Monte Carlo simulations of multiple populations in globular clusters:
  constraints on the initial size of the second generation from binary stars
  We present the result of a survey of Monte Carlo simulations of globular
clusters hosting two generations of stars including a large (f_b=50%) fraction
of primordial binaries in both populations. The dynamical evolution of the two
stellar populations is followed for a Hubble time taking into account the
effect of the tidal field, two-body relaxation, stellar evolution and
three/four-bodies interactions. The fraction of surviving binaries, once
accounted for the observational bias and uncertainties, is compared with the
available radial velocity time-series performed in real globular clusters, and
it is used to constrain the initial spatial concentration of the second
generation. The fraction of second generation binaries appears to depend only
on the ratio between the total cluster mass and the initial size of the second
generation which determines the average velocity dispersion across the extent
of this stellar population. In spite of the various uncertainties, we find that
the observed fraction can be obtained only assuming a strong initial
concentration of the second generation (r_h,S~ 0.1 (M/10^6 M_s) pc). The
evolution of the first generation binary fraction is more sensitive to the
tidal field strength (with a non negligible effect of the cluster orbital
eccentricity) since the tidal field has a direct impact on the first generation
structural properties.
