On the circularity of orbit of certain spectroscopic binaries
Abstract
Conclusions drawn from a previously employed test of the hypothesis that the orbits of certain spectroscopic binaries are circular are shown not to be justified statistically. Two approximate methods are discussed for obtaining the distribution of the statistic defined by the ratio of the weighted sums of squares of residuals for circular and elliptical orbits: the maximumlikelihood ratio test and a test described by Lucy and Sweeney (1971). The values of the statistics used in both approximate tests are presented for the spectroscopic binaries HD 204934, HR 1970, HD 90385, HD 200428, 1 Gem B, HD 43930, HD 13738, and HD 188753. The results of the two tests are found to be the same in each case, and it is concluded that a circular orbit is inconsistent with the data for HD 13738, HD 43930, HD 188753, HD 204934, and HR 1970. Elliptical orbits are confirmed for HD 13738 and HD 43930; revised orbital elements are provided for HR 1970, HR 204934, and HD 188753.
 Publication:

The Observatory
 Pub Date:
 June 1978
 Bibcode:
 1978Obs....98..122B
 Keywords:

 Binary Stars;
 Circular Orbits;
 Statistical Tests;
 Stellar Motions;
 Astronomical Spectroscopy;
 Asymptotes;
 Elliptical Orbits;
 Least Squares Method;
 Maximum Likelihood Estimates;
 Statistical Distributions;
 Astronomy