Nonthermal radiation from cosmic-ray modified shocks

We calculate nonthermal radiation from cosmic-ray (CR) protons and electrons accelerated at CR modified plane and spherical shocks, using time-dependent, diffusive shock acceleration (DSA) simulations that include radiative losses of CR electrons. Strong non-relativistic shocks with physical parameters relevant for young supernova remnants (SNRs) are considered in both the plane-parallel and spherically symmetric geometries, and compared at times when their dynamical and CR properties are concordant. A thermal leakage injection model and a Bohm-like diffusion coefficient are adopted. After DSA energy gains balance radiative losses, the electron spectrum at the plane shock approaches a time-asymptotic spectrum with a super-exponential cutoff above the equilibrium momentum. The postshock electron spectrum cuts off at a progressively lower momentum downstream from the shock due to the energy losses. That results in the steepening of the volume integrated electron energy spectrum by one power of the particle energy. These features evolve toward lower energies in the spherical, SNR shocks. In a CR modified shock, pion decay gamma-ray emission reveals distinct signatures of nonlinear DSA due to the concave proton momentum spectrum. Although the electron momentum spectrum has a much weaker concavity, the synchrotron spectral slope at the shock may flatten by about 0.1-0.3 between radio and X-ray bands. The slope of the volume integrated emission spectrum behaves nonlinearly around the break frequency.