Active galactic nuclei hosting jets

Context. Three-dimensional (3D) simulations of relativistic jets are a useful tool in studying the evolution of jets and radio galaxies in detail. However, computationally demanding as they are, their use is limited to a relatively small number of representative cases. When compared to the distribution of large samples of objects in the luminosity-distance plane (i.e. the P − D plane), the most efficient approach is to use analytical or semi-analytical models that reproduce the evolution of the main parameters governing the dynamics and radio luminosity of the sources. Aims. Our aim is to build a semi-analytical model that allows us to produce mock samples of radio galaxies that can be compared with real populations and use this approach to constrain the general properties of active galaxies with jets in a cosmological context. Methods. In this work, we present a new model for the evolution of radio galaxies based on the resolution of ordinary differential equations and inspired by previous experience on numerical simulations of jets across several orders of magnitude in power and by observational evidence. Results. Our results show a remarkable agreement between the results given by the semi-analytical model and those obtained by both 2D and 3D relativistic hydrodynamics simulations of jets ranging from 1035 W to 1039 W. From the derived trajectories of powerful radio galaxies through the P − D diagram (at powers greater than 1036 W), our model agrees with typical lifetimes of galactic activity of ≤500 Myr. We also compared our results with previous model results from the literature. In a follow-up paper, we will use this model to generate mock populations of radio galaxies at low redshifts and compare them to the LoTSS sample.