Statistics – Computation
Scientific paper
May 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986apj...304..739j&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 304, May 15, 1986, p. 739-766.
Statistics
Computation
114
Abundance, Computational Astrophysics, Intergalactic Media, Interstellar Matter, Spectral Line Width, Spectrum Analysis, Line Spectra, Monte Carlo Method, Normal Density Functions
Scientific paper
It is shown that the combined equivalent widths for a large population of Gaussian-like interstellar line components, each with different central optical depths tau(0) and velocity dispersions b, exhibit a curve of growth (COG) which closely mimics that of a single, pure Gaussian distribution in velocity. Two parametric distributions functions for the line populations are considered: a bivariate Gaussian for tau(0) and b and a power law distribution for tau(0) combined with a Gaussian dispersion for b. First, COGs for populations having an extremely large number of nonoverlapping components are derived, and the implications are shown by focusing on the doublet-ratio analysis for a pair of lines whose f-values differ by a factor of two. The consequences of having, instead of an almost infinite number of lines, a relatively small collection of components added together for each member of a doublet are examined. The theory of how the equivalent widths grow for populations of overlapping Gaussian profiles is developed. Examples of the composite COG analysis applied to existing collections of high-resolution interstellar line data are presented.
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