A simulation-based analytic model of radio galaxies

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.

RAiSE X: searching for radio galaxies in X-ray surveys

“…The Turner et al (2018a) model assumes that the radiative losses are not taken into account selfconsistently in the evolution of the lobe pressure. Hardcastle (2018) confirms that synchrotron radiation comprises less than ten percent of the input power for typical radio galaxies (at z = 0), whilst inverse-Compton and bremsstrahlung radiation contribute even less to the energy loss during the source expansion. However, the cosmic microwave background radiation responsible for the inverse-Compton losses increases with redshift as (1 + z) 4 ; the inverse-Compton radiation can reach up to 40% of the input power in a 100 Myr source at z = 1, or all of the input power for a 10 Myr source at z = 4.…”

Numerical modelling of the lobes of radio galaxies in cluster environments – IV. Remnant radio galaxies

“…As shown by Hardcastle et al (2019), the properties of low-z radio galaxies are consistent with having a more or less uniform distribution of active times up to 1 Gyr, and a more realistic calculation of remnant fraction would require us to simulate jets that switch off over a much wider distribution of lifetimes and of jet powers than is practical in these models. Qualitatively, however, since we find a faster initial drop in the synchrotron luminosity in our simulations than is seen in analytical models, we might expect the true remnant fraction at low z to be lower than the ∼ 50 per cent of Godfrey, Morganti & Brienza (2017) or the ∼ 30 per cent calculated by Hardcastle (2018), and we suggest that a consideration of these effects would bring the models closer to the observations. Figures 10 and 11 show the decline in surface brightness for our r75-60 model in a more visual form, with Figure 10 showing the synchrotron emission maps from a time-step shortly after the jet is switched off and Figure 11 showing the same model, with the same scaling, at the end of the simulation.…”

“…These cooling processes have a significant effect on the calculated luminosities of our models (Figure 7); for a model at a redshift of z = 0.6 the luminosity has dropped by around an order of magnitude more when cooling is included, mostly due to the inverse-Compton losses. However, relative to the analytic models of Hardcastle (2018), the uncorrected synchrotron luminosity drops more rapidly once the jet is switched off. We attribute this to the effects of the returning cluster-centre gas on the dynamics, as discussed in Section 3.1, since the continued pressure-driven expansion of the remnant lobes is accounted for in the analytical models.…”

“…Results are then compared to the 3CRR flux density limit of 10 Jy and to a surface brightness limit of 300 µJy beam −1 for a 6-arcsec Gaussian restoring beam, matched to the properties of the LOFAR Two-Metre Sky Survey, LoTSS (Shimwell et al 2017(Shimwell et al , 2019. We include the effects of cooling due to synchrotron and inverse-Compton emission using the code from Hardcastle (2018), which calculates a time-dependent correction factor that is applied to our synchrotron emissivities assuming that a population of electrons in a power-law distribution is supplied at a constant rate while the jet is active, and uses the average magnetic field strength history in the lobes. These cooling processes have a significant effect on the calculated luminosities of our models (Figure 7); for a model at a redshift of z = 0.6 the luminosity has dropped by around an order of magnitude more when cooling is included, mostly due to the inverse-Compton losses.…”

Investigating the spectral age problem with powerful radio galaxies

“…We use the analytic model of (hereafter the analytic model; Hardcastle 2018), which models the evolution of a 'shocked shell' that is driven by a radio lobe in a particular environment for a particular set of radio source properties (see Hardcastle (2018) for further details of model setup, input and output parameters). The modelled dynamics of the shocked shell can be used to approximate the physical properties of the expanding lobes as a function of its dynamical age.…”