2008ApJ...682L..73S

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.