The Splashback Radius as a Physical Halo Boundary and the Growth of Halo Mass

The boundaries of cold dark matter halos are commonly defined to enclose a density contrast relative to a reference (mean or critical) density. We argue that a more physical boundary of halos is the radius at which accreted matter reaches its first orbital apocenter after turnaround. This splashback radius, Rₒ₏, manifests itself as a sharp density drop in the halo outskirts, at a location that depends upon the mass accretion rate. We present calibrations of Rₒ₏ and the enclosed mass, Mₒ₏, as a function of the accretion rate and alternatively peak height. We find that Rₒ₏ varies between 0. 8-1R₂₀₀₌ for rapidly accreting halos and 1. 5R₂₀₀₌ for slowly accreting halos. The extent of a halo and its associated environmental effects can thus extend well beyond the conventionally defined "virial" radius. We show that Mₒ₏ and Rₒ₏ evolve relatively strongly compared to other commonly used definitions. In particular, Mₒ₏ evolves significantly even for the smallest dwarf-sized halos at z=0. We also contrast Mₒ₏ with the mass enclosed within four scale radii of the halo density profile, M<₄ₑₒ, which characterizes the inner halo. During the early stages of halo assembly, Mₒ₏ and M<₄ₑₒ evolve similarly, but in the late stages M<₄ₑₒ stops increasing while Mₒ₏ continues to grow significantly. This illustrates that halos at low z can have "quiet" interiors while continuing to accrete mass in their outskirts. We discuss potential observational estimates of the splashback radius and show that it may already have been detected in galaxy clusters.