Dark Halo Cusp: Asymptotic Convergence

Abstract

We propose a model for how the buildup of dark halos by merging satellitesproduces a characteristic inner cusp, with a density profile {ρ}~r^{-??in},where {α}_{in}--{\gt}{α}_{as}{\gt}~1, as seen incosmological N-body simulations of hierarchical clustering scenarios.Dekel, Devor, {\amp} Hetzroni argue that a flat core of {α}_{in}{\lt}1exerts tidal compression that prevents local deposit of satellitematerial; the satellite sinks intact into the halo center, thus causinga rapid steepening to {α}_{in}{\gt}1. Using merger N-bodysimulations, we learn that this cusp is stable under a sequence ofmergers and derive a practical tidal mass transfer recipe in regionswhere the local slope of the halo profile is {α}{\gt}1. Accordingto this recipe, the ratio of mean densities of the halo and initialsatellite within the tidal radius equals a given function {ψ}({α}),which is significantly smaller than unity (compared to being ~1according to crude resonance criteria) and is a decreasing functionof {α}. This decrease makes the tidal mass transfer relativelymore efficient at larger {α}, which means steepening when{α} is small and flattening when {α} is large, thuscausing convergence to a stable solution. Given this mass transferrecipe, linear perturbation analysis, supported by toy simulations,shows that a sequence of cosmological mergers with homologous satellitesslowly leads to a fixed-point cusp with an asymptotic slope {α}_{as}{\gt}1.The slope depends only weakly on the fluctuation power spectrum,in agreement with cosmological simulations. During a long interimperiod the profile has an NFW-like shape, with a cusp of 1{\lt}{α}_{in}{\lt}{α}_{as}.Thus, a cusp is enforced if enough compact satellite remnants makeit intact into the inner halo. In order to maintain a flat core,satellites must be disrupted outside the core, possibly as a resultof a modest puffing up due to baryonic feedback.