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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.