ZFIRE: Galaxy Cluster Kinematics, H$\alpha$ Star Formation Rates, and Gas-Phase Metallicities of XMM-LSS J02182-05102 at z=1.6233

We spectroscopically survey the galaxy cluster XMM-LSS J02182-05102 (hereafter IRC 0218) using LRIS (optical) and MOSFIRE (near-infrared) on Keck I as part of the ZFIRE survey. IRC 0218 has a narrow redshift range of $1.612<z_{\rm spec}<1.635$ defined by 33 members of which 20 are at R$_{\rm proj}<1$ Mpc. The cluster redshift and velocity dispersion are $z_{\rm cl}=1.6233\pm0.0003$ and $\sigma_{\rm cl}=254\pm50$ km s$^{-1}$. We reach NIR line sensitivities of $\sim0.3\times10^{-17}$ erg s$^{-1}$ cm$^{-2}$ that, combined with multi-wavelength photometry, provide extinction-corrected H$\alpha$ star formation rates (SFR), gas phase metallicities from [NII]/H$\alpha$, and stellar masses. We measure an integrated H$\alpha$ SFR of $\sim325{\rm M}_{\odot}$ yr$^{-1}$ (26 members; R$_{\rm proj}<2$ Mpc) and show that the elevated star formation in the cluster core (R$_{\rm proj}<0.25$ Mpc) is driven by the concentration of star-forming members, but the average SFR per H$\alpha$-detected galaxy is half that of members at R$_{\rm proj}\sim1$ Mpc. However, we do not detect any environmental imprint when comparing attenuation and gas phase metallicities: the cluster galaxies show similar trends with M$_{\star}$ as to the field, e.g. more massive galaxies have larger stellar attenuation. IRC 0218's gas phase metallicity-M$_{\star}$ relation (MZR) is offset to lower metallicities relative to $z\sim0$ and has a slope of $0.13\pm0.10$. Comparing the MZR in IRC 0218 to the COSMOS cluster at $z=2.1$ shows no evolution ($\Delta t\sim1$ Gyr): the MZR for both galaxy clusters are remarkably consistent with each other and virtually identical to several field surveys at $z\sim2$.