How can young massive clusters reach their present-day sizes?

Context. The classic question of how young massive star clusters attain the shapes and sizes, as we find them today, is still a difficult one. Both observational and computational studies of star-forming massive molecular gas clouds suggest that massive cluster formation is primarily triggered along the small-scale (less than or similar to 0 : 3 pc) filamentary substructures within the clouds. Aims. The present study investigates the possible ways in which a filament-like, compact, massive star cluster (e ff ective radius 0.1-0.3 pc) can expand more than 10 times, still remaining massive enough (greater than or similar to 10(4) M-circle dot) to become the young massive star cluster that we observe today. Methods. To this end, model massive clusters (initially 10(4)-10(5)M(circle dot)) are evolved using Sverre Aarseth's state-of-the-art N-body code NBODY7. Apart from the accurate calculation of two-body relaxation of the constituent stars, these evolutionary models take into account stellar-evolutionary mass loss and dynamical energy injection due to massive, tight primordial binaries and stellar-remnant black holes and neutron stars. These calculations also include a solar-neighbourhood-like external tidal field. All the computed clusters expand with time, and their sizes (e ff ective radii) are compared with those observed for young massive clusters (less than or similar to 100 Myr) in the Milky Way and other nearby galaxies. Results. In this study, it is found that beginning from the above compact sizes, a star cluster cannot expand on its own, i. e., due to two-body relaxation, stellar mass loss, and dynamical heating by primordial binaries and compact stars up to the observed sizes of young massive clusters; star clusters always remain much more compact than the observed ones. Conclusions. This calls for additional mechanisms that boost the expansion of a massive cluster after its assembly. Using further N-body calculations, it is shown that a substantial residual gas expulsion with approximate to 30% star formation e ffi ciency can indeed swell the newborn embedded cluster adequately. The limitations of the present calculations and their consequences are discussed.