A comprehensive Gaia DR3 study of the open cluster NGC 6134: Bayesian distances, present-day mass function, mass segregation, and structural decomposition

Open clusters are key laboratories for studying the formation and dynamical evolution of stellar populations. We present a comprehensive characterization of the intermediate-age open cluster NGC 6134 using Gaia DR3 astrometry and photometry. Adopting the 890-member Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) membership catalog, we determine the cluster distance and individual member distances with the Bayesian hierarchical code Kalkayotl under a King spatial prior, derive the fundamental parameters with the automated isochrone-fitting code ASteCA, quantify mass segregation, and decompose the projected spatial distribution into structural components. We obtain a Bayesian cluster distance of 1070.8+21.0-19.0 pc (mode and 68% credible interval), consistent with the ASteCA value (d = 1064.4 plus or minus 15.2 pc), with member distances peaking at 1071.2 plus or minus 2.5 pc. ASteCA yields[Fe/H] = 0.08 plus or minus 0.06, (t) = 9.14 plus or minus 0.01, and A V = 1.03 plus or minus 0.05 mag. The present-day mass function (PDMF) follows a broken power law with slopes Γ A = -2.10+0.10-0.10 and Γ B = 1.59+0.14-0.14 and break mass M c = 0.95+0.02-0.02 M, with a negative low-mass slope and a high-mass slope steeper than the canonical Salpeter value (Γ= 1.35), consistent with the preferential loss of the most massive stars through stellar evolution rather than with dynamical depletion. The observed mass segregation is consistent with an origin in long-term dynamical evolution. The cluster comprises a core, a diffuse halo, and a coherent plane-of-sky elongated feature that is unlikely to arise from noise based on a size-matched isotropic null test, and that lies beyond the radius at which masses are available. The observed main-sequence gap is closely linked to the cluster's binary fraction.