Monte Carlo simulation of complex spectra for opacity calculations

Physics – Atomic Physics

Scientific paper

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Algorithms, Computerized Simulation, Energy Levels, Monte Carlo Method, Opacity, Stellar Spectra, Statistical Distributions, Variations

Scientific paper

Calculating stellar opacities often involves calculating spectra containing millions of lines. Current methods for doing this are not always adequate. Exact calculations of these spectra can take too long to be practical, and the Unresolved Transition Array (UTA) approach, which assumes individual lines are not resolved, often gives very poor results. We are developing a new, Monte-Carlo approach to calculating opacities of complex spectra which is much faster than exact calculations and gives much better results than the UTA approach. The key idea is that to calculate opacities over small wavelength ranges, it is not necessary to know the correct wavelengths or strengths of individual lines. As long as certain statistical properties of the spectrum are correct, calculated opacities will be approximately right. All the atomic physics in our model is of a statistical nature; we do not calculate the real strength or energy of any lines. Specific properties which our Monte Carlo Spectra reproduce are the total strength of all lines, their mean wavelength, and their wavelength spread, as well as the statistical distribution of line strengths. We do this separately for each transition array in the spectrum. In several test cases where exact calculations are possible, our model gives Rosseland mean opacities from about three times less than to the same as the exact result. By comparison, the UTA approach gives results orders of magnitude too large. In these cases our results vary by about 10 percent from run to run due to statistical fluctuations; in cases of real interest, which involve more lines, these variations should be smaller.

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