We study the evolution of the energy spectrum of cosmic-ray electrons accelerated at spherically expanding shocks with low Mach numbers and the ensuing spectral signatures imprinted in radio synchrotron emission. Time-dependent simulations of diffusive shock acceleration (DSA) of electrons in the test-particle limit have been performed for spherical shocks with parameters relevant for typical shocks in the intracluster medium. The electron and radiation spectra at the shock location can be described properly by the test-particle DSA predictions with instantaneous shock parameters. However, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws, because the shock compression ratio and the flux of injected electrons at the shock gradually decrease as the shock slows down in time. So one needs to be cautious about interpreting observed radio spectra of evolving shocks based on simple DSA models in the test-particle regime.

We present results from an extensive synthetic observation analysis of numerically-simulated radio galaxy (RG) jets. This analysis is based on the first three-dimensional simulations to treat cosmic ray acceleration and transport self-consistently within a magnetohydrodynamical calculation. We use standard observational techniques to calculate both minimum-energy and inverse-Compton field values for our simulated objects. The latter technique provides meaningful information about the field. Minimum-energy calculations retrieve reasonable field estimates in regions physically close to the minimum-energy partitioning, though the technique is highly susceptible to deviations from the underlying assumptions. We also study the reliability of published rotation measure analysis techniques. We find that gradient alignment statistics accurately reflect the physical situation, and can uncover otherwise hidden information about the source. Furthermore, correlations between rotation measure (RM) and position angle (PA) can be significant even when the RM is completely dominated by an external cluster medium.

Most of high energy cosmic rays (CRs) are thought to be produced by diffusive shock acceleration (DSA) at supernova remnants (SNRs) within the Galaxy. Fortunately, nonthermal emissions from CR protons and electrons can provide direct observational evidence for such a model and place strong constraints on the complex nonlinear plasma processes in DSA theory. In this study we calculate the energy spectra of CR protons and electrons in Type Ia SNRs, using time-dependent DSA simulations that incorporate phenomenological models for some wave-particle interactions. We demonstrate that the timedependent evolution of the self-amplified magnetic fields, Alfvénic drift, and escape of the highest energy particles affect the energy spectra of accelerated protons and electrons, and so resulting nonthermal radiation spectrum. Especially, the spectral cutoffs in X-ray and γ-ray emission spectra are regulated by the evolution of the highest energy particles, which are injected at the early phase of SNRs. Thus detailed understandings of nonlinear wave-particle interactions and time-dependent DSA simulations of SNRs are crucial in testing the SNR hypothesis for the origin of Galactic cosmic rays.