The Ionizing Photon Production Efficiency ($\xi_{ion}$) Of Lensed Dwarf
  Galaxies At $z \sim 2 $
  We measure the ionizing photon production efficiency ($\xi_{ion}$) of
low-mass galaxies ($10^{7.8}$-$10^{9.8}$ $M_{\odot}$) at $1.4<z<2.7$, allowing
us to better understand the contribution of dwarf galaxies to the ionizing
background and cosmic reionization. We target galaxies that are magnified by
the strong lensing galaxy clusters Abell 1689, MACS J0717, and MACS J1149. We
utilize Keck/MOSFIRE spectra to measure optical nebular emission line fluxes
and HST imaging to measure the rest-UV and rest-optical photometry. We present
two methods of stacking. First, we take the average of the log(L$_{H\alpha}$
/L$_{UV}$) of galaxies in our sample to determine the typical log($\xi_{ion}$).
Second, we take the logarithm of the total L$_{H\alpha}$ over the total
L$_{UV}$. We prefer the latter as it provides the total ionizing UV luminosity
density of galaxies when multiplied by the non-ionizing UV luminosity density
from the UV luminosity function. log($\xi_{ion}$) calculated from the second
method is $\sim$ 0.2 dex higher than the first method. We do not find any
strong dependence between log($\xi_{ion}$) and stellar mass, M$_{UV}$ or UV
spectral slope ($\beta$). We report a value of log($\xi_{ion}$) $\sim25.47\pm
0.09$ for our UV-complete sample ($-22<M_{UV}<-17.3$) and $\sim25.37\pm0.11$
for our mass-complete sample ($7.8<\log(M_*)<9.8)$. These values are consistent
with measurements of more massive, more luminous galaxies in other
high-redshift studies that use the same stacking technique. Our
log($\xi_{ion}$) is $0.2-0.3$ dex higher than low-redshift galaxies of similar
mass, indicating an evolution in the stellar properties, possibly due to
metallicity, age, or the prevalence of binary stars. We also find a correlation
between log($\xi_{ion}$) and the equivalent widths of H$\alpha$ and
[OIII]$\lambda$5007 fluxes, confirming that these equivalent widths can be used
to estimate $\xi_{ion}$.
