The Fanaroff-Riley Break Revisited: Jet Power, Host Light and the Deceleration Divide

This paper addresses a single accounting question in the physics of relativistic jets: whether the luminosity dividing the two Fanaroff-Riley morphologies is a fixed radio power or a moving threshold set by the host galaxy, as a jet-deceleration picture requires. Using the published dependence of the break luminosity on host optical luminosity, evaluated across five magnitudes of host brightness, 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: break at Mminus23 = 2e+25, dynamic range = 759. Across the host range the break moves by more than two orders of magnitude in radio luminosity. 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.