Consistency of Hitomi, XMM-Newton and Chandra 3.5 keV data from Perseus

\emph{Hitomi} observations of Perseus with the Soft X-ray Spectrometer (SXS) provide a high-resolution look at the 3.5 keV feature reported by multiple groups in the Perseus cluster. The \emph{Hitomi} spectrum -- which involves the sum of diffuse cluster emission and the point-like central Active Galactic Nucleus (AGN) -- does not show any excess at $E \sim 3.5 {\rm keV}$, giving an apparent inconsistency with previous observations of excess diffuse emission. We point out that 2009 \emph{Chandra} data reveals a strong dip in the AGN spectrum at $E = (3.54 \pm 0.02) {\rm keV}$ (cluster frame) -- the identical energy to the diffuse excess observed by \emph{XMM-Newton}. Scaling this dip to the 2016 AGN luminosity and adding it to the diffuse \emph{XMM-Newton} excess, this predicts an overall dip in the SXS field of view of $(-5.9 \pm 4.4) \times 10^{-6} \, {\rm ph} \, {\rm cm}^{-2} \, {\rm s}^{-1}$ at $E= 3.54$ keV -- a precise match to the \emph{Hitomi} data when broadened by the dark matter virial velocity. We describe models of Fluorescent Dark Matter that can reproduce this physics, in which dark matter absorbs and then re-emits 3.5 keV photons emitted from the central AGN.