FLAMINGO: Tracing the co-evolution of hot gas and black holes in galaxy groups and clusters

The gas mass fraction of galaxy groups and clusters is a key physical quantity for constraining the impact of feedback processes on large-scale structure. While several modern cosmological simulations use the gas fraction-halo mass relation to calibrate their feedback implementations, we note that this relation exhibits substantial intrinsic scatter whose origin has not been fully elucidated. Using the large-volume FLAMINGO hydrodynamical simulations, we examine the role of both central and satellite supermassive black holes (BHs) in shaping this scatter, probing higher halo masses than previously possible. For haloes with M500 < 10^13 Msun, we find that central BH mass correlates strongly and negatively with gas fraction, such that higher BH masses give rise to lower gas fractions at fixed halo mass, consistent with previous studies. Interestingly, however, for 10^13 Msun < M500 < 10^14.5 Msun the correlation reverses and becomes positive, with overmassive BHs residing in haloes with above-average gas fractions. By tracing progenitor BHs and haloes through cosmic time, we show that this behaviour is driven by the expulsion and subsequent re-accretion of halo gas, regulated by the timing of BH growth and feedback. Specifically, haloes that collapse earlier form BHs earlier, leading to earlier gas expulsion and re-accretion and a high gas fraction compared to haloes of the same present-day mass that formed later. Our results demonstrate that present-day scatter in the gas fraction-halo mass relation is strongly shaped by the early growth history of BHs and their haloes, a prediction that can be tested with future observational measurements.