The requirement for mixing-heating to utilize bubble cosmic rays to heat the intracluster medium

Abstract

I conduct simple analytical estimates and conclude that mixing by vortices is a more efficient process to transfer the cosmic ray energy of jet-inflated bubbles to the intracluster medium (ICM) than streaming of cosmic rays along magnetic field lines. Jets and the bubbles they inflate transfer heat to the ambient gas in cooling flows in cluster of galaxies and in galaxies. The internal energy of the jet-inflated bubbles is dominate by very hot thermal gas and/or cosmic rays. Cosmic rays that stream along magnetic field lines that connect the bubbles with the ICM heat the ICM as their energy is dissipated there. I find that about half of the cosmic ray energy is dissipated in the bubbles themselves. I also find that the ICM volume that the cosmic ray streaming process heats is only about five times as large as the volume of the bubbles. The outcome of heating by streaming only is that the cosmic rays form a larger bubble filled with very hot thermal gas. Therefore, there is a requirement for a more efficient process to transfer the internal energy of the bubbles to the ICM. I suggest that this process is heating by mixing that operates very well for both cosmic rays and the very hot thermal gas inside the bubbles. This leaves mixing-heating to be the dominant heating process of cooling flows.