X-ray study of the double source plane gravitational lens system Eye of Horus observed with XMM-Newton

A double source plane (DSP) system is a precious probe for the density profile of distant galaxies and cosmological parameters. However, these measurements could be affected by the surrounding environment of the lens galaxy. Thus, it is important to evaluate the cluster-scale mass for detailed mass modeling. We observed the {\it Eye of Horus}, a DSP system discovered by the Subaru HSC--SSP, with XMM--Newton. We detected two X-ray extended emissions, originating from two clusters, one centered at the {\it Eye of Horus}, and the other located $\sim100$ arcsec northeast to the {\it Eye of Horus}. We determined the dynamical mass assuming hydrostatic equilibrium, and evaluated their contributions to the lens mass interior of the Einstein radius. The contribution of the former cluster is $1.1^{+1.2}_{-0.5}\times10^{12}~M_{\odot}$, which is $21-76\%$ of the total mass within the Einstein radius. The discrepancy is likely due to the complex gravitational structure along the line of sight. On the other hand, the contribution of the latter cluster is only $\sim2\%$ on the {\it Eye of Horus}. Therefore, the influence associated with this cluster can be ignored.