Accretion history dependence of the halo depletion radius

We investigate the role of the accretion history in shaping the depletion radius of dark matter halos using a large cosmological N-body simulation. We show that the inner depletion radius, rescaled by the virial radius, depends strongly on the recent mass accretion rate (MAR) measured over a dynamical timescale, while exhibiting only weak dependence on halo mass. While this dependence mirrors that of the splashback radius and the two radii are tightly correlated, the depletion radius exhibits a more nuanced response to the detailed accretion mode. Specifically, we find that the dependence on MAR steepens at lower redshifts, aligning with self-similar spherical collapse models yet contrasting with the behavior of the splashback radius. This redshift dependence is largely driven by dynamic events, as it diminishes significantly when halos undergoing recent major mergers are excluded. Furthermore, we identify a dichotomy in the drivers of the depletion radius. For slowly accreting halos, the MAR is the primary dependence, whereas for rapidly accreting halos, other properties (shape, spin, concentration, and formation time of the central subhalo) related to the anisotropic or perturbed accretion mode also play a significant role. These results establish the depletion radius as a sensitive physical probe of the detailed accretion history of dark matter halos, complementary to the splashback radius.