Cooling Times in Cluster Cores: Where Radiative Losses Outrun the Age of the Universe

This paper computes where radiative losses outrun the age of the universe from stated published inputs, with every number produced by the deposited script. The headline results are: cooling time at n=0.05 per cm^3 and 4 keV = 9.37e+08 years, cooling time at n=0.01 per cm^3 and 6 keV = 6.16e+09 years, cooling radius where the cooling time equals 7.7 Gyr = 150 kpc, classical mass deposition rate inside the cooling radius = 577 solar masses per year, cooling time of the typical core as a fraction of the Hubble time = 0.447. The calculation is a computation from standard plasma and gravitation physics applied to values reported by Chandra, XMM-Newton and eROSITA studies; it is simulated and computed, not measured. The inputs, the formulae and the sensitivity of each result to its assumptions are stated in full, so that the arithmetic can be checked, rerun with different inputs, and used as a reference for the systems concerned.