Numerical modeling of the physical mechanism of anomalous heating of the solar atmosphere

Background and Objectives: Processing and analysis of observational data on the study of physical processes occurring in the Sun's atmosphere at various stages of the activity cycle requires a systematic identification of stable components for all physical parameters related to the stationary solar atmosphere. The first attempts at numerical calculation of the structure of the stationary atmosphere gave a sharp discrepancy with direct measurements of the distribution of the physical parameters of the solar atmosphere in height. In model calculations, the temperature decreases monotonically from 5700 K at the photosphere level as the altitude increases, and the energy flow is formed due to the radiant and kinetic thermal conductivity. In the observational data from the photospheric level to heights of about 500 km the temperature decreases (in agreement with theoretical calculations), passes through the temperature minimum, but then begins to grow. At the altitude of 28 000 km, the temperature reaches 1.5$\cdot$10$^6$ K, and remains stable at this level at altitudes of the order of several radii of the Sun. So there was a problem of “abnormal warming” of the solar atmosphere . In this work the phenomenon of anomalous heating of the solar atmosphere due to the dissipation of the energy of weak shock waves generated in the upper layers of the convective zone is studied. Materials and Methods: The distributions of plasma characteristics are calculated based on the empirical model of the solar atmosphere and the convective zone of the Sun. It is shown that in the convective zone and the chromosphere of the Sun the model of single-liquid gas dynamics is used to describe the movement of gas. A system of equations for single-liquid gas dynamics is used. The model problem takes into account the effect of thermal conductivity and viscosity, which plays an important role in the formation of the resulting distribution of thermodynamic parameters of the solar atmosphere. On the basis of completely conservative difference schemes of gravitational gas dynamics the method of establishing calculated the distribution of thermodynamic parameters in height within the solar chromosphere. Results: The method of determination was used to calculate the anomalous heating during the generation of acoustic waves from the photospheric level, as well as in the upper layers of the convective zone. These calculations implement a direct test of the Schwarzschild-Birman hypothesis in the original formulation about the mechanism of excitation of acoustic waves by stochastic pulsations of convective flows near the photospheric level. Due to the influence of dissipative processes (viscosity, radiant heat conduction) the calculated distributions weakly depend on the frequency and depth of wave flow generation in the upper layers of the solar convective zone. Conclusion: The calculation results are in satisfactory agreement with the observational data. Keywords: atmosphere of the Sun, abnormal heating, shock wave, initial and boundary conditions of the problem.