Connecting Cluster Substructure in Galaxy Cluster Cores at z=0.2 With Cluster Assembly Histories
Abstract
We use semi-analytic models of structure formation to interpret gravitational lensing measurements of substructure in galaxy cluster cores (R<=250kpc/h) at z=0.2. The dynamic range of the lensing-based substructure fraction measurements is well matched to the theoretical predictions, both spanning fsub~0.05-0.65. The structure formation model predicts that fsub is correlated with cluster assembly history. We use simple fitting formulae to parameterize the predicted correlations: Delta90 = tau90 + alpha90 * log(fsub) and Delta50 = tau50 + alpha50 * log(fsub), where Delta90 and Delta50 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: alpha90 = (-1.34+/-0.79)Gyr, tau90 = (0.31+/-0.56)Gyr and alpha50 = (-2.77+/-1.66)Gyr, tau50 = (0.99+/-1.18)Gyr. Therefore (i) observed clusters with fsub<~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, (ii) observed clusters with fsub>~0.4 (e.g. A68, A773) are interpreted as, on average, forming since z~0.4 and suffering >10% mass growth in the ~500Myr 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 clusters samples that are becoming available.