PAKAL: a 3D model to solve the radiative transfer equation

• Grant number: 10/07672-6
• Support Opportunities: Regular Research Grants - Publications - Scientific article
• Start date: June 01, 2010
• End date: November 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Astronomy - Stellar Astrophysics
• Principal Investigator: Caius Lucius Selhorst
• Grantee: Caius Lucius Selhorst
• Host Institution: Instituto de Pesquisa e Desenvolvimento (IP&D). Universidade do Vale do Paraíba (UNIVAP). São José dos Campos , SP, Brazil

Abstract

We present a new numerical model called "PAKAL" intended to solve the radiative transfer equation in a three dimensional (3D) geometry, using the ap- proximation for a locally plane parallel atmosphere. Pakal uses pre-calculated radial proles of density and temperature (based on hydrostatic, hydrodynamic or MHD models) to compute the emission from 3D source structures with high spacial 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 algo- rithm 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 proles, which reproduce the observations with high accuracy, giving in this way, 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 a Hydrogen-Helium gas in thermodynamic equilibrium. We also present the convergences test of the code. We computed the synthetic spectrum of the centimetric - millimetric solar emission and found bet- ter agreement with observations (up to 10^4 K at 20 GHz) than previous models reported in 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. (AU)