Connecting Cluster Substructure in Galaxy Cluster Cores at z=0.2 With Cluster Assembly Histories

TL;DR

This paper links gravitational lensing measurements of galaxy cluster substructure at z=0.2 with theoretical models to infer cluster formation histories and assembly timelines.

Contribution

It introduces a method to interpret lensing-based substructure fractions using structure formation models to estimate cluster ages and assembly histories.

Findings

Clusters with low substructure likely formed before z~0.8.

High substructure clusters formed since z~0.4.

Substructure fraction correlates with cluster assembly timeline.

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 f_sub~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 (i) observed clusters with f_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, (ii) 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 ~500Myr preceding z=0.2, i.e. since z=0.25. In summary, observational measurements of f_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 clusters samples that are becoming available.