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A fast, robust algorithm for the solution of the equation of state for late-type stellar atmospheres Bennett, Philip Desmond
Abstract
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.
Item Metadata
Title |
A fast, robust algorithm for the solution of the equation of state for late-type stellar atmospheres
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1983
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Description |
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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Genre | |
Type | |
Language |
eng
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Date Available |
2010-04-19
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0085777
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.