A Unified Photometric–Dynamical Framework for Globular Clusters: New Structural Diagnostics and Jeans-based Consistency Tests

Abstract We present a framework that links photometric reconstruction with Jeans-based consistency checks for 18 Galactic globular clusters. We fit King, Plummer, and Nuker surface-brightness profiles, deproject the best-fitting models through an Abel inversion, reconstruct density and potential profiles, and compare the resulting mass models with Hubble Space Telescope proper-motion velocity-dispersion data. The comparison uses the radial proper-motion dispersion profile and, where available, an empirical projected-anisotropy proxy. The goal is not to build a full simultaneous dynamical model, but to test whether the photometrically preferred profiles also give plausible kinematic behaviour under a common set of assumptions. We introduce three model-based summary quantities: the Mass Gradient Index at the projected half-light reference radius, MGI R h ; the Core Binding Parameter, CBP; and the Energy Gradient Index, EGI R h . In the adopted sample, AICc selects Nuker profiles for 14 clusters and King profiles for four clusters; the Plummer model is not selected for any cluster. The Jeans comparison shows that a good surface-brightness fit does not always imply low kinematic tension. Several clusters require elevated effective mass-to-light scaling or show large Jeans-consistency residuals. We treat these cases as mass-model-tension flags, not as detections of a specific hidden component. Monte Carlo perturbations, bootstrap resampling, and smoothing and binning tests indicate that the main summary quantities are generally stable, although extended and unevenly sampled profiles require caution. The framework provides a reproducible way to screen photometric models against kinematic consistency. Calibration with mock clusters and numerical simulations will be required before the diagnostic space can be used as a quantitative physical classifier.

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