UBC Theses and Dissertations
A fast, robust algorithm for the solution of the equation of state for late-type stellar atmospheres Bennett, Philip Desmond
A fast, but accurate procedure to solve the equation of state for late-type stellar atmospheres is an essential component of a realistic model atmosphere code. This requires the determination of the chemical equilibrium of a gas containing significant amounts of perhaps one to two hundred species, over a wide range of temperature, pressure and composition. A general method of solution, based on a linearization approach, is derived first. This is accurate but has the disadvantage of requiring the solution of a linear system of equations of order N, where N is the number of elements considered in the equilibrium, for each iteration. I then show that the order of this system can be reduced to 8 by the introduction of a "fictitious" metal element, thereby tripling the solution timing without significant loss of accuracy. Both the general and economized algorithms make no assumptions as to the particular species to be considered in the equilibrium; all such information is read from a specification file at execution time. Finally, the equilibrium abundances of significant species are displayed graphically over a range of temperature, pressure and composition (C/0 ratio), with these results plotted both as a function of temperature and C/0 ratio. The importance of obtaining accurate equilibrium abundances of the various opacity sources, and the implications for model atmosphere construction are discussed.
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