An archetype hydrogen atmosphere problem

Abstract

Populations for the first three bound states and the continuum of hydrogen are determined for an isothermal, hydrostatic atmosphere at 20 000 K. The atmosphere is treated as being optically thin in the Balmer and Paschen continua and illuminated by continuum radiation at these wavelengths with prescribed radiation temperatures. The atmosphere is optically thick in the 2-1, 3-1, 3-2 and c-1 transitions. Three stages of approximation are treated:

• (1) radiative detailed balance in the 2-1, 3-1 and 3-2 transitions,

• (2) radiative detailed balance in the 3-1 and 3-2 transitions, and

• (3) all transitions out of detailed balance.

The solution of this problem is non-trivial, and presents sufficient difficulty to have caused failure of at least one rather standard technique. The problem is thus a good archetype against which new methods, or new implementations of old methods may be tested.