Discovery of a Strong Lensing Galaxy Embedded in a Cluster at z = 1.62

We identify a strong lensing galaxy in the cluster IRC 0218 (also known as XMM-LSS J02182$-$05102) that is spectroscopically confirmed to be at $z=1.62$, making it the highest-redshift strong lens galaxy known. The lens is one of the two brightest cluster galaxies and lenses a background source galaxy into an arc and a counterimage. With Hubble Space Telescope (HST) grism and Keck/LRIS spectroscopy, we measure the source redshift to be $z_{\rm S}=2.26$. Using HST imaging in ACS/F475W, ACS/F814W, WFC3/F125W, and WFC3/F160W, we model the lens mass distribution with an elliptical power-law profile and account for the effects of the cluster halo and nearby galaxies. The Einstein radius is $\theta_{\rm E}=0.38^{+0.02}_{-0.01}$" ($3.2_{-0.1}^{+0.2}$ kpc) and the total enclosed mass is M$_{\rm tot} (< \theta_{\rm E})=1.8^{+0.2}_{-0.1}\times10^{11}~{\rm M}_{\odot}$. We estimate that the cluster environment contributes $\sim10$% of this total mass. Assuming a Chabrier IMF, the dark matter fraction within $\theta_{{\rm E}}$ is $f_{\rm DM}^{{\rm Chab}} = 0.3_{-0.3}^{+0.1}$, while a Salpeter IMF is marginally inconsistent with the enclosed mass ($f_{\rm DM}^{{\rm Salp}} = -0.3_{-0.5}^{+0.2}$). The total magnification of the source is $\mu_{\rm tot}=2.1_{-0.3}^{+0.4}$. The source has at least one bright compact region offset from the source center. Emission from Ly$\alpha$ and [O III] are likely to probe different regions in the source.