The Cluster X-Ray Luminosity-Temperature Relation: How Far the Observed Slope Departs from Self-Similar Bremsstrahlung

This paper computes how far the observed slope departs from self-similar bremsstrahlung from stated published inputs, with every number produced by the deposited script. The headline results are: observed-relation luminosity at 2 keV = 7.69e+42 erg/s, observed-relation luminosity at 10 keV = 6.96e+44 erg/s, observed to self-similar luminosity ratio at 2 keV = 0.48, observed to self-similar luminosity ratio at 10 keV = 1.74, difference between observed and self-similar logarithmic slopes = 0.8, central electron density implied at 5 keV for a 500 kpc uniform sphere = 6.53e-04 per cm^3. 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.