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 $\Delta$ 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, $R_{sp}$, 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 $R_{sp}$ and the enclosed mass, $M_{sp}$, as a function of the
accretion rate and alternatively peak height. We find that $R_{sp}$ varies
between $\approx0.8-1R_{200m}$ for rapidly accreting halos and
$\approx1.5R_{200m}$ 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 $M_{sp}$ and $R_{sp}$ evolve relatively
strongly compared to other commonly used definitions. In particular, $M_{sp}$
evolves significantly even for the smallest dwarf-sized halos at $z=0$. We also
contrast $M_{sp}$ with the mass enclosed within four scale radii of the halo
density profile, $M_{<4rs}$, which characterizes the inner halo. During the
early stages of halo assembly, $M_{sp}$ and $M_{<4rs}$ evolve similarly, but in
the late stages $M_{<4rs}$ stops increasing while $M_{sp}$ 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.
