Numerical studies of vertically propagating acoustic and magnetoacoustic waves in an isothermal atmosphere (III)

In this paper we investigate, numerically, the generation and propagation of acoustic and magnetoacoustic waves and their roles in the heating process of the chromosphere. The combined effects of viscosity, thermal conduction and a uniform horizontal magnetic field on an upward and a downward propagating wave in an isothermal atmosphere are considered. It is shown that when the heating mechanisms are dominated by the effects of thermal conduction. The chromosphere atmosphere can be divided into three distinct regions, low, middle and high. The middle region acts like a semitransparent transition layer and it is produced by thermal conduction and connects middle and high chromosphere. In the transition region part of the energy transmitted upward, part is dissipated and the other part is reflected downward. Moreover, viscosity creates an absorbing and reflecting layer and the magnetic field forms a totally reflecting barrier because of its dissipationless nature. When the combined effects of the viscosity and magnetic field dominated the oscillatory process, thermal conduction can be eliminated because the solution decays exponentially with attitude before the effects of thermal conduction take place. The formulation of the model leads to a system of differential equations of the velocity and temperature and it will be used for the numerical solutions, and for the analytical solutions we have a fourth order differential equation. The differential equations in both cases are linear but with exponential coefficients. Approximate and exact solutions of the mathematical model are studied, in low, middle, and high chromospheres, both numerically and analytically. The analysis of both studies is in complete agreement with previously observed and reported results and conclusions about the heating process of the chromosphere. The results of the numerical solutions are discussed in connection with the heating mechanisms of the three regions of the chromosphere. Finally, the case where the values of thermal conduction, viscosity and magnetic field are arbitrary is considered. (C) 2003 Published by Elsevier B.V.