A re-examination of mass-luminosity relations from binary-star data

The empirical stellar mass-luminosity relationship has been investigated with the help of a recent careful compilation of binary-star data which includes estimates of errors in mass and luminosity measurements. Several different statistical methods of fitting straight-line relationships to logarithmic plots of the data have been used. One of these, standard least-squares, is well known. For comparison, the generalized least-squares method, which takes into account the instrumental errors on both abscissa and ordinate, and a robust nonparametric method due to Theil (1950) have been applied. Parameters of the best-fit lines produced by the three methods agree within the calculated statistical errors. Goddness-of-fit has been assessed using the Chi-squared test. The data can be fitted in a statistically satisfactory manner by three straight-line segments which indicate a flattening of the slope of the empirical mass-luminosity relation at the extremes of the mass range, in agreement with the conclusions of previous investigations. An alternative sinusoidal fit of slightly lower accuracy is also given for the region of interest. The result is compared with recent theoretical predictions.