Simulating the dark matter decay signal from the Perseus galaxy cluster
  The nearby Perseus galaxy cluster is a key target for indirect detection
searches for decaying dark matter. We use the C-EAGLE simulations of galaxy
clusters to predict the flux, width and shape of a dark matter decay line,
paying particular attention to the unexplained 3.55keV line detected in the
spectra of some galaxies and clusters, and the upcoming XRISM X-ray observatory
mission. We show that the line width in C-EAGLE clusters similar to Perseus is
typically [600-800]$\mathrm{kms^{-1}}$, and therefore narrower than the
amplitude of the velocity dispersion of galaxies in the cluster. Haloes that
are significantly disturbed can, however, exhibit galaxy velocity dispersions
higher than $1000\mathrm{kms^{-1}}$, and in this case will show a large
difference between the line profiles of on- and off-center observations. We
show that the line profile is likely to be slightly asymmetric, but still well
approximated by a Gaussian at the 10% level, and that the halo asymmetry can
lead to fluxes that vary by a factor of two. In summary, we predict that, if
the previously reported 3.55keV line detections do originate from dark matter
decay, the XRISM mission will detect a line with a roughly Gaussian profile at
a rest frame energy of 3.55keV, with a width $>600\mathrm{kms^{-1}}$ and flux
approximately in the range $[4-9]\times10^{-8}\mathrm{counts/sec/cm^{2}}$.
