Beta-Model Density Profiles of Cluster Gas: Gas Mass, Central Density and the Distance to Any Density Bound

This paper computes gas mass, central density and the distance to any density bound from stated published inputs, with every number produced by the deposited script. The headline results are: coolcore electron density at 100 kpc = 0.0132 per cm^3, typical gas mass within 1 Mpc = 6.43e+13 solar masses, typical bolometric luminosity within 1 Mpc = 1.56e+45 erg/s, merger electron density at 500 kpc = 0.0012 per cm^3, typical central mass density as a fraction of the density bound = 2.01e-81. 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.