Abstract
Aims: It is important to know the binary mass-ratio distribution to better understand the evolution of stars in binary systems and to constrain their formation. However, in most cases, that is, for single-lined spectroscopic binaries, the mass ratio cannot be measured directly, but can only be derived as the convolution of a function that depends on the mass ratio and on the unknown inclination angle of the orbit on the plane of the sky. Methods: We extend our previous method for deconvolving this inverse problem by obtaining the cumulative distribution function (CDF) for the mass-ratio distribution as an integral. Results: After a suitable transformation of variables, this problem becomes the same as the problem of rotational velocities vsini, allowing a close analytic formulation for the CDF. We here apply our method to two real datasets: a sample of Am star binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 association. Conclusions: We are able to reproduce previous results for the sample of Am stars. In addition, the mass-ratio distribution of massive stars shows an excess of systems with a low mass ratio, in contrast to what was claimed elsewhere. Our method proves to be very reliable and deconvolves the distribution from a sample in one single step.
Author
Curé, Michel; Rial, Diego F.; Cassetti, Julia; Christen, Alejandra; Boffin, Henri M. J.
Journal
Astronomy & Astrophysics
Paper Publication Date
January 2015
Paper Type
Astrostatistics