Simulating electron transport and synchrotron emission in radio galaxies: Shock acceleration and synchrotron aging in axisymmetric flows

We introduce a simple and economical but effective method for including relativistic electron transport in multidimensional simulations of radio galaxies. The method is designed to follow explicitly diffusive acceleration at shocks, and, in smooth flows, second-order Fermi acceleration, plus adiabatic and synchrotron losses for electrons in the energy range responsible for radio emission in these objects. We are able to follow both the spatial and the energy (momentum) distributions of the electrons, so that direct synchrotron emission properties can be modeled in time-dependent simulated flows of this type for the first time. That feature is essential if simulations are to bridge successfully the fundamental physical gap between flow dynamics and observed emissions. As an initial step toward that goal, we present results from some axisymmetric MHD simulations of Mach 20 light jet flows. These explicitly explore the effects of shock acceleration, as well as adiabatic expansion and synchrotron aging in smooth flows. The simulations demonstrate the importance of the fact that even for steady inflows jet terminal shocks are not simple, steady plane structures. Most importantly, this should play a very major role in determining the properties of synchrotron emission within the terminal hot spot and in the lobes generated by the jet back flow. In fact, the outflows are inherently complex, because of the basic "driven" character of a jet flow. Consequently, the nonthermal electron population emerging from the jet may encounter a wide range of shock types and strengths, as well as of magnetic field environments. We may expect to find a complex range in synchrotron spectral and brightness patterns associated with terminal hot spots and lobes. These include the possibility of steep spectral gradients (of either sign) within hot spots, the potential in lobes for islands of flat-spectrum electrons within steeper spectral regions (or the reverse), and spectral gradients coming from the dynamical history of a given flow element rather than from synchrotron aging of the embedded electrons. Finally, synchrotron "aging" in the lobes tends to proceed more slowly than one would estimate from regions of high emissivity. This is a consequence of the fact that those regions are ordinarily places where the magnetic fields are the strongest, so that the instantaneous rates of energy loss are atypical of the full history of the electron population. This feature supports earlier suggestions that nonuniform field structures may help to explain why dynamical ages of FR II sources often seem to be greater than the apparent age of the electrons radiating in the lobes, as measured in terms of spectral steepening, or the absence thereof.