Origin of open clusters revealed by the evolution of the <i>m</i> max– <i>M</i> ecl relation

ABSTRACT Using the Gaia DR3 open cluster catalogue, we identified the most massive star in each observed cluster. Examining the $m_{\rm max}$–$M_{\rm cluster}$ relations across different age ranges, we find that as clusters age, the relation gradually deviates from the initial $m_{\rm max}$–$M_{\rm ecl}$ relation and eventually exhibits clear age stratification. We conducted N-body simulations for both individual cluster evolution and subcluster coalescence. Four gas expulsion modes were tested for individual clusters, and two scenarios were modelled for cluster coalescence. Under all four gas expulsion modes, the evolution of the $m_{\rm max}$–$M_{\rm cluster}$ relation follows a similar trajectory, differing mainly in evolutionary speed. The coalescence simulations show comparable behaviour but align better with the observations, as both exhibit systematically lower $m_{\rm max}$–$M_{\rm cluster}$ relations than individual cluster simulations. This systematically lower observed $m_{\rm max}$–$M_{\rm cluster}$ relation suggests slower cluster mass loss and smaller masses for the most massive stars – both conditions reproduced in the coalescence simulations. Observations also show that clusters older than 5 Myr have most massive stars significantly deviating from the initial $m_{\rm max}$–$M_{\rm ecl}$ relation. From this perspective, the coalescence simulations also provide a better match to the observations. In conclusion, the evolution of the $m_{\rm max}$–$M_{\rm ecl}$ relation supports subcluster coalescence as a dominant pathway for open cluster formation, consistent with our previous work.