2013ApJ...779...10P

Feedback by active galactic nuclei (AGNs) appears to be critical in balancing radiative cooling of the low-entropy gas at the centers of galaxy clusters and in mitigating the star formation of elliptical galaxies. New observations of M87 enable us to put forward a comprehensive model for the physical heating mechanism. Low-frequency radio observations by LOFAR revealed the absence of fossil cosmic-ray (CR) electrons in the radio halo surrounding M87. This puzzle can be resolved by accounting for the CR release from the radio lobes and the subsequent mixing of CRs with the dense ambient intracluster gas, which thermalizes the electrons on a timescale similar to the radio halo age of 40 Myr. Hadronic interactions of similarly injected CR protons with the ambient gas should produce an observable gamma-ray signal in accordance with the steady emission of the low state of M87 detected by Fermi and H.E.S.S. Hence, we normalize the CR population to the gamma-ray emission, which shows the same spectral slope as the CR injection spectrum probed by LOFAR, thereby supporting a common origin. We show that CRs, which stream at the Alfvén velocity with respect to the plasma rest frame, heat the surrounding thermal plasma at a rate that balances that of radiative cooling on average at each radius. However, the resulting global thermal equilibrium is locally unstable and allows for the formation of the observed cooling multi-phase medium through thermal instability. Provided that CR heating balances cooling during the emerging "cooling flow," the collapse of the majority of the gas is halted around 1 keV–in accordance with X-ray data. We show that both the existence of a temperature floor and the similar radial scaling of the heating and cooling rates are generic predictions of the CR heating model.