Cosmic Rays or Turbulence can Suppress Cooling Flows (Where Thermal
  Heating or Momentum Injection Fail)
  The quenching `maintenance' and `cooling flow' problems are important from
the Milky Way through massive cluster elliptical galaxies. Previous work has
shown that some source of energy beyond that from stars and pure
magnetohydrodynamic processes is required, perhaps from AGN, but even the
qualitative form of this energetic input remains uncertain. Different scenarios
include thermal `heating,' direct wind or momentum injection, cosmic ray
heating or pressure support, or turbulent `stirring' of the intra-cluster
medium (ICM). We investigate these in $10^{12}-10^{14}\,{\rm M}_{\odot}$ halos
using high-resolution non-cosmological simulations with the FIRE-2 (Feedback In
Realistic Environments) stellar feedback model, including simplified toy
energy-injection models, where we arbitrarily vary the strength, injection
scale, and physical form of the energy. We explore which scenarios can quench
without violating observational constraints on energetics or ICM gas. We show
that turbulent stirring in the central $\sim100\,$kpc, or cosmic-ray injection,
can both maintain a stable low-SFR halo for $>$Gyr timescales with modest
energy input, by providing a non-thermal pressure which stably lowers the core
density and cooling rates. In both cases, associated thermal-heating processes
are negligible. Turbulent stirring preserves cool-core features while mixing
condensed core gas into the hotter halo and is by far the most energy efficient
model. Pure thermal heating or nuclear isotropic momentum injection require
vastly larger energy, are less efficient in lower-mass halos, easily over-heat
cores, and require fine-tuning to avoid driving unphysical temperature
gradients or gas expulsion from the halo center.
