Pakal: A Three-dimensional Model to Solve the Radiative Transfer Equation

Abstract: We present a new numerical model called "Pakal" intended to solve the radiative transfer equation in a three-dimensional (3D) geometry, using the approximation for a locally plane-parallel atmosphere. Pakal uses pre-calculated radial profiles of density and temperature (based on hydrostatic, hydrodynamic, or MHD models) to compute the emission from 3D source structures with high spatial resolution. Then, Pakal solves the radiative transfer equation in a set of (3D) ray paths, going from the source to the observer. Pakal uses a new algorithm to compute the radiative transfer equation by using an intelligent system consisting of three structures: a cellular automaton; an expert system; and a program coordinator. The code outputs can be either two-dimensional maps or one-dimensional profiles, which reproduce the observations with high accuracy, giving detailed physical information about the environment where the radiation was generated and/or transmitted. We present the model applied to a 3D solar radial geometry, assuming a locally plane-parallel atmosphere, and thermal free-free radio emission from hydrogen-helium gas in thermodynamic equilibrium. We also present the convergence test of the code. We computed the synthetic spectrum of the centimetric-millimetric solar emission and found better agreement with observations (up to $10^4$ K at 20 GHz) than previous models reported in the literature. The stability and convergence test show the high accuracy of the code. Finally, Pakal can improve the integration time by up to an order of magnitude compared against linear integration codes.