Dark Halo Cusp: Asymptotic Convergence

We propose a model for how the buildup of dark halos by merging satellitesproduces a characteristic inner cusp, of a density profile \rho \prop r^-a witha -> a_as > 1, as seen in cosmological N-body simulations of hierarchicalclustering scenarios. Dekel, Devor & Hetzroni (2003) argue that a flat core ofa<1 exerts tidal compression which prevents local deposit of satellitematerial; the satellite sinks intact into the halo center thus causing a rapidsteepening to a>1. Using merger N-body simulations, we learn that this cusp isstable under a sequence of mergers, and derive a practical tidal mass-transferrecipe in regions where the local slope of the halo profile is a>1. Accordingto this recipe, the ratio of mean densities of halo and initial satellitewithin the tidal radius equals a given function psi(a), which is significantlysmaller than unity (compared to being 1 according to crude resonance criteria)and is a decreasing function of a. This decrease makes the tidal mass transferrelatively more efficient at larger a, which means steepening when a is smalland flattening when a is large, thus causing converges to a stable solution.Given this mass-transfer recipe, linear perturbation analysis, supported by toysimulations, shows that a sequence of cosmological mergers with homologoussatellites slowly leads to a fixed-point cusp with an asymptotic slope a_as>1.The slope depends only weakly on the fluctuation power spectrum, in agreementwith cosmological simulations. During a long interim period the profile has anNFW-like shape, with a cusp of 1

ReadCiteExport

Add to List

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Sign up to Zendy

Having issues? You can contact us here