CONNECTING SUBSTRUCTURE IN GALAXY CLUSTER CORES AT z p 0.2 WITH CLUSTER ASSEMBLY HISTORIES

We use semianalytic models of structure formation to interpret gravitational lensing measurements of substructure in galaxy cluster cores ( h 1 kpc) at . The dynamic range of the lensing-based substructure R ≤ 250 z p 0.2 fraction measurements is well matched to the theoretical predictions, both spanning . The structure f ∼ 0.05–0.65 sub formation model predicts that is correlated with cluster assembly history. We use simple fitting formulae to fsub parameterize the predicted correlations: and , where and D p t a log ( f ) D p t a log ( f ) D 90 90 90 sub 50 50 50 sub 90 are the predicted lookback times from to when each theoretical cluster had acquired 90% and 50%, D z p 0.2 50 respectively, of the mass it had at . The best-fit parameter values are , z p 0.2 a p 1.34 0.79 Gyr t p 90 90 and , . Therefore, (1) observed clusters with 0.31 0.56 Gyr a p 2.77 1.66 Gyr t p 0.99 1.18 Gyr 50 50 (e.g., A383, A1835) are interpreted, on average, to have formed at and to have suffered ≤10% f 0.1 z 0.8 sub mass growth since , and (2) observed clusters with (e.g., A68, A773) are interpreted as, on z 0.4 f 0.4 sub average, forming since and suffering 110% mass growth in the ∼500 Myr preceding , i.e., since z 0.4 z p 0.2 . In summary, observational measurements of can be combined with structure formation models to z p 0.25 fsub 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. Subject headings: cosmology: observations — cosmology: theory — galaxies: clusters: general — galaxies: clusters: individual (A68, A209, A267, A383, A773, A963, A1763, A1835, A2218, A2219) — gravitational lensing Online material: color figure