The fraction of globular cluster second-generation stars in the Galactic halo

Many observational studies have revealed the presence of multiple stellar generations in Galactic globular clusters. These studies suggest that second-generation stars make up a significant fraction of the current mass of globular clusters, with the second-generation mass fraction ranging from ~50 to 80 per cent in individual clusters. In this Letter we carry out hydrodynamical simulations to explore the dependence of the mass of second-generation stars on the initial mass and structural parameters and stellar initial mass function (IMF) of the parent cluster. We then use the results of these simulations to estimate the fraction, f_{SG,H}, of the mass of the Galactic stellar halo composed of second-generation stars that originated in globular clusters. We study the dependence of f_{SG,H} on the parameters of the initial mass function of the Galactic globular cluster system. For a broad range of initial conditions, we find that the fraction of mass of the Galactic stellar halo in second-generation stars is always small, f_{SG,H}<4-6 per cent for a Kroupa-1993 IMF and f_{SG,H}<7-9 per cent for a Kroupa-2001 IMF.