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

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 catalogue of E. Vasiliev & H. Baumgardt (2021a). 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 (ωCen) 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.