Strong Lensing Analysis of PLCK G004.5$-$19.5, a Planck-Discovered Cluster Hosting a Radio Relic at $z=0.52$

The recent discovery of a large number of galaxy clusters using the Sunyaev-Zel'dovich (SZ) effect has opened a new era on the study of the most massive clusters in the Universe. Multi-wavelength analyses are required to understand the properties of these new sets of clusters, which are a sensitive probe of cosmology. We aim at a multi-wavelength characterization of PLCK G004.5$-$19.5, one of the most massive X-ray validated SZ effect-selected galaxy clusters discovered by the Planck satellite. We have observed PLCK G004.5$-$19.5 with GMOS on Gemini South for optical imaging and spectroscopy, and performed a strong lensing analysis. We also searched for associated radio emission in published catalogs. An analysis of the optical images confirms that this is a massive cluster, with a dominant central galaxy (the BCG) and an accompanying red sequence of galaxies, plus a $14''$-long strong lensing arc. Longslit pectroscopy of 6 cluster members shows that the cluster is at $z=0.516\pm0.002$. We also targeted the strongly lensed arc, and found $z_{\rm arc}=1.601$. We use LensTool to carry out a strong lensing analysis, from which we measure a median Einstein radius $\theta_E(z_s=1.6)\simeq30''$ and estimate an enclosed mass $M_E=2.45_{-0.47}^{+0.45}\times10^{14}\,M_\odot$. By extrapolating an NFW profile we find a total mass $M_{500}^{SL}=4.0_{-1.0}^{+2.1}\times10^{14}M_\odot$. Including a constraint on the mass from previous X-ray observations yields a slightly higher mass, $M_{500}^{SL+X}=6.7_{-1.3}^{+2.6}\times10^{14}M_\odot$, marginally consistent with the value from strong lensing alone. High-resolution radio images from TGSS at 150~MHz reveal that PLCK G004.5$-$19.5 hosts a powerful radio relic on scales $\lesssim500$ kpc. Emission at the same location is also detected in low resolution images at 843~MHz and 1.4~GHz. This is one of the higher redshift radio relics known to date.