The Mass-Temperature Relation: Virial Scaling Tested Against the Chandra Cluster Population

This paper computes virial scaling tested against the chandra cluster population from stated published inputs, with every number produced by the deposited script. The headline results are: virial temperature of a cluster of mass 1e14 solar masses = 1.91 keV, virial temperature of a cluster of mass 3.5e14 solar masses = 4.4 keV, virial temperature of a cluster of mass 1e15 solar masses = 8.86 keV, mass whose virial temperature is 5 keV = 4.24e+14 solar masses, characteristic radius of that cluster = 1.07e+03 kpc. 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.