{Twisted Poincar\'e Series and Geometric Factorization of Affine Weyl Groups

We study the relation between the alternating product of twisted Poincar'e series of parabolic subgroups of affine Weyl groups and hyperbolic stabilizers of geodesic tubes. Moreover, from such relation, we find a length-preserving factorization of affine Weyl groups of type $\tilde{A}_n$ and $\tilde{C}_n$

Re-acceleration of Nonthermal Particles at Weak Cosmological Shock Waves

We examine diffusive shock acceleration (DSA) of the pre-exisiting as well as freshly injected populations of nonthermal, cosmic-ray (CR) particles at weak cosmological shocks. Assuming simple models for thermal leakage injection and Alfv\'enic drift, we derive analytic, time-dependent solutions for the two populations of CRs accelerated in the test-particle regime. We then compare them with the results from kinetic DSA simulations for shock waves that are expected to form in intracluster media and cluster outskirts in the course of large-scale structure formation. We show that the test-particle solutions provide a good approximation for the pressure and spectrum of CRs accelerated at these weak shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number M \la 3. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The enhancement in synchrotron radiation across the shock is estimated to be about a few to several for $M \sim 1.5$ and $10^2-10^3$ for $M \sim 3$, depending on the detail model parameters. The implication of our findings for observed bright radio relics is discussed.Comment: Submitted to ApJ. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/kr.pd

Nonthermal radiation from relativistic electrons accelerated at spherically expanding shocks

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.Comment: corrected typos and figures, 12 pages, 7 figures, Accepted for publication at Journal of Korean Astronomical Societ