Toward a comprehensive model for feedback by active galactic nuclei: new
  insights from M87 observations by LOFAR, Fermi and H.E.S.S
  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 cocoons 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 Alfven 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.
