Are the ONC, Pleiades, and Hyades snapshots of the same embedded cluster?

Abstract: Using direct $N$-body simulations, we investigate the initial conditions and evolution of a star-forming region resembling the Orion Nebula Cluster (ONC) with the advanced \textsc{NBODY6} code. By varying the initial conditions, we aim to identify a model that closely aligns with observed parameters such as the half-mass radius, core radius, and total mass. Additionally, we examine the cluster's evolution over 800 Myr to determine whether it could reproduce the present-day properties of the Pleiades and Hyades along its evolutionary path. Under the influence of a Milky Way-like tidal field, the ONC experiences significant mass loss, primarily due to rapid gas expulsion, retaining approximately 47\% of its initial 4200 stars by about 100 Myr and only 9\% by about 700 Myr. These evolutionary stages closely match the properties of the Pleiades and Hyades, suggesting that an ONC-like cluster may have been their precursor. Additional models with varying degrees of primordial mass segregation indicate that the ONC likely had an initial half-mass radius of 0.2-0.3 pc, a total mass of 1200 - 2000 M$\odot$, and a high degree of mass segregation. Models with an initial stellar count of about $N{\text{in}} \approx 4 \times 10^3 - 5 \times 10^3$, rich in binaries and exhibiting mass segregation, show excellent agreement with observed cluster properties.