Exploring the consequences of pairing algorithms for binary stars

Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments (see, e.g., Blaauw 1991, and references therein). Binarity is also a key ingredient in stellar population studies, and is a prerequisite to calibrate the binary evolution channels. In this paper we present an overview of several commonly used methods to pair 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 the interpretation of 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 for 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 disk 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 discriminate between the different star formation scenarios.