Inferring Gravitational Potentials from Mass Densities in Cluster-sized Halos

Abstract: We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a LambdaCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10^13 < M_200 < 10^15 M_sun, with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological constant when inferring the potential from the Poisson equation. We consider three density models and find that the Einasto and Gamma profiles provide a better joint estimate of the density and potential profiles than the Navarro, Frenk and White profile, which fails to accurately represent the escape velocity. For individual halos, the 1 sigma scatter between the measured escape velocity and the density-inferred potential profile is small (<5%). Finally, while the sub-halos show 15% biases in their representation of the particle velocity dispersion profile, the sub-halo escape velocity profile matches the dark matter escape velocity profile to high accuracy with no evidence for velocity bias outside 0.4r_200.