Abstract
I derive and discuss a simple semi-analytical model of the evolution of powerful radio galaxies which is not based on assumptions of self-similar growth, but rather implements some insights about the dynamics and energetics of these systems derived from numerical simulations, and can be applied to arbitrary pressure/density profiles of the host environment. The model can qualitatively and quantitatively reproduce the source dynamics and synchrotron light curves derived from numerical modelling. Approximate corrections for radiative and adiabatic losses allow it to predict the evolution of radio spectral index and of inverse-Compton emission both for active sources and for `remnant' sources after the jet has turned off. Code to implement the model is publicly available. Using a standard model with a light relativistic (electron-positron) jet, sub-equipartition magnetic fields, and a range of realistic group/cluster environments, I simulate populations of sources and show that the model can reproduce the range of properties of powerful radio sources as well as observed trends in the relationship between jet power and radio luminosity, and predicts their dependence on redshift and environment. I show that the distribution of source lifetimes has a significant effect on both the source length distribution and the fraction of remnant sources expected in observations, and so can in principle be constrained by observations. The remnant fraction is expected to be low even at low redshift and low observing frequency due to the rapid luminosity evolution of remnants, and to tend rapidly to zero at high redshift due to inverse-Compton losses.
Highlights
1.1 The evolution of radio sourcesA key problem in the study of radio-loud active galaxies (RLAGN) is the difficulty of inferring their dynamical state from observation
The objective of this paper is to develop a model that is conceptually simpler than that of Turner & Shabala (2015), in the sense that it solves a simpler system of equations, without losing the ability to describe the key physics, encoding the understanding developed from recent numerical simulations, and to use it with atmosphere models that are well matched to observations
The second is the so-called universal pressure profile of Arnaud et al (2010). This is derived from the observed pressure profiles of a well-studied sample of clusters, and has the great advantage that it is calibrated in terms of a single free parameter, the total mass of the system, M500 – a given M500 uniquely specifies the pressure profile
Summary
A key problem in the study of radio-loud active galaxies (RLAGN) is the difficulty of inferring their dynamical state from observation. The large-scale structures we see are dynamic, not static; the size, shape, and luminosity of the lobes of RLAGN change with time. The basic nature of radio source dynamics has been understood since at least Scheuer (1974), but is complex in detail. Let us first consider a source that starts in a spherically symmetric environment, at t = 0 and continues with a constant two-sided jet power Q (determined by the accretion system) until the jet turns off at time t = T. I denote the total source radio luminosity at some fixed observing frequency as L and the lobe length as R. At later times t < T, the growth of the lobe (dR/dt) is determined by the balance of the jet momentum flux and the internal lobe pressure, on the one hand, against the external thermal pressure and
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