The Limits of Photometric Dynamics: Benchmarking Cluster Relaxation Diagnostics

Galaxy clusters are key probes of cosmology and structure formation, yet their dynamical classification traditionally relies on spectroscopic redshifts, which do not scale efficiently with survey size. As large photometric surveys such as LSST become available, photometric redshifts offer an attractive alternative, but their impact on velocity-based diagnostics remains poorly constrained. We quantify the sensitivity of two Gaussianity diagnostics—the Anderson–Darling (AD) test and Gaussian mixture modeling (Mclust)—to different photometric redshift error prescriptions. By propagating Gaussian and Student-t uncertainties through velocity distributions constructed from SDSS photometric redshifts, we assess how the choice of error model affects the recovery of cluster dynamical states established by the independent Γ morphological proxy. Using 1672 SDSS clusters with pre-existing relaxation parameters (Γ), we perform Monte Carlo resampling under Gaussian and Student-t error models, the latter used to mimic heavy-tailed uncertainties and catastrophic outliers. We also conduct a spectroscopic control experiment in which mock photometric redshifts are generated from spectroscopic measurements. Under Gaussian errors, relaxed clusters are recovered in ∼95% of realizations, whereas unrelaxed systems are detected in only ∼5%, revealing a strong bias toward relaxed classifications. Student-t errors reduce relaxed recovery to ∼60–70% and increase unrelaxed recovery to ∼30–45%, although this remains incomplete. Paired Wilcoxon tests confirm that these differences are statistically significant. This limitation has direct implications for large photometric surveys, suggesting that dynamical studies based primarily on photometric data may significantly underestimate the fraction of disturbed clusters unless supported by robust spectroscopic calibration, catastrophic-outlier mitigation, and validation with realistic survey mock catalogs.