The post-gas expulsion coalescence of embedded clusters as an origin of open clusters

Abstract

The mismatch between the mass function of the Milky Way's embedded clusters (ECs) and that of open clusters (OCs) raises the question of whether each OC originates from a single EC. In this work, we explore a scenario in which OCs form as a result of post-gas expulsion coalescence of ECs within the same parental molecular cloud. We model this process using N-body simulations of ECs undergoing expansion due to gas expulsion. Our initial conditions are based on the observed spatial, kinematic, and mass distributions of ECs in three representative massive star-forming regions (MSFRs). Initially, ECs are isolated. After further expansion, interactions between ECs begin, mutually influencing their evolution. We examine this process as a function of gas expulsion timescales, spatial separations between ECs, and their relative velocities. Our results demonstrate that, within a reasonable range of these parameters, the coalescence of ECs is robust and largely insensitive to initial conditions. The mass of ECs plays a critical role in the coalescence process. More massive ECs form stable gravitational cores, which greatly facilitate coalescence and help the resulting cluster resist expansion and Galactic tidal forces. Additionally, the number of ECs also enhances coalescence. The current mass distribution of clumps in the Milky Way suggests that directly forming massive ECs is challenging. However, the coalescence of multiple low-mass ECs can account for the observed parameter space of OCs in the Milky Way.