Connecting Substructure in Galaxy Cluster Cores at z = 0.2 with Cluster Assembly Histories

We use semianalytic models of structure formation to interpret gravitational lensing measurements of substructure in galaxy cluster cores (R ⩽ 250 h⁻¹ kpc) at z = 0.2. The dynamic range of the lensing-based substructure fraction measurements is well matched to the theoretical predictions, both spanning f_sub ∼ 0.05–0.65. The structure formation model predicts that f_sub is correlated with cluster assembly history. We use simple fitting formulae to parameterize the predicted correlations: Δ₉₀ = τ₉₀ + α₉₀log (f_sub) and Δ₅₀ = τ₅₀ + α₅₀log (f_sub) , where Δ₉₀ and Δ₅₀ are the predicted lookback times from z = 0.2 to when each theoretical cluster had acquired 90% and 50%, respectively, of the mass it had at z = 0.2. The best-fit parameter values are α₉₀ = − 1.34 ± 0.79 Gyr , τ₉₀ = 0.31 ± 0.56 Gyr and α₅₀ = − 2.77 ± 1.66 Gyr , τ₅₀ = 0.99 ± 1.18 Gyr . Therefore, (1) observed clusters with f_sub≲ 0.1 (e.g., A383, A1835) are interpreted, on average, to have formed at z≳ 0.8 and to have suffered ≤10% mass growth since z≃ 0.4, and (2) observed clusters with f_sub≳ 0.4 (e.g., A68, A773) are interpreted as, on average, forming since z≃ 0.4 and suffering >10% mass growth in the ~500 Myr preceding z = 0.2, i.e., since z = 0.25. In summary, observational measurements of f_sub can be combined with structure formation models to estimate the age and assembly history of observed clusters. The ability to "age date" approximately clusters in this way has numerous applications to the large samples of clusters that are becoming available.