Study of the mass-ratio distribution of spectroscopic binaries – I. A novel algorithm

• Published in: Monthly notices of the Royal Astronomical Society 2017-12, Vol.472 (4), p.4497-4507
• Main Authors: Shahaf, S., Mazeh, T., Faigler, S.
• Format: Article
• Language: English
• Subjects: Algorithms; Computer simulation; Markov chains; Mass ratios; Mathematical analysis; Monte Carlo simulation; Parameters
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stx2257

Abstract We have developed a novel direct algorithm to derive the mass-ratio distribution (MRD) of short-period binaries from an observed sample of single-lined spectroscopic binaries (SB1s). The algorithm considers a class of parametrized MRDs and finds the set of parameters that best fits the observed sample. The algorithm consists of four parts. First, we define a new observable, the modified mass function, that can be calculated for each binary in the sample. We show that the distribution of the modified mass function follows the shape of the underlying MRD, making it more advantageous than the previously used mass function, reduced mass function or reduced mass function logarithm. Second, we derive the likelihood of the sample of modified mass functions to be observed given an assumed MRD. A Markov chain Monte Carlo search enables the algorithm to find the parameters that best fit the observations. Third, we propose that the unknown MRD is expressed by a linear combination of a basis of functions that spans the possible MRDs, and we suggest two such bases. Fourth, we show how to account for the undetected systems that have a radial-velocity amplitude below a certain threshold. Without the correction, this observational bias suppresses the derived MRD for low mass ratios. Numerous simulations show that the algorithm works well with either of the two suggested bases. The four parts of the algorithm are independent, but the combination of these four parts makes the algorithm highly effective at deriving the MRD of the binary population.