A natural boundary of dark matter haloes revealed around the minimum
  bias and maximum infall locations
  We explore the boundary of dark matter haloes through their bias and velocity
profiles. Using cosmological $N$-body simulations, we show that the bias
profile exhibits a ubiquitous trough that can be interpreted as created by halo
accretion that depletes material around the boundary. The inner edge of the
active depletion region is marked by the location of the maximum mass inflow
rate that separates a growing halo from the draining environment. This inner
depletion radius can also be interpreted as the radius enclosing a highly
complete population of splashback orbits, and matches the optimal exclusion
radius in a halo model of the large-scale structure. The minimum of the bias
trough defines a characteristic depletion radius, which is located within the
infall region bounded by the inner depletion radius and the turnaround radius,
while approaching the turnaround radius in low mass haloes that have stopped
mass accretion. The characteristic depletion radius depends the most on halo
mass and environment. It is approximately $2.5$ times the virial radius and
encloses an average density of $\sim 40$ times the background density of the
universe, independent on halo mass but dependent on other halo properties. The
inner depletion radius is smaller by $10-20\%$ and encloses an average density
of $\sim 63$ times the background density. These radii open a new window for
studying the properties of haloes.
