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.
