2025MNRAS.537..343Q

The energy coupling efficiency of active galactic nucleus (AGN) outbursts is known to vary significantly with factors including the jet kinetic power, duration of the outburst, and properties of the host galaxy group or cluster. As such, constraints on their jet power and lifetime functions are crucial to quantify the role of kinetic-mode AGN feedback on the evolution of galaxies since $z \sim 1$. In this work, we address this issue by measuring the energetics of a sample of 79 low-redshift (0.02 $\lt z \lt $ 0.2) remnant radio galaxies compiled from large-sky radio surveys - remnants uniquely probe the full duration of an AGN outburst. The jet kinetic power and outburst duration of each remnant are determined using the RAISE dynamical model based on the surface brightness distribution observed in multifrequency radio images. We compare the energetics constrained for this sample to those predicted for mock radio source populations - with various intrinsic functions for jet power and lifetime distributions - to correct for sample selection biases imposed on our sample. The intrinsic jet power and lifetime functions that yield a selection-biased mock population most similar to our observed sample are determined using Bayesian inference. Our analysis places robust constraints on assumed power-law indices for the intrinsic jet power and lifetime functions: $p(Q)\propto Q^{-1.49\pm 0.07}$ and $p(t_{\mathrm{on}})\propto t_{\mathrm{on}}^{-0.97\pm 0.12}$, respectively. We discuss the implications of these findings for feedback-regulated accretion and the self-regulating nature of jet activity. The methodology proposed in this work can be extended to active radio galaxies in future studies.