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

We use semi-analytic models of structure formation to interpret gravitational lensing measurements of substructure in galaxy cluster cores (R≤250h−1kpc) 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: ∆90 = τ90 +α90 log( fsub) and ∆50 = τ50 +α50 log( fsub), where ∆90 and ∆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: 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 (i) observed clusters with fsub∼< 0.1 (e.g. A 383, A 1835) 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. A 68, A 773) 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. Subject headings: gravitational lensing — cosmology:dark matter — galaxies:clusters:individual (A 68, A 209, A 267, A 383, A 773, A 963, A 1763, A 1835, A 2218, A 2219)