MHD Simulations of Relic Radio Bubbles in Clusters

Abstract

In order to better understand the origin and evolution of relic radio bubbles in clusters of galaxies, we report on an extensive set of 2D MHD simulations of hot buoyant bubbles evolving in a realistic intracluster medium. Our bubbles are inflated near the base of the ICM over a finite time interval from a region whose magnetic field is isolated from the ICM. We confirm both the early conjecture from linear analysis and the later results based on preformed MHD bubbles; namely, that very modest ICM magnetic fields can stabilize the rising bubbles against disruption by Rayleigh-Taylor and Kelvin-Helmholtz instabilities. We find in addition that amplification of the ambient fields as they stretch around the bubbles can be sufficient to protect the bubbles or their initial fragments even if the fields are initially much too weak to play a significant role early in the evolution of the bubbles. Indeed, even with initial fields less than a micro-Gauss and values of $β= P_g/P_b$ approaching $10^5$, magnetic stresses in our simulations eventually became large enough to influence the bubble evolution. Magnetic field influence also depends significantly on the geometry of the ICM field and on the topology of the field at the bubble/ICM interface. For example, reconnection of anti-parallel fields across the bubble top greatly reduced the ability of the magnetic field to inhibit disruptive instabilities. Our results confirm earlier estimates of $10^8$ yr for relic radio bubble lifetimes and show that magnetic fields can account for the long term stability of these objects against disruption by surface instabilities. In addition these calculations show that lifting and mixing of the ambient ICM may be a critical function of field geometries in both the ICM and in the bubble interior.