The Iron Mass of the Intracluster Medium: Counting Supernovae from an X-Ray Abundance

This paper computes counting supernovae from an x-ray abundance from stated published inputs, with every number produced by the deposited script. The headline results are: iron mass in the cluster gas within r500 = 2.98e+10 solar masses, Type Ia supernovae supplying seventy per cent of the iron = 2.98e+10 supernovae, core-collapse supernovae supplying thirty per cent of the iron = 1.28e+11 supernovae, mean Type Ia rate over ten billion years = 2.98 per year, iron mass in a group with gas mass 5e11 solar masses at 0.2 solar abundance = 1.24e+08 solar masses, combined kinetic energy of the cluster Type Ia population = 2.98e+61 erg. 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.