Selecting and Modelling Remnant AGNs with Limited Spectral Coverage
  Quantifying the energetics and lifetimes of remnant radio-loud active
galactic nuclei (AGNs) is much more challenging than for active sources due to
the added complexity of accurately determining the time since the central black
hole switched off. Independent spectral modelling of remnant lobes enables the
derivation of the remnant ratio, $R_\mathrm{rem}$, (i.e. `off-time/source
age'), thus reducing this complexity back to that of active sources however,
the requirement of high-frequency ($\gtrsim5\,$GHz) coverage makes the
application of this technique over large-area radio surveys difficult. In this
work we propose a new method, which relies on the observed brightness of
backflow of Fanaroff-Riley type~II lobes, combined with the \emph{Radio AGN in
Semi-Analytic Environments} (RAiSE) code, to measure the duration of the
remnant phase. Sensitive radio observations of the remnant radio galaxy
J2253-34 are obtained to provide a robust comparison of this technique with the
canonical spectral analysis and modelling methods. We find that the remnant
lifetimes modelled by each method are consistent; spectral modelling yields
$R_\mathrm{rem} = 0.23\pm0.02$, compared to $R_\mathrm{rem} = 0.26\pm0.02$ from
our new method. We examine the viability of applying our proposed technique to
low-frequency radio surveys using mock radio source populations, and examine
whether the technique is sensitive to any intrinsic properties of radio AGNs.
Our results show that the technique can be used to robustly classify active and
remnant populations, with the most confident predictions for the remnant ratio,
and thus off-time, in the longest-lived radio sources ($>50~$Myr) and those at
higher redshifts ($z > 0.1$).
