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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 ƒ_ (sub) ~ 0. 05–0. 65. The structure formation model predicts that ƒ_ (sub) is correlated with cluster assembly history. We use simple fitting formulae to parameterize the predicted correlations: Δ_ (90) = τ_ (90) + α_ (90) log (ƒ_ (sub) ) and Δ_ (50) = τ_ (50) + α_ (50) log (ƒ_ (sub) ), where Δ_ (90) and Δ_ (50) 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 α_ (90) = − 1. 34 ± 0. 79 Gyr, τ_ (90) = 0. 31 ± 0. 56 Gyr and α_ (50) = − 2. 77 ± 1. 66 Gyr, τ_ (50) = 0. 99 ± 1. 18 Gyr. Therefore, (1) observed clusters with ƒ_ (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 ƒ_ (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.
Smith et al. (Tue,) studied this question.