Cluster Counts in the eROSITA All-Sky Survey: Integrating the Luminosity Function Over the Sky

This paper computes integrating the luminosity function over the sky from stated published inputs, with every number produced by the deposited script. The headline results are: comoving volume to redshift 0.5 over the extragalactic sky = 1.85e+10 Mpc^3, expected clusters above that luminosity within redshift 0.5 = 1.77e+05 clusters, expected clusters above that luminosity within redshift 0.5 = 1.57e+04 clusters, luminosity corresponding to flux 1e-13 at redshift 0.3 = 2.88e+43 erg/s, luminosity corresponding to flux 1e-13 at redshift 0.5 = 9.60e+43 erg/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.