(abridged) We use newly available empirical binary fractions for globular clusters to carry out a direct test of the binary evolution hypothesis, and of collisional channels that involve binary stars. More specifically, using the previously reported correlation between blue straggler numbers and core mass as a benchmark, we test for correlations with the number of binary stars, as well as with the rates of single-single, single-binary, and binary-binary encounters. Surprisingly, we find that the simple correlation with core mass remains by far the strongest predictor of blue straggler population size, even in our joint models. This is despite the fact that the binary fractions themselves strongly anti-correlate with core mass, just as expected in the binary evolution model. At first sight, these results do not fit neatly with either binary evolution or collisional models in their simplest forms. Arguably the simplest and most intriguing possibility to explain this unexpected result is that observational errors on the core binary fractions are larger than the true intrinsic dispersion associated with their dependence on core mass. In the context of the binary evolution model, this would explain why the combination of binary fraction and core mass is a poorer predictor of blue straggler numbers than core mass alone. It would also imply that core mass is a remarkably clean predictor of core binary fractions. This would be of considerable importance for the dynamical evolution of globular clusters, and provides an important benchmark for models attempting to understand their present-day properties.

10 pages, 9 figures, accepted for publication in MNRAS