Monte Carlo simulations of multiple populations in globular clusters: constraints on the cooling flow versus accretion scenario using million bodies simulations

I simulate the evolution of a stellar system hosting two stellar populations whose initial set-up is defined according to the two main scenarios proposed for the origin of multiple populations in Galactic globular clusters: (i) formation of a second generation from a cooling flow of pristine+polluted gas and (ii) accretion of polluted gas on to the proto-stellar discs of a fraction of low-mass stars. For this purpose, Monte Carlo simulations containing from 10⁵ up to 3 × 10⁶ particles have been run including the effect of stellar evolution, binary interactions, external tidal field, and a detailed modelling of the proto-stellar disc structure. The early accretion of gas on to proto-stellar discs is unable to produce discrete populations and to alter the chemical composition of a significant ( $\gt 10{{\ \rm per\ cent}}$ ) fraction of stars unless a disc lifetime larger (t_disc ∼ 20 Myr) than that predicted by models is assumed. Moreover, in this scenario the mixing time-scale of the two populations is too short to reproduce the observed segregation of the chemically enriched population. On the other hand, simulations run within the cooling flow scenario can evolve after a Hubble time into stellar systems with a first-to-second population mass ratio similar to that observed in globular clusters, provided that an initial filling-factor r_h/r_J > 0.15 is adopted. However, in the weak tidal field regime a radial segregation of the second population stronger than what observed in Milky Way globular clusters at large Galactocentric distances is predicted. This discrepancy disappears in simulations following eccentric orbits in a realistic axisymmetric potential.