Estimating a Local Source Approximation for the Ultraviolet Background Radiation in Cosmological Settings Using Lambda Iteration
After the epoch of reionization, Lyman continuum radiation permeate the universe. Immediately after reionization (redshifts $z\approx3-7$), the influence of the cosmic Ultraviolet (UV) background on the Intergalactic Medium (IGM) and the Circumgalactic Medium (CGM) is important to understand. We focus on building a 1D radiative transfer algorithm using the Accelerated Lambda Iteration scheme and the Lambda Iteration scheme to solve the time-independent radiative transfer equation. This approach captures the dynamics of radiation fields, and the convergence, accuracy, and mathematical limitations of these schemes are thoroughly tested. We then expand the algorithm to include a 4th order Runge-Kutta scheme to trace the fraction of Hydrogen atoms between the UV background and the center of a massive galaxy. In our calculations, the UV background dominates the ionization of the IGM and CGM near our example star-forming galaxy.