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) similar to 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: Delta(90) = tau(90) + alpha(90) log(f(sub)) and Delta(50) = tau(50) + alpha(50) log (f(sub)), where Delta(90) and Delta(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 alpha(90) = -1.34 +/- 0.79 Gyr, tau(90) = 0.31 +/- 0.56 Gyr and alpha(50) = -2.77 +/- 1.66 Gyr,tau(50) = 0.99 +/- 1.18 Gyr. Therefore, (1) observed clusters with fsub less than or similar to 0.1 (e.g., A383, A1835) are interpreted, on average, to have formed at z greater than or similar to 0.8 and to have suffered <= 10% mass growth since z similar or equal to 0.4, and (2) observed clusters with fsub greater than or similar to 0.4 (e.g., A68, A773) are interpreted as, on average, forming since z similar or equal to 0.4 and suffering > 10% mass growth in the similar to 500 Myr preceding z = 0.2, i.e., since z = 0.25. In summary, observational measurements of fsub 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.