An Analytic Model for Blue Straggler Formation in Globular Clusters

We present an analytic model for blue straggler formation in globular clusters. We assume that blue stragglers are formed only through stellar collisions and binary star evolution, and compare our predictions to observed blue straggler numbers taken from the catalogue of Leigh, Sills & Knigge (2011). We can summarize our key results as follows: (1) Binary star evolution consistently dominates blue straggler production in all our best-fitting models. (2) In order to account for the observed sub-linear dependence of blue straggler numbers on the core masses (Knigge, Leigh & Sills 2009), the core binary fraction must be inversely proportional to the total cluster luminosity and should always exceed at least a few percent. (3) In at least some clusters, blue straggler formation must be enhanced by dynamical encounters (either via direct collisions or by stimulating mass-transfer to occur by altering the distribution of binary orbital parameters) relative to what is expected by assuming a simple population of binaries evolving in isolation. (4) The agreement between the predictions of our model and the observations can be improved by including blue stragglers that form outside the core but later migrate in due to dynamical friction. (5) Longer blue straggler lifetimes are preferred in models that include blue stragglers formed outside the core since this increases the fraction that will have sufficient time to migrate in via dynamical friction.