Abundance profiles in cooling-core clusters: a fossil record of past AGN-driven convection?

Central peaks in the iron abundance of intracluster plasma are a common feature of cooling-core galaxy clusters. These abundance peaks have a much broader profile than the stars of the central brightest cluster galaxy (BCG), which produce the excess iron, indicating that metal-enriched plasma is transported out of the BCG by some process such as turbulent diffusion. At the same time, cooling-core clusters are likely heated by central active galactic nuclei (AGNs) by means of jets, cosmic-ray bubbles, and convection. The recent AGN-driven convection model of Chandran&Rasera predicts the turbulent velocity profile in a steady-state cluster in which radiative cooling is balanced by heating from a combination of AGN-driven convection and thermal conduction. We use the velocity profiles as input into an advection/diffusion model for the transport of metals in the intracluster medium, taking the iron to be injected by the BCG. We compare the results of our model to XMM and Chandra observations of eight clusters. Assuming a constant turbulence level over a cluster's lifetime, the turbulent velocities in the model can explain the observed abundance profiles in only five of the eight clusters. However, we go on to develop an analytic fit of the turbulent velocity profile as a function of the AGN power. We then deduce for each cluster the average AGN power (during the past 10 Gyr) required to match the abundance profiles. The required average values are between 10^43 and 2.10^44 erg/s, while the present AGN powers span a much larger range from 6.10^41 (Virgo) to 2.10^44 erg/s (Hydra A). Our results suggest that AGN-driven convection can account for the observed abundance profiles if the AGN power varies over a cluster's lifetime between Virgo-like and Hydra-A-like values, with average values in the above-quoted range.