The Extended Fe distribution in the intracluster medium and the implications regarding AGN Heating

We present a systematic analysis of XMM-Newton observations of 8 cool-core clusters of galaxies and determine the Fe distribution in the intracluster medium relative to the stellar distribution in the central dominant galaxy (CDG). Our analysis shows that the Fe is significantly more extended than the stellar mass in the CDG in all of the clusters in our sample, with a slight trend of increasing extent with increasing central cooling time. The excess Fe within the central 100 kpc in these clusters can be produced by Type Ia supernovae from the CDG over the past 3-7 Gyr. Since the excess Fe primarily originates from the CDG, it is a useful probe for determining the motion of the gas and the mechanical energy deposited by AGN outbursts over the past $\sim$ 5 Gyr in the centers of clusters. We explore two possible mechanisms for producing the greater extent of the Fe relative to the stars in the CDG, including: bulk expansion of the gas and turbulent diffusion of Fe. Assuming the gas and Fe expand together, we find that a total energy of $10^{60} - 10^{61}$~erg~s$^{-1}$ must have been deposited into the central 100 kpc of these clusters to produce the presently observed Fe distributions. Since the required enrichment time for the excess Fe is approximately 5 Gyr in these clusters, this gives an average AGN mechanical power over this time of $10^{43} - 10^{44}$~erg~s$^{-1}$. The extended Fe distribution in cluster cores can also arise from turbulent diffusion. Assuming steady-state (i.e., the outward mass flux of Fe across a given surface is equal to the mass injection rate of Fe within that surface) we find that diffusion coefficients of $10^{29} - 10^{30}$ cm$^2$~s$^{-1}$ are required to maintain the presently observed Fe profiles (abridged).