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We investigate the build-up of the halo profile out to large scale in acosmological simulation, focusing on the roles played by the recently proposeddepletion radii. We explicitly show that halo growth is accompanied by thedepletion of the environment, with the inner depletion radius demarcating thetwo. This evolution process is also observed via the formation of a trough inthe bias profile, with the two depletion radii identifying key scales in theevolution. The ratio between the inner depletion radius and the virial radiusis approximately a constant factor of 2 across redshifts and halo masses. Theratio between their enclosed densities is also close to a constant of 0.18.These simple scaling relations reflect the largely universal scaled massprofile on these scales, which only evolves weakly with redshift. The overallpicture of the boundary evolution can be broadly divided into three stagesaccording to the maturity of the depletion process, with cluster halos laggingbehind low mass ones in the evolution. We also show that the traditional slowand fast accretion dichotomy of halo growth can be identified as acceleratedand decelerated depletion phases respectively.

Physical evolution of dark matter halo around the depletion boundary