The bound fraction of young star clusters

Abstract

The residual gas within newly formed star clusters is expelled through stellar feedback on timescales ~ 1 Myr. The subsequent expansion of the cluster results in an unbinding of a fraction of stars before the remaining cluster members can re-virialize and form a surviving cluster. We investigate the bound fraction after gas expulsion as a function of initial cluster mass in stars and gauge the influence of primordial mass segregation, stellar evolution and the tidal field at the solar distance. We also assess the impact of the star-formation efficiency and gas expulsion velocity. We perform N-body simulations using Sverre Aarseth's NBODY7 code, starting with compact clusters in their embedded phase and approximate the gas expulsion by means of an exponentially depleting external gravitational field. We follow the process of re-virialization through detailed monitoring of different Lagrange radii over several Myr, examining initial half-mass radii of 0.1 pc, 0.3 pc and 0.5 pc and initial masses usually ranging from $5\times10^3 M_\odot$ to $5\times10^4 M_\odot$. The adopted star-formation efficiency of 0.33 in the cluster volume results in a distinct sensitivity to the gas expulsion velocity over a wide mass range, while a variation of the star-formation efficiency can make the cluster robust to the rapidly decreasing external potential. We confirm that primordial mass segregation leads to a smaller bound fraction, its influence possibly decreasing with mass. Stellar evolution has a higher impact on lower mass clusters, but heating through dynamical friction could expand the cluster to a similar extent. The examined clusters expand well within their tidal radii and would survive gas expulsion even in a strong tidal field.