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.