## 2. Test problemsIn order to test Monte Carlo codes, it is necessary to apply them first to special cases where simplifying assumptions have allowed exact or highly accurate solutions to be derived with conventional analytic or numerical techniques. Here, where the aim is to derive the temperature distribution throughout a medium in radiative equilibrium, the simplest test cases are provided by the theory of grey stellar atmospheres. In this case, the exact solution is known for plane-parallel geometry (the Hopf function) and accurate numerical solutions are available for spherical, extended atmospheres. Although results for grey atmospheres will be briefly reported,
they are essentially trivial in the present context, in that they do
not test our ability to improve solutions iteratively in the presence
of Monte Carlo noise. Accordingly, a more meaningful and challenging
test problem has been sought from the extensive literature on
The chosen problem is that considered by Castor (1974). Motivated
by evidence that the continuum-forming layers in the Of star
Puppis and in a number of
Wolf-Rayet stars are extended, he created In view of its closely similar scientific motivation, Castor's work provided a natural test problem for testing Monte Carlo techniques that would allow the Abbott-Lucy code to include continuum formation in model winds for hot stars. However, because of this aim, an acceptable technique should not merely reproduce Castor's results, it must also permit the treatment of line transfer - fundamental to the dynamics of the winds - and allow radiative equilibrium to be imposed in the matter frame rather than the rest frame (Lucy & Abbott 1993). The technique described below meets these conditions as well as not being restricted to 1-D geometry. In Castor's work, both the density and the temperature
stratification were computed. However, given our present understanding
of the © European Southern Observatory (ESO) 1999 Online publication: March 10, 1999 |