An Independent Derivation of the Oxford Jet Kinetic Luminosity Formula

Abstract

This letter presents a theoretical derivation of an estimate for a radio source jet kinetic luminosity. The expression yields jet powers that are quantitatively similar to a more sophisticated empirical relation published by the Willott, Blundell and Rawlings at Oxford. The formula allows one to estimate the jet kinetic luminosity from the measurement of the optically thin radio lobe emission in quasars and radio galaxies. Motivated by recent X-ray observation, the derivation assumes that most of the energy in the lobes is in plasma thermal energy with a negligible contribution from magnetic energy (not equipartition). The close agreement of the two independent expressions makes the veracity of these estimates seem very plausible.