
($\sim$440 deg$^{-2}$) [OIII]$\lambda$5007-emitters over $1.5\leq z \leq 2.3$
with line fluxes $\geq 2 \times 10^{-16}$ erg s$^{-1}$ cm$^{-2}$. The median of
the Halpha+[NII] equivalent width distribution is $\sim$250\r{A}, and the
effective radii of the continuum and Halpha+[NII] emission are correlated with
a median of $\sim$0.38" and significant scatter ($\sigma \sim $0.2"$-$0.35").
Finally, we explore the prevalence of redshift misidentification in future
Euclid samples, finding potential contamination rates of $\sim$14-20% and
$\sim$6% down to $2\times 10^{-16}$ and $6 \times 10^{-17}$ erg s$^{-1}$
cm$^{-2}$, respectively, though with increased wavelength coverage these
percentages drop to nearly zero.
