The Extended Fe Distribution in the Intracluster Medium and the Implications Regarding AGN Heating

We present a systematic analysis of XMM-Newton observations of eight 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 ~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, bulk expansion of the gas and turbulent diffusion of the Fe. Assuming that the gas and Fe expand together, we find that a total energy of 10⁶⁰-10⁶¹ erg s^-1 must have been deposited into the central 100 kpc of these clusters in order to produce the currently 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 10⁴³-10⁴⁴ erg s^-1. The extended Fe distribution in cluster cores can also arise from turbulent diffusion. Assuming a 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 10²⁹-10³⁰ cm² s^-1 are required in order to maintain the currently observed Fe profiles. We find that heating by both turbulent diffusion of entropy and dissipation are important heating mechanisms in cluster cores. In half of the clusters with central cooling times greater than 1 Gyr, we find that heating by turbulent diffusion of entropy alone can balance radiative losses. In the remaining clusters, some additional heating by turbulent dissipation, with turbulent velocities of 150-300 km s^-1, is required in order to balance radiative cooling. We also find that the average Type Ia supernova fraction within the central 100 kpc of these clusters is 0.53 (roughly twice the solar value), on the basis of the Si-to-Fe mass ratio. This implies a total (Type Ia plus core-collapse) supernova heating rate of less than 10% of the bolometric X-ray luminosity within the centers of clusters.