Lensing-Reconstructed Dark Matter-Intracluster Medium Coherence as a Probe of Cluster Dynamical State: Application to HSTFF, RELICS, and CLASH Clusters
We present the first application of Fourier-space coherence analysis between the lensing-reconstructed projected mass distribution and the X-ray-emitting intracluster medium to a sample of 49 observed galaxy clusters. Using publicly available HST convergence maps from the Hubble Frontier Fields, CLASH, and RELICS programs, together with Chandra X-ray imaging, we measure the scale-dependent coherence between the dark-matter-dominated surface mass density and the hot baryonic gas. We use the coherence length, l_CR, defined as the scale above which the two maps remain at least 90% coherent, as a diagnostic of cluster dynamical state. Across the sample, dynamically relaxed systems exhibit high coherence over a broad range of scales and small l_CR/r500, while disturbed and merging systems show a loss of coherence on intermediate and small scales, yielding larger l_CR/r500. The inferred coherence lengths show sensitivity to lens-model assumptions and to the heterogeneous extent of the available convergence maps. Nevertheless, the coherence signal remains physically interpretable and provides a stringent measure of dark-matter-gas alignment. Applying a conservative threshold, l_CR/r500 < 0.2, we find that only 16% of the sample is relaxed; this fraction rises to 41% for a more permissive threshold of l_CR/r500 < 0.4. Relative to previous X-ray and morphological classifications, we find a 24% disagreement, with the coherence method identifying more systems as dynamically disturbed. These results demonstrate that lensing-X-ray coherence provides a complementary, scale-resolved probe of cluster dynamical state, while highlighting the need for homogeneous, wide-field weak-lensing maps to control reconstruction and field-of-view systematics.