Spectral Ageing in Radio Lobes: An Upper Bound on Source Age from the Break Frequency

This paper addresses a single accounting question in the physics of relativistic jets: how old a radio lobe can be, at most, before synchrotron and inverse-Compton losses move its spectral break below the frequency where a break is observed. Using published break frequencies and field estimates for five lobes, with redshifts for the microwave-background loss term, 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 age Myr = 157. Cygnus A: 6.56, 3C 223: 59.8, 3C 265: 13.5, Fornax A: 157, Hercules A: 12.9. The ages fall in the range of a few million to a few tens of millions of years. 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.