On the population of remnant FRII radio galaxies and implications for radio source dynamics

The purpose of this work is two-fold: (1) to quantify the occurrence of ultra-steep spectrum remnant FRII radio galaxies in a 74 MHz flux limited sample, and (2) perform Monte-Carlo simulations of the population of active and remnant FRII radio galaxies to confront models of remnant lobe evolution, and provide guidance for further investigation of remnant radio galaxies. We find that fewer than 2$\%$ of FRII radio galaxies with S$_{ \rm74~MHz} > 1.5$ Jy are candidate ultra-steep spectrum remnants, where we define ultra-steep spectrum as $\alpha_{\rm 74~MHz}^{\rm 1400~MHz} > 1.2$. Our Monte-Carlo simulations demonstrate that models involving Sedov-like expansion in the remnant phase, resulting in rapid adiabatic energy losses, are consistent with this upper limit, and predict the existence of nearly twice as many remnants with normal (not ultra-steep) spectra in the observed frequency range as there are ultra-steep spectrum remnants. This model also predicts an ultra-steep remnant fraction approaching 10$\%$ at redshifts $z < 0.5$. Importantly, this model implies the lobes remain over-pressured with respect to the ambient medium well after their active lifetime, in contrast with existing observational evidence that many FRII radio galaxy lobes reach pressure equilibrium with the external medium whilst still in the active phase. The predicted age distribution of remnants is a steeply decreasing function of age. In other words young remnants are expected to be much more common than old remnants in flux limited samples. For this reason, incorporating higher frequency data $\gtrsim 5$ GHz will be of great benefit to future studies of the remnant population.