A Reliability-Audited Jeans Model Comparison for Galactic Globular Clusters: Constraints on Extended Non-luminous Mass Profiles

Abstract Dynamical searches for unseen mass in globular clusters (GCs) are intrinsically degenerate: radial variations in the stellar mass-to-light ratio, velocity anisotropy, dark remnants, unresolved binaries, rotation, and a central point mass can produce similar signatures in projected velocity-dispersion profiles. We present a reliability-audited spherical Jeans model comparison for 15 Galactic GCs that separates statistical model ranking from physical interpretation. We compare the nine Jeans parameterizations using three-dimensional tracer-density profiles reconstructed from the observed surface-density or surface-brightness data, together with published proper-motion and line-of-sight velocity-dispersion profiles. Nine model variants span mass-follows-light, radial mass-to-light-ratio gradients, central point-mass models, extended non-luminous mass profiles, hybrid mass-to-light-gradient plus extended non-luminous models, and variable-anisotropy variants. Model comparison uses a fixed Gaussian kinematic likelihood with identical data support across variants within each cluster, with BIC as the primary ranking statistic and AICc as a sensitivity diagnostic. The BIC census contains four mass-follows-light, six mass-to-light-gradient, three extended non-luminous, and two hybrid cases. Thus, five clusters favour a model class that includes additional extended non-luminous radial mass-profile freedom. No IMBH-containing model class is BIC-preferred. The extended non-luminous component is therefore interpreted phenomenologically rather than as a direct measurement of any unique compact-object population. More generally, the framework provides a reproducible way to identify which apparent mass-profile features survive controlled robustness tests and therefore merit follow-up with more physically self-consistent models capable of stronger compact-object attribution.

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