The insignificance of "heating flows" in "cooling flow" clusters of galaxies

We consider the possibility that so-called "cooling flow" clusters are really "heating flow" clusters, in which cold gas clouds evaporate in the hot intracluster medium. Saturated evaporation is treated following the work of Cowie & McKee. We estimate the total X-ray luminosity to be ∼2.2 × 10³⁸(Ṁ_evap/1 M_⊙ yr^-1) ergs s^-1, where Ṁ_evap is the total evaporation rate. This is ∼ 10,000 times smaller than the X-ray luminosity of material that is cooling at the same rate. We also compute the X-ray line emissivity for evaporating clouds. Because the time scale for an atom to move from the cold cloud to the hot surrounding medium is much shorter than the ionization time scale for ions of interest, our computation uses a nonequilibrium ionization code. Again, we find that the effective line emissivities of evaporating clouds are ∼ 1000 times smaller than for cooling clouds. More specific comparisons are made using measured line fluxes for M87 and the Perseus cluster, for which we derive evaporation rates of ∼10⁴ and ∼10⁶ M_⊙ yr^-1, respectively. We conclude that evaporative heating flow models require mass fluxes many orders of magnitude higher than cooling flow models to explain the same X-ray emission. This requirement greatly exceeds any plausible mass source by similar factors. We show that these conclusions are very general and serve to reject all heating flow models as viable alternatives to cooling flows.