Determination of the Physical Parameters of Binary Systems: A Statistical Approach
Source: Astrophysics and Space Science, Volume 260, Number 4, 1998 , pp. 469-491(23)
Abstract:A statistical analysis of the solutions of binary systems from light and radial velocity curves is a very critical task, but necessary for labeling the parameters characterizing the solutions with suitable uncertainties in connection with the precision of the observations and the quality of the model used for the description of the systems. For this task, we introduced the χ^2 test for variance, that is probably the best technique for statistical analysis of solutions, which has the not negligible advantage that it can be easily integrated in procedures like the Wilson-Price code. This procedure, developed by our group for the solution of eclipsing binary systems, is mainly based on the Wilson code (1992) for light curves and radial velocity curves synthesis and on the Price algorithm for the optimization of the solution. Within this context, we give first an heuristic proof of the convergence of the Price algorithm and then we discuss a general statistical approach to the solution of binary systems in order to establish the level of significance of the solutions together with a statistical estimate of the errors on the parameters. For the latter task, we used the Wilson code to generate the synthetic light and radial velocity curves of tens of systems (contact systems, semi-detached systems and detached systems), added with different levels of gaussian noise in agreement with the precision of modern photoelectric and spectroscopic observations. In this paper, we report the results of seven test cases, three contact systems, three semi-detached systems and one detached system, discussing the most relevant and general results obtained. We also show that the analysis of systems with and without radial velocity curves exhibits a good agreement, within the estimated errors, for the mass-ratios of all the statistically meaningful solutions.
Document Type: Regular Paper
Affiliations: 1: Istituto Nazionale di Fisica Nucleare, sez. Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, I-80126 Napoli, Italia 2: Universitádi Napoli `Federico II', Dipartimento di Scienze Fisiche, Complesso Universitario di Monte S. Angelo, Via Cinthia, I-80126 Napoli, Italia 3: Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza
Publication date: January 1, 1998