Physical and numerical stability and instability of AGN bubbles in a hot intracluster medium

While feedback from Active Galactic Nuclei (AGN) is an important heating source in the centre of galaxy clusters, it is still unclear how the feedback energy is injected into the intracluster medium (ICM) and what role different numerical approaches play. Here, we compare four hydrodynamical schemes in idealized simulations of a rising bubble inflated by AGN feedback in a hot stratified ICM: (traditional) smoothed particle hydrodynamics (TSPH), a pressure flavour of SPH (PSPH), a meshless finite mass (MFM) scheme, as well as an Eulerian code with adaptive mesh refinement. In the absence of magnetic fields, the bubble is Kelvin-Helmholtz unstable on short enough time scales to dissolve it fully in the ICM, which is captured by MFM and RAMSES simulations, while in the TSPH simulation the bubble survives. When the ICM is turbulent, mixing of the bubble with the ICM is accelerated. This occurs if the numerical scheme can capture the instabilities well. The differences in the evolution of the bubble has a surprisingly small influence on the thermal structure of the ICM. However, in the simulations with MFM and RAMSES the bubble disruption leads to turbulent stirring of the ICM which is suppressed in SPH. In the latter the thermal energy remains trapped in the bubble and is transported to large radii. We discuss if the choice of hydrodynamical schemes can lead to systematic differences in the outcomes of cosmological simulations.