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We explore the boundary of dark matter haloes through their bias and velocityprofiles. Using cosmological $N$-body simulations, we show that the biasprofile exhibits a ubiquitous trough that can be interpreted as created by haloaccretion that depletes material around the boundary. The inner edge of theactive depletion region is marked by the location of the maximum mass inflowrate that separates a growing halo from the draining environment. This innerdepletion radius can also be interpreted as the radius enclosing a highlycomplete population of splashback orbits, and matches the optimal exclusionradius in a halo model of the large-scale structure. The minimum of the biastrough defines a characteristic depletion radius, which is located within theinfall region bounded by the inner depletion radius and the turnaround radius,while approaching the turnaround radius in low mass haloes that have stoppedmass accretion. The characteristic depletion radius depends the most on halomass and environment. It is approximately $2.5$ times the virial radius andencloses an average density of $\sim 40$ times the background density of theuniverse, independent on halo mass but dependent on other halo properties. Theinner depletion radius is smaller by $10-20\%$ and encloses an average densityof $\sim 63$ times the background density. These radii open a new window forstudying the properties of haloes.

A natural boundary of dark matter haloes revealed around the minimum bias and maximum infall locations