Intra-Cluster Light as a Dynamical Clock for Galaxy Clusters: Insights from the MAGNETICUM, IllustrisTNG, Hydrangea and Horizon-AGN Simulations

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 different galaxy clusters can vary significantly. To inform upcoming large surveys, we aim to identify observables that can distinguish galaxy cluster formation pathways. Using four different hydrodynamical simulations, Magneticum, TNG100 of IllustrisTNG, Horizon-AGN, and Hydrangea, we study how the fraction of stellar mass in the BCG and ICL ($f_{ICL+BCG}$) relates to the galaxy cluster mass assembly history. For all simulations, $f_{ICL+BCG}$ is the best tracer for the time at which the cluster has accumulated 50% of its mass ($z_{f}$), performing better than other typical dynamical tracers, such as the subhalo mass fraction, the halo mass, and the center shift. More relaxed clusters have higher $f_{ICL+BCG}$, in rare cases up to 90%, 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 $f_{ICL+BCG}$ from stripping and mergers to be between 3-4% per Gyr. $f_{ICL+BCG}$ 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 $z_{f}=0.67$ (about 6 Gyr ago), though individual histories vary significantly from $z_{f}=0.06$ to $z_{f}=1.77$ (0.8 to 10 Gyr ago). As all four cosmological simulations consistently find that $f_{ICL+BCG}$ is an excellent tracer of the cluster dynamical state, upcoming surveys can leverage measurements of $f_{ICL+BCG}$ to statistically quantify the assembly of the most massive structures.