Exploring the consequences of pairing algorithms for binary stars

¹ Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, Sheffield, UK e-mail: [t.kouwenhoven;s.goodwin]@sheffield.ac.uk
² Astronomical Institute “Anton Pannekoek”, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands e-mail: l.kaper@uva.nl
³ Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The Netherlands e-mail: brown@strw.leidenuniv.nl
⁴ Section Computer Science, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands e-mail: s.f.portegieszwart@uva.nl

Received: 21 May 2008
Accepted: 20 November 2008

Abstract

Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments. Binarity is also a key ingredient in stellar population studies, and is a prerequisite for calibrating the binary evolution channels. In this paper we present an overview of several commonly used methods of pairing individual stars into binary systems, which we refer to as pairing functions. These pairing functions are frequently used by observers and computational astronomers, either for their mathematical convenience or because they roughly describe the expected outcome of the star forming process. We discuss the consequences of each pairing function for interpreting observations and numerical simulations. The binary fraction and mass ratio distribution generally depend strongly on the selection of the range in primary spectral type in a sample. The mass ratio distribution and binary fraction derived from a binarity survey among a mass-limited sample of targets is thus not representative of the population as a whole. Neither theory nor observations indicate that random pairing of binary components from the mass distribution, the simplest pairing function, is realistic. It is more likely that companion stars are formed in a disc around a star or that a pre-binary core fragments into two binary components. The results of our analysis are important for (i) the interpretation of the observed mass ratio distribution and binary fraction for a sample of stars; (ii) a range of possible initial condition algorithms for star cluster simulations; and (iii) how to distinguish between the different star formation scenarios.