| Summary: | We present a systematic study of the density profiles of dark matter halos in ΛCDM cosmologies, focusing on the question whether these profiles are "universal", i.e., whether they follow the same functional form regardless of halo mass, redshift, cosmology, and other parameters. The inner profiles (r <∼ Rvir) can be described as a function of only mass and concentration, and we thus begin by investigating whether there is a universal, cosmology-independent relation between those two parameters. We propose a model in which concentration is a function only of a halo's peak height and the local slope of the matter power spectrum. This model matches the concentrations in ΛCDM and scale-free simulations, correctly extrapolates over 16 orders of magnitude in halo mass, and differs significantly from all previously proposed models at high masses and redshifts. We find that the outer profiles (r >∼ Rvir) are remarkably universal across redshifts when radii are rescaled by R200m, whereas the inner profiles are most universal in units of R200c, highlighting that universality depends upon the definition of the halo boundary. Furthermore, we discover that the profiles exhibit significant deviations from the supposedly universal analytic formulae previously suggested in the literature, such as the NFW and Einasto forms. In particular, the logarithmic slope of the profiles of massive or rapidly accreting halos steepens more sharply than predicted around r ≈ R200m, where the steepness increases with increasing peak height or mass accretion rate. We propose a new, accurate fitting formula that takes these dependencies into account. Finally, we demonstrate that the profile steepening corresponds to the caustic at the apocenter of infalling matter on its first orbit. We call the location of the caustic the splashback radius, Rsp, and propose this radius as a new, physically motivated definition of the halo boundary. We discuss potential observational signatures of Rsp that would allow us to estimate the mass accretion rate of halos.
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