Deep-Field Source Counts: The Log N-Log S Relation and the Resolved Fraction of the Background

This paper computes the log n-log s relation and the resolved fraction of the background from stated published inputs, with every number produced by the deposited script. The headline results are: cumulative source count above flux 1e-15 erg/cm^2/s = 1.7e+03 per deg^2, cumulative source count above flux 1e-16 erg/cm^2/s = 1.20e+04 per deg^2, fraction of the background resolved by the counts integral = 0.814, whole-sky source count above 1e-15 erg/cm^2/s = 7.01e+07 sources, flux above which half of the resolved intensity originates = 1.18e-14 erg/cm^2/s. 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.