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The boundaries of cold dark matter halos are commonly defined to enclose adensity contrast $\Delta$ relative to a reference (mean or critical) density.We argue that a more physical boundary of halos is the radius at which accretedmatter reaches its first orbital apocenter after turnaround. This splashbackradius, $R_{sp}$, manifests itself as a sharp density drop in the halooutskirts, at a location that depends upon the mass accretion rate. We presentcalibrations of $R_{sp}$ and the enclosed mass, $M_{sp}$, as a function of theaccretion rate and alternatively peak height. We find that $R_{sp}$ variesbetween $\approx0.8-1R_{200m}$ for rapidly accreting halos and$\approx1.5R_{200m}$ for slowly accreting halos. The extent of a halo and itsassociated environmental effects can thus extend well beyond the conventionallydefined "virial" radius. We show that $M_{sp}$ and $R_{sp}$ evolve relativelystrongly compared to other commonly used definitions. In particular, $M_{sp}$evolves significantly even for the smallest dwarf-sized halos at $z=0$. We alsocontrast $M_{sp}$ with the mass enclosed within four scale radii of the halodensity profile, $M_{<4rs}$, which characterizes the inner halo. During theearly stages of halo assembly, $M_{sp}$ and $M_{<4rs}$ evolve similarly, but inthe late stages $M_{<4rs}$ stops increasing while $M_{sp}$ continues to growsignificantly. This illustrates that halos at low $z$ can have "quiet"interiors while continuing to accrete mass in their outskirts. We discusspotential observational estimates of the splashback radius and show that it mayalready have been detected in galaxy clusters.

The splashback radius as a physical halo boundary and the growth of halo mass