Heating of a thermally conducting stratified medium. II. A simple plane model of an atmosphre
Exact solutions of the following theroretical problem are present: A plane atmosphere is in hydrostatic equilibrium with a uniform gravity. The ideal gas law is assumed. Heat is generated everywhere at a rate proportional to the local density. The atmosphere is maintained in a steady state through cooling by thermal conduction and radiation. This problem is reducible to quadratures for a thermal conductivity which is an arbitrary, but prescribed, function of the temperature, and for a radiative loss which is expressible as the product of the density and an arbitrary, but prescribed, function of the pressure. The analysis is carried out for the case of power law thermal conductivity, and a radiative loss proportional to the square of the density and to the first power of the temperature. The radiative cooling function adopted here has the basic mathematical form for an optically thin medium. The solutions reproduce the macroscopic ordering of a hot ''corona'' separated from a ''photosphere'' by a layer of temperature minimum. The analytic solutions allow direct illustration of the interplay between steady energy transport and the requirements of hydorstatic equilibrium.
- Research Organization:
- Department of Physics and the Enrico Fermi Institute, University of Chicago
- OSTI ID:
- 6918833
- Journal Information:
- Astrophys. J.; (United States), Vol. 241:1
- Country of Publication:
- United States
- Language:
- English
Similar Records
Pressure and energy balance of the cool corona over sunspots
Neutrino and photon emission from a dense, high temperature atmosphere