Cooling+Heating Flows in Galaxy Clusters: Turbulent Heating, Spectral Modeling, and Cooling Efficiency

The discrepancy between expected and observed cooling rates of X-ray emitting gas has led to the 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 and cooling mechanisms. In this paper, we argue that the heating timescale is set by the magnetohydrodynamic (MHD) turbulent viscous heating for the Intracluster plasma, parameterized by the Shakura-Sunyaev viscosity parameter, α. Using a cooling+heating flow model, we show that a value of α ≃ 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, {∊ }_cool}={0.33}_-0.15^+0.63. Our inferred values for α 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.