2018MNRAS.476.2522T

Deriving the energetics of remnant and restarted active galactic nuclei (AGNs) is much more challenging than for active sources due to the complexity in accurately determining the time since the nucleus switched-off. I resolve this problem using a new approach that combines spectral ageing and dynamical models to tightly constrain the energetics and duty-cycles of dying sources. Fitting the shape of the integrated radio spectrum yields the fraction of the source age the nucleus is active; this, in addition to the flux density, source size, axis ratio, and properties of the host environment, provides a constraint on dynamical models describing the remnant radio source. This technique is used to derive the intrinsic properties of the well-studied remnant radio source B2 0924+30. This object is found to spend 50_–12⁺¹⁴ Myr in the active phase and a further 28_–5⁺⁶ Myr in the quiescent phase, have a jet kinetic power of 3.6_–1.7^+3.0×10³⁷ W, and a lobe magnetic field strength below equipartition at the 8σ level. The integrated spectra of restarted and intermittent radio sources are found to yield a 'steep-shallow' shape when the previous outburst occurred within 100 Myr. The duty-cycle of B2 0924+30 is hence constrained to be δ < 0.15 by fitting the shortest time to the previous comparable outburst that does not appreciably modify the remnant spectrum. The time-averaged feedback energy imparted by AGNs into their host galaxy environments can in this manner be quantified.