Numerical Approaches Towards the Galactic Synchrotron Emission

The Galactic synchrotron emission contains abundant physics of the magnetized Galactic interstellar medium and has a non-negligible influence on detecting the B-mode polarization of the Cosmic microwave background radiation and understanding the physics during the re-ionization epoch. To catch up with the growing precision in astrophysical measurements, we need not only better theoretical modelings, but also more powerful numerical simulations and analyzing pipelines for acquiring deeper understandings in both the Galactic environment and the origin of the Universe. In this dissertation, we focus on the Galactic synchrotron emission which involves the turbulent and magnetized interstellar medium and energetic cosmic-ray electrons. To study the Galactic synchrotron emission consistently we need a non-trivial Bayesian analyzer with specially designed likelihood function, a fast and precise radiative transfer simulator, and cosmic ray electron propagation solver. We first present version X of the hammurabi package, the HEALPix-based numeric simulator for Galactic polarized emission. Two fast methods are proposed for realizing divergence-free Gaussian random magnetic fields either on the Galactic scale where a field alignment and strength modulation are imposed or on a local scale where more physically motivated models like a parameterized magneto-hydrodynamic turbulence can be applied. Secondly, we present our effort in using the finite element method for solving the cosmic ray (electron) transport equation within the phase-space domain that has a number of dimensions varying from two to six. The numeric package BIFET is developed on top of the deal.ii library with support in the adaptive mesh refinement. Our first aim with BIFET is to build the basic framework that can support a high dimensional PDE solving. Finally, we introduce the work related to the complete design of IMAGINE, which is proposed particularly with the ensemble likelihood for inferring the distributions of Galactic components.