Statistics
Scientific paper
Oct 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003mnras.344.1175w&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Volume 344, Issue 4, pp. 1175-1186.
Statistics
3
Stars: Distances, Stars: Evolution, Hertzsprung-Russell (Hr) Diagram, Stars: Statistics, Globular Clusters: General, Open Clusters And Associations: General
Scientific paper
An objective process for estimation of star cluster parameters from Hertzsprung-Russell (HR) diagrams is introduced, with direct inclusion of multiple stars, a least-squares fitting criterion, and standard error estimates. No role is played by conventional isochrones. Instead the quantity compared between observation and theory is the density of points (areal ) as it varies over the diagram. With as the effective observable quantity, standard parameter adjustment theory can be brought to bear on HR diagram analysis. Here we use the method of differential corrections with a least-squares fitting criterion, but any of the many known fitting methods should be applicable to comparison of observed and theoretical distributions. Diverse numerical schemes were developed to make the overall algorithm workable, including two that improve differentiability of by rendering point distributions effectively equivalent to continuous distributions in certain respects. Statistics of distributions are handled not via Monte Carlo methods but by the Functional Statistics Algorithm (hereafter FSA), a statistical algorithm that has been developed for HR diagram fitting but should serve as an alternative to Monte Carlo in many other applications. FSA accomplishes the aims of Monte Carlo with orders of magnitude less computation. Analysis of luminosity functions is included within the HR diagram algorithm as a special case. Areal density analysis of HR diagrams is acceptably fast because we handle stellar evolution via approximation functions, whose output also is more precisely differentiable than that of a full stellar evolution program. Evolution by approximation functions is roughly a million times as fast as full evolution and has virtually no numerical noise. The algorithmic ideas that lead to objective solutions can be applied to many kinds of HR diagram analysis that are now done subjectively. The present solution program is limited by speed considerations to use of one evolution program and exploration of variations in evolutionary physics is left for future versions. The program has miscellaneous refinements, such as allowing for distributions of chemical composition and interstellar extinction, as well as inclusion of binary star evolution, but so far not all have been tried in solutions. An algorithm is described for dealing with field stars directly in terms of , but has not yet been actively implemented. A synthetic globular cluster with known properties is analysed to demonstrate parameter convergence, solution consistency and comparison with known answers.
Hurley Jarrod R.
Wilson Robert E.
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