Blue Straggler Bimodality: A Brownian Motion Model

The shape of the radial distribution of blue straggler stars (BSS), when normalized to a reference population of horizontal branch (HB) stars, has been found to be a powerful indicator of the dynamical evolution reached by a globular cluster (GC). In particular, observations suggest that the BSS distribution bimodality is modulated by the dynamical age of the host GC; dynamically unrelaxed GCs show a flat BSS distribution, and more relaxed GCs show a minimum at a radius that increases for increasing dynamical age, resulting in a natural "dynamical clock." While direct N-body simulations are able to reproduce the general trend, thus supporting its dynamical origin, the migration of the minimum of the distribution appears to be noisy and not well defined. Here we show that a simple unidimensional model based on dynamical friction (drift) and Brownian motion (diffusion) correctly reproduces the qualitative motion of the minimum, without adjustable parameters except for the BSS to HB stars mass ratio. Differential dynamical friction effects combine with diffusion to create a bimodality in the BSS distribution and to determine its evolution, driving the migration of the minimum to larger radii over time. The diffusion coefficient is strongly constrained by the need to reproduce the migratory behavior of the minimum, and the radial dependence of diffusion set by fundamental physical arguments automatically satisfies this constraint. Therefore, our model appears to capture the fluctuation-dissipation dynamics that underpins the dynamical clock.