The Physical Conditions, Metallicity and Metal Abundance Ratios In a
  Highly Magnified Galaxy at z = 3.6252
  We present optical and near-IR imaging and spectroscopy of SGAS
J105039.6$+$001730, a strongly lensed galaxy at z $=$ 3.6252 magnified by
$>$30$\times$, and derive its physical properties. We measure a stellar mass of
log(M$_{*}$/M$_{\odot}$) $=$ 9.5 $\pm$ 0.35, star formation rates from [O
II]$\lambda$$\lambda$3727 and H-$\beta$ of 55 $\pm$ 20 and 84 $\pm$ 17
M$_{\odot}$ yr$^{-1}$, respectively, an electron density of n$_{e} \leq$
10$^{3}$ cm$^{-2}$, an electron temperature of T$_{e} \leq$ 14000 K, and a
metallicity of 12+log(O/H) $=$ 8.3 $\pm$ 0.1. The strong C
III]$\lambda$$\lambda$1907,1909 emission and abundance ratios of C, N, O and Si
are consistent with well-studied starbursts at z $\sim$ 0 with similar
metallicities. Strong P Cygni lines and He II$\lambda$1640 emission indicate a
significant population of Wolf-Rayet stars, but synthetic spectra of individual
populations of young, hot stars do not reproduce the observed integrated P
Cygni absorption features. The rest-frame UV spectral features are indicative
of a young starburst with high ionization, implying either 1) an ionization
parameter significantly higher than suggest by rest-frame optical nebular
lines, or 2) differences in one or both of the initial mass function and the
properties of ionizing spectra of massive stars. We argue that the observed
features are likely the result of a superposition of star forming regions with
different physical properties. These results demonstrate the complexity of star
formation on scales smaller than individual galaxies, and highlight the
importance of systematic effects that result from smearing together the
signatures of individual star forming regions within galaxies.
