A Better Way to Define Dark Matter Haloes

Dark matter haloes have long been recognized as one of the fundamental building blocks of large scale structure formation models. Despite their importance -- or perhaps because of it! -- halo definitions continue to evolve towards more physically motivated criteria. Here, we propose a new definition that is physically motivated, and effectively unique and parameter-free: ''A dark matter halo is comprised of the collection of particles orbiting in their own self-generated potential.'' This definition is enabled by the fact that, even with as few as $\approx 300$ particles per halo, nearly every particle in the vicinity of a halo can be uniquely classified as either orbiting or infalling based on its dynamical history. For brevity, we refer to haloes selected in this way as physical haloes. We demonstrate that: 1) the mass function of physical haloes is Press-Schechter, provided the critical threshold for collapse is allowed to vary slowly with peak height; and 2) the peak-background split prediction of the clustering amplitude of physical halos is statistically consistent with the simulation data, with an accuracy no worse than $\approx 5\%$.