Dependence of the outer density profiles of halos on their mass accretion rate

We present a systematic study of the density profiles of ΛCDM halos, focusing on the outer regions, 0.1 < r/R _vir < 9. We show that the median and mean profiles of halo samples of a given peak height exhibit significant deviations from the universal analytic profiles discussed previously in the literature, such as the Navarro-Frenk-White and Einasto profiles, at radii r ≳ 0.5R _200m. In particular, at these radii the logarithmic slope of the median density profiles of massive or rapidly accreting halos steepens more sharply than predicted. The steepest slope of the profiles occurs at r ≈ R _200m, and its absolute value increases with increasing peak height or mass accretion rate, reaching slopes of –4 and steeper. Importantly, we find that the outermost density profiles at r ≳ R _200m are remarkably self-similar when radii are rescaled by R _200m. This self-similarity indicates that radii defined with respect to the mean density are preferred for describing the structure and evolution of the outer profiles. However, the inner density profiles are most self-similar when radii are rescaled by R _200c. We propose a new fitting formula that describes the median and mean profiles of halo samples selected by their peak height or mass accretion rate with accuracy ≲ 10% at all radii, redshifts, and masses we studied, r ≲ 9R _vir, 0 < z < 6, and M _vir > 1.7 × 10¹⁰ h ^–1 M _☉. We discuss observational signatures of the profile features described above and show that the steepening of the outer profile should be detectable in future weak-lensing analyses of massive clusters. Such observations could be used to estimate the mass accretion rate of cluster halos.