Eddington Luminosities and Ultraluminous X-Ray Sources: The Mass, Beaming and Super-Eddington Budgets

This paper computes the mass, beaming and super-eddington budgets from stated published inputs, with every number produced by the deposited script. The headline results are: Eddington luminosity of a 1.4 solar mass accretor = 1.76e+38 erg/s, Eddington luminosity of a 10 solar mass accretor = 1.26e+39 erg/s, minimum mass radiating 1e40 erg/s at the Eddington limit = 79.5 solar masses, beaming factor required for a 10 solar mass black hole to appear at 1e40 erg/s = 0.126, Eddington ratio of a 30 solar mass black hole radiating 1e40 erg/s = 2.65, Eddington accretion rate of a 10 solar mass black hole at ten per cent efficiency = 2.22e-07 solar masses per year. 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.