Phase-space Crystallization in Galactic Globular Clusters: A Gaia-based Metric and Implications for Technosignature Searches

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Abstract
We develop a model-independent framework to quantify phase-space “crystallization,” the degree of ordered radial and kinematic substructure, in 79 Galactic globular clusters using the Gaia EDR3–based membership catalog of E. Vasiliev & H. Baumgardt. We construct a scalar crystallization index, C index , by combining a radial inhomogeneity metric ( z rad ) and a local, cluster-centric tangential-velocity metric ( z vel ) standardized against empirical nulls. The population distribution is strongly non-Gaussian: most clusters are consistent with smooth, equilibrium expectations, while a small high- C tail ( C index ≥ 2) identifies dynamically complex systems, including NGC 5139 ( ω Cen) and NGC 104 (47 Tuc). Correlation and fixed- N tests show that sample size affects detectability, but does not by itself explain all high-rank objects. Through synthetic injection tests in dynamically “quiet” control clusters, we demonstrate sensitivity to ultra-cold, shell-confined kinematic components, ruling out single-shell structures comprising more than a few to ∼10%–20% of core stars in the best-sampled control clusters. We find no evidence, within the sensitivity of the adopted diagnostics, for phase-space structures that require explanations beyond known dynamical processes. However, C index provides a useful tool for ranking clusters by dynamical extremeness, serving both as a diagnostic for internal complexity and as a quantitative metric for prioritizing follow-up dynamical or technosignature-oriented observations.

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