Dynamical Evolution and the Missing Mass Problem in 44 Galactic Open Clusters: Machine Learning Membership and Maximum Likelihood Kinematics using Gaia DR3

We present a dynamical analysis of 44 Galactic open clusters to investigate the impact of observational limits and the Galactic environment on their virial states. Utilizing Gaia DR3 data, we isolate high-purity cluster members via a robust hybrid approach combining spatial-kinematic density-based clustering, a Gaussian Mixture Model, and photometric filtering. To address the radial velocity incompleteness for faint stars, we derive the intrinsic kinetic energy using high-precision tangential velocities in the cluster rest frame, assuming kinematic isotropy. To mitigate kinematic inflation driven by astrometric noise, we employ a maximum likelihood estimation technique that deconvolves instrumental uncertainties from the true intrinsic velocity dispersion. The gravitational potential energy is computed via direct N -body summation, explicitly projecting stars into 3D Cartesian coordinates using individual stellar parallaxes. Our results reveal a stark physical dichotomy: dynamically stable clusters exhibit expected virial states, whereas heavily truncated clusters display unphysically inflated apparent virial ratios ( Q obs ≫ 1). We empirically demonstrate through deep photometric completeness analysis across a diverse benchmark sample spanning different evolutionary stages that these extreme ratios are observational artifacts driven by the “missing mass” of unobserved low-mass stars (e.g., M-dwarfs), rather than genuine signatures of rapid tidal disruption. By applying a virial scaling relation, we reconstruct the intrinsic total dynamical mass for clusters severely affected by instrumental truncation.