Stability Analysis for Cosmic-Ray Heating of Cool Cores in Galaxy Clusters

TL;DR

This paper investigates cosmic-ray heating as a stable mechanism to prevent cooling flows in galaxy cluster cores, demonstrating through analysis and simulations that it can maintain observed profiles over cosmic timescales.

Contribution

The study provides a stability analysis of cosmic-ray heating in galaxy clusters, showing it can produce steady states consistent with observations and remain stable over billions of years.

Findings

Steady state solutions exist under certain magnetic field conditions.

Solutions are globally stable according to perturbation analysis.

Profiles remain stable over 100 Gyr, matching observations.

Abstract

We study the heating of the cool cores in galaxy clusters by cosmic-rays (CRs) accelerated by the central active galactic nuclei (AGNs). We especially focus on the stability of the heating. The CRs stream with Alfv\'en waves in the intracluster medium (ICM) and heat the ICM. First, assuming that the heating and radiative cooling is balanced, we search steady state solutions for the ICM and CR profiles of clusters by solving a boundary value problem. The boundary conditions are set so that the solutions are consistent with observations of clusters. We find steady state solutions if the magnetic fields are strong enough and the association between the magnetic fields and the ICM is relatively weak. Then, we analyse the stability of the solutions via a Lagrangian perturbation analysis and find that the solutions are globally stable. We confirm the results by numerical simulations. Using the steady state solutions as the initial conditions, we follow the evolution of the profiles for 100 Gyr. We find that the profiles do not evolve on time scales much larger than cluster lifetimes. These results, as well as consistency with observations of radio mini-halos, suggest that the CR heating is a promising mechanism to solve the so-called "cooling flow problem".