Unstable Modes in the Solar Hydrogen Convection Zone.

Abstract

view Abstract Citations (57) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Unstable Modes in the Solar Hydrogen Convection Zone. Böhm, Karl-Heinz Abstract For the model of the solar hydrogen convection zone suggested by Bbhm-Vitense (1958), the fundamental modes with horizontal scales in the range 500 km < (X/2) < 50000 km and their growth rates (degree of instability) have been calculated, using the linearized hydrodynamic equations and including the effects of radiative transfer. The variation of the mean temperature T0 and density Po with depth, the dependence of the other thermodynamic functions on T0 and Po for a partially ionized mixture of hydrogen and helium, and the detailed depth dependence of the opacity and its derivates have been taken into account. A detailed model of the stable photosphere and a schematic model of the lower parts of the chromosphere have been incorporated in the -Vitense model, in order to study the penetration of the convective motion into the stable part of the atmosphere. These computations may be considered as a first preparation for a later application of the non-linear convection theory of Ledoux, Schwarzschild, and Spiegel (1961) to the solar hydrogen convection zone. The conclusions from the results of the present calculations are as follows: 1. The growth rates increase approximately linearly with increasing wave number of the perturbation,i.e., much faster than in the case of a polytropic atmosphere. 2. At a scale (X/2) = 500 km, we are not yet close to the maximal rate of instability. Consequently, the "cutoff" of the unstable modes due to the radiative smoothing of temperature fluctuations must occur only at a considerable smaller (X/2). This is due to the fact that the modes are mainly driven in layers a few hundred kilometers below the photosphere, where the opacity is some orders of magnitude higher than in the photosphere. 3. Modes of a small horizontal scale are essentially restricted to a (vertically) thin layer at the top of the convection zone. 4. The overshooting of the convective motion into the stable parts of the atmosphere is larger for modes with larger values of X In the stable parts of the atmosphere the convective motion is mainly horizontal. Modes with a horizontal X larger than about 6000 km probably penetrate a few thousand kilometers into the chromosphere. Publication: The Astrophysical Journal Pub Date: April 1963 DOI: 10.1086/147565 Bibcode: 1963ApJ...137..881B full text sources ADS |