Jet Kinetic Luminosity from X-Ray Cavities: The Calorimetry of Radio Bubbles in Cluster Gas

This paper addresses a single accounting question in the physics of relativistic jets: how much kinetic power a jet must have supplied, averaged over a bubble's life, to inflate the cavities it is observed to have excavated in hot cluster gas. Using published cavity pressures, radii and surrounding sound speeds for five systems including Perseus, Hydra A and MS 0735, the calculation derives new bounds and budgets from standard synchrotron and special-relativistic relations, with every number produced by the deposited compute script. The headline results are: max power = 1.44e+46, min power = 1.91e+43. Perseus: 2.01e+44, Hydra A: 2.09e+44, MS 0735: 1.44e+46, Cygnus A cluster: 2.55e+44, M87 Virgo: 1.91e+43. The inferred powers range from around ten to the forty-three to above ten to the forty-five erg per second, with the largest cavity system requiring the most. The study is a computation from stated assumptions and published inputs; it is simulated, not measured, and its conclusions are stated at the precision those inputs support.