The FLAMINGO Project: A comparison of galaxy cluster samples selected on mass, X-ray luminosity, Compton-Y parameter, or galaxy richness

Galaxy clusters provide an avenue to expand our knowledge of cosmology and galaxy evolution. Because it is difficult to accurately measure the total mass of a large number of individual clusters, cluster samples are typically selected using an observable proxy for mass. Selection effects are therefore a key problem in understanding galaxy cluster statistics. We make use of the $(2.8~\rm{Gpc})^3$ FLAMINGO hydrodynamical simulation to investigate how selection based on X-ray luminosity, thermal Sunyaev-Zeldovich effect or galaxy richness influences the halo mass distribution. We define our selection cuts based on the median value of the observable at a fixed mass and compare the resulting samples to a mass-selected sample. We find that all samples are skewed towards lower mass haloes. For X-ray luminosity and richness cuts below a critical value, scatter dominates over the trend with mass and the median mass becomes biased increasingly low with respect to a mass-selected sample. At $z\leq0.5$, observable cuts corresponding to median halo masses between $M_\text{500c}=10^{14}$ and $10^{15}~\rm{M_{\odot}}$ give nearly unbiased median masses for all selection methods, but X-ray selection results in biased medians for higher masses. For cuts corresponding to median masses $<10^{14}$ at $z\leq0.5$ and for all masses at $z\geq1$, only Compton-Y selection yields nearly unbiased median masses. Importantly, even when the median mass is unbiased, the scatter is not because for each selection the sample is skewed towards lower masses than a mass-selected sample. Each selection leads to a different bias in secondary quantities like cool-core fraction, temperature and gas fraction.