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 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 .