Scale-free fragmentation models for binary star formation: Observational implications

I set out the statistical properties of binaries formed through a scale-free fragmentation scenario, in which binaries result from the splitting into two of noninteracting, Jeans-unstable clumps with a range of masses. The predictions of such a scenario are contrasted with those of 'capture' models, in which dynamical interactions involving more than two stars are important in binary formation. It is found that the binary pairing statistics for a range of primary masses should provide clear diagnostics of the mode of binary formation involved. The particular predictions of scale-free fragmentation models are that both the mass ratio distribution and the total binary fraction are only weakly dependent on primary mass. 'Capture' models, by contrast, predict a companion mass distribution that is invariant with primary mass, and a binary fraction increasing strongly with primary mass. It is also shown that scale-free fragmentation models can give rise to apparent random pairing only if the initial mass function (IMF) is a power law.