Generation of Internal Waves by Buoyant Bubbles in Galaxy Clusters and Heating of Intracluster Medium

Buoyant bubbles of relativistic plasma in cluster cores plausibly play a key role in conveying the energy from a supermassive black hole to the intracluster medium (ICM) - the process known as radio-mode AGN feedback. Energy conservation guarantees that a bubble loses most of its energy to the ICM after crossing several pressure scale heights. However, actual processes responsible for transferring the energy to the ICM are still being debated. One attractive possibility is the excitation of internal waves, which are trapped in the cluster's core and eventually dissipate. Here we show that a sufficient condition for efficient excitation of these waves in stratified cluster atmospheres is flattening of the bubbles in the radial direction. In our numerical simulations, we model the bubbles phenomenologically as rigid bodies buoyantly rising in the stratified cluster atmosphere. We find that the terminal velocities of the flattened bubbles are small enough so that the Froude number ${\rm Fr}\lesssim 1$. The effects of stratification make the dominant contribution to the total drag force balancing the buoyancy force. In particular, clear signs of internal waves are seen in the simulations. These waves propagate horizontally and downwards from the rising bubble, spreading their energy over large volumes of the ICM. If our findings are scaled to the conditions of the Perseus cluster, the expected terminal velocity is $\sim100-200{\,\rm km\,s^{-1}}$ near the cluster cores, which is in broad agreement with direct measurements by the Hitomi satellite.