The bound fraction of young star clusters

Context. 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. Aims. We investigate the bound fraction after gas expulsion as a function of initial cluster mass in stars Mecl and gauge the influence of primordial mass segregation, stellar evolution and the tidal field at solar distance. We also assess the impact of the star-formation efficiency εSFE and gas expulsion velocity vg. Methods. 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 Mecl usually ranging from 5 × 103M⊙ to 5 × 104M⊙. Results. The strong impact of the relation between the gas expulsion timescale and the crossing time means that clusters with the same initial core density can have very different bound fractions. The adopted εSFE = 0.33 in the cluster volume results in a distinct sensitivity to vg over a wide mass range, while a variation of εSFE 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.