Cooling+Heating Flows in Galaxy clusters: Turbulent heating, spectral
  modelling, and cooling efficiency
  The discrepancy between expected and observed cooling rates of X-ray emitting
gas has led to the {\it cooling flow problem} at the cores of clusters of
galaxies. A variety of models have been proposed to model the observed X-ray
spectra and resolve the cooling flow problem, which involves heating the cold
gas through different mechanisms. As a result, realistic models of X-ray
spectra of galaxy clusters need to involve both heating {\it and} cooling
mechanisms. In this paper, we argue that the heating time-scale is set by the
magnetohydrodynamic (MHD) turbulent viscous heating for the Intracluster
plasma, parametrised by the Shakura-Sunyaev viscosity parameter, $\alpha$.
Using a cooling+heating flow model, we show that a value of $\alpha\simeq 0.05$
(with 10\% scatter) provides improved fits to the X-ray spectra of cooling
flow, while at the same time, predicting reasonable cooling efficiency,
$\epsilon_{cool} = 0.33^{+0.63}_{-0.15}$. Our inferred values for $\alpha$
based on X-ray spectra are also in line with direct measurements of turbulent
pressure in simulations and observations of galaxy clusters. This simple
picture unifies astrophysical accretion, as a balance of MHD turbulent heating
and cooling, across more than 16 orders of magnitudes in scale, from neutron
stars to galaxy clusters.
