Galaxy Groups and the Steepened Luminosity-Temperature Relation: The Energy Cost of Raising Gas Entropy

This paper computes the energy cost of raising gas entropy from stated published inputs, with every number produced by the deposited script. The headline results are: luminosity deficit factor of groups at 1.0 keV = 5.52, luminosity deficit factor of groups at 0.5 keV = 8.97, energy to inject 1 keV per particle into the group gas = 1.59e+60 erg, injection energy as a fraction of binding energy = 0.00371, black hole mass whose accretion at ten per cent efficiency supplies the injection = 8.88e+06 solar masses, radiative cooling time of the injected energy at the 1 keV group luminosity = 2.51e+11 years. 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.