The effect of stellar helium abundance on dynamics of multiple populations in globular clusters

We incorporate a semi-analytic formula for the main-sequence lifetime of helium-rich stars in N-body simulations of multiple population globular clusters to investigate how the enriched helium stars impact the dynamics of globular clusters. We show that a globular cluster with a helium-rich concentrated population will be slightly smaller than a globular cluster with a normal-helium second generation, with the largest difference seen in the extended normal-helium population. This effect is shown both for a cluster in isolation and one in a realistic Milky Way tidal field. We show that this effect is a result of mass segregation, and the earlier loss of more massive stars in a helium-rich concentrated population due to their decreased main-sequence lifetime. The two populations will therefore become dynamically mixed at a slightly earlier time than if they have the same helium abundance. Furthermore, we find that it is possible for the helium-enriched population to become more extended than the normal-helium population if it forms with a low initial concentration or the cluster is able to evolve for a large number of relaxation times. We conclude that the dynamical effects of helium on stellar masses are modest, and that the initial concentration of the two populations and the strength of the Milky Way tidal field are more important in determining the relative radial distributions of multiple populations.