Intra-cluster light as a dynamical clock for galaxy clusters: Insights from the MAGNETICUM, IllustrisTNG, Hydrangea, and Horizon-AGN simulations

Context. As the most massive nodes of the cosmic web, galaxy clusters represent the best probes of structure formation. Over time, they grow by accreting and disrupting satellite galaxies, adding those stars to the brightest cluster galaxy (BCG) and the intra-cluster light (ICL). However, the formation pathways of galaxy clusters can vary significantly. Aims. To inform upcoming large surveys, we aim to identify observables that can distinguish galaxy cluster formation pathways. Methods. Using four different hydrodynamical simulations, Magneticum, TNG100 of IllustrisTNG, Horizon-AGN, and Hydrangea, we studied how the fraction of stellar mass in the BCG and ICL (fICL + BCG) relates to the galaxy cluster mass assembly history. Results. For all simulations, fICL + BCG is the best tracer for the time at which the cluster has accumulated 50% of its mass (zform), performing better than other typical dynamical tracers, such as the subhalo mass fraction, the halo mass, and the position offset of the cluster mass barycenter to the BCG. More relaxed clusters have a higher fICL + BCG, in rare cases up to 90% of all stellar mass, while dynamically active clusters have lower fractions, down to 20%, which we find to be independent of the exact implemented baryonic physics. We determine the average increase in fICL + BCG from stripping and mergers to be between 3–4% per gigayear. Furthermore, fICL + BCG is tightly traced by the stellar mass ratio between the BCG and both the second (M12) and fourth (M14) most massive cluster galaxy. The average galaxy cluster has assembled half of its halo mass by zform = 0.67 (about 6 gigayears ago), though individual histories vary significantly from zform = 0.06 to zform = 1.77 (0.8–10 gigayears ago). Conclusions. As all four cosmological simulations consistently find that fICL + BCG is an excellent tracer of the cluster dynamical state, upcoming surveys can leverage measurements of fICL + BCG to statistically quantify the assembly of the most massive structures through cosmic time.