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, with
dynamically unrelaxed GCs showing a flat BSS distribution, and more relaxed GCs
showing 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 in creating a bimodality in the BSS distribution and determining
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 behaviour 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.
