The bound fraction of young star clusters

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
e-mail: brinkmann@mpifr-bonn.mpg.de
² Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
³ Helmholz-Institut für Strahlen-und Kernphysik, Auf dem Hügel 71, 53121 Bonn, Germany
⁴ California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
⁵ Charles University in Prague, Faculty of Mathematics and Physics, Astronomical Institute, V Holešovičkách 2, 180 00 Praha 8, Czech Republic

Received: 14 July 2016
Accepted: 20 October 2016

Abstract

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 M_ecl 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 ε_SFE and gas expulsion velocity v_g.

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 M_ecl 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 ε_SFE = 0.33 in the cluster volume results in a distinct sensitivity to v_g over a wide mass range, while a variation of ε_SFE 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.