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Monte Carlo simulations of multiple populations in globular clusters: constraints on the cooling flow vs. 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 onto the proto-stellar disks of a fraction of low-mass stars. For this purpose, Monte Carlo simulations containing from $10^{5}$ up to $3\cdot 10^{6}$ particles have been run including the effect of stellar evolution, binary interactions, external tidal field and a detailed modelling of the proto-stellar disk structure. The early accretion of gas onto proto-stellar disks is unable to produce discrete populations and to alter the chemical composition of a significant ($>10\%$) fraction of stars unless a disk lifetime larger ($t_{disk}\sim20~Myr$) than that predicted by models is assumed. Moreover, in this scenario the mixing timescale 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.