The life and times of dark matter haloes: what will I be when I grow up?

Abstract: Are the most massive objects in the Universe today the direct descendants of the most massive objects at higher redshift? We address this question by tracing the evolutionary histories of haloes in the MultiDark Planck2 simulation. By following the 100 most massive halos at $z = 0$ across cosmic time, we find that only 40\% of them were among the largest 100 halos at $z = 1$. This suggests that many of today's most massive clusters were not the most dominant structures at earlier times, while some of the most massive objects at high redshift do not remain in the top mass ranks at later epochs. The hierarchical nature of structure formation predicts that, on average, massive haloes grow over time, with their abundance in comoving space decreasing rapidly at higher redshifts. However, individual clusters exhibit diverse evolutionary paths: some undergo early rapid growth, while others experience steady accretion or significant merger-driven mass changes. A key assumption in self-similar models of cluster evolution is that the most massive objects maintain their rank in the mass hierarchy across cosmic time. In this work, we test this assumption by constructing a mass-complete sample of haloes within the $(1 h^{-1}{\rm Gpc})^3$ volume of MultiDark and analysing when clusters enter and exit a high-mass-selected sample. Our results demonstrate that cluster selections must be carefully constructed, as significant numbers of objects can enter and leave the sample over time. These findings have important implications for observational cluster selection and comparisons between simulations and surveys, especially at high redshift.