  (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.
